CHSE Odisha Class 12 Foundations of Education Unit 1 Contribution of Educators Long Answer Questions

Odisha State Board CHSE Odisha Class 12 Foundations of Education Solutions Unit 1 Contribution of Educators Long Answer Questions.

CHSE Odisha 12th Class Foundations of Education Unit 1 Contribution of Educators Long Answer Questions

Long Answer Questions With Answers

Question 1:
Discuss the life philosophy of Gandhi.
Answer:
Gandhi enunciated integral philosophy of fife. He was a naturalist, an idealist,
individualist in one. His ‘Experiment on Truth’ was the outcome of his experience and prominent philosophical activities are his concept of God, truth, doctrines of morality, non¬violence, satyagraha, labor, equality, citizenship, brotherhood of man His life was concerned with:

  • His concept of truth.
  • His concept of karma.
  • His concept of non-violence.
  • His concept of satyagraha.
  • His idea of centralization.
  • His idea of machine.
  • His concept of the village.
  • His news of morality.

1) His concept of truth – Gandhiji believed in truth to be the ultimate reality and God can be realized through truth. God is truth, and truth is God. He said truth is manifested both externally and it is expressed through the voice of God. He was the pioneer of truth and non¬violence and conquered the brutal force. One can realise god through truth.

2) His concept of Karma – In Gita, there is view on life and karma. Gandhiji was deeply influenced by Gita for a religious dedication to the service of man. Service of humanity is God. Religion is not a part from human activity. Action takes its origin from Brahma and Brahma is present in all kinds of sacrifice of service. To Gandhi, society and social service are an integral part of life and they are sacred activities.

3) His concept of non-violence – Non-violence of Gandhi was equivalent to love. His concept of non-violence retained deeply in Indian spirituality. The concept ofAhimsa or non-violence of Gandhi was a means and that an end. Man is the end of his material, mental and moral well-being and growth.

4) His concept of Satyagraha – Gandhiji’s concept of Satyagraha was dynamic aspect of non-violence and a tool that created a human context for social conflict. Truth is the end and non-violence is the means to human activities.The term ‘ Satyagraha’ is derived from the Gujarati word ‘agrapha’ which means firmness. For Gandhiji satyagraha is dynamic quality of non-violence. Satyagraha for Gandhiji’s way a truth force for acting socially and humanely.

5) His idea of decentralization – Gandhiji was against concentration of power and individualism of capitalism. He wished a kind of society where economic and social structure of decentralization on the basis of industry and agriculture. This is the productivity aim of education.

6) His idea of machine – Gandhiji was not against the machine, but he did not want it to become the master of machine. He opposed strongly machines because it created unemployment and exploitation of the poor workers by capitalists and too much dependence on man on machine. So he suggested to limit the manufacture of machine and emphasized on cottage industry and handicrafts.

7) His concept of the village – To Gandhiji, village is a small group of people, consisting a unit of society. So the village should be self-governing. He considered that it should be self¬sufficient in the matter of its vital necessities of life like food, clothing and shelter. Secondly his village was not an agricultural community, there should be a balance between agriculture and the village industries. He desired to create agro-industrial community.

8) Gandhiji’s gramraj – Village self government was the opinion of Gandhi. His idea of Gram raj or village self government means it is a complete republic independent or its neighbours are independent with other necessaries. Thus, for every villages the first concern will be no caste and hopes to abandon untouchability and create a class less society.

9) His views on morality – To Gandhiji, the end of all knowledge is the development of morality. The society and individual progress through morality, purity in thought, speech and deeds. So a social foundation of truth and purity should be established through education. To him moral education is to be imparted in schools. Morality is the best virtue of humanity. By participation in games and sports discipline in thought and action is maintained.

Question 2:
Write a note on the Educational Philosophy of Gandhi.
Answer:
As a socio-political, reformer, educationist, idealist, naturalist, social leader and practical philosopher, Gandhiji father of the Nation, the apostle ofpeace and non-violence, the champion of Freedom movement led a scheme of education of India known as ‘Basic Education’. In another way it is known as “Nayee Talim”. His educational philosophy is the potent force for social reconstruction. To him true education is “An all round drawing out of the best in child and man” – body, mind and spirit. The chieftenents ofhis educational philosophy are as follows:

  • Education should be free and compulsory.
  • Craft centred education.
  • Self supporting education
  • Emphasis on mother tongue.
  • Child centredness.
  • Emphasis of education on non-violence.

1) Education should be free and compulsory : Gandhi advocated free and compulsory education for 7 to 14 years and wanted to combine primary education with secondary education called it English Less Matriculation Courses. To him democracy will become successful when education will be free and compulsory. It will develop love for creative work. As India is a poor land and 60 % of population are below the poverty line so education should be free and compulsory for them.

2) Craft centred education : He believed in the principle of learning by doing’ of John Dewey. The basic education aimed at providing education on crafts. He introduced basic crafts like spinning and weaving, carpentry and agriculture. Introduction of crafts evoke the spirit of love for work and teach them the dignity of labour. To him the whole educative process be imparted through handicraft. They will leam the motto “work is worship”. It will develop the dignity of labour.

3) Self-supporting education: Gandhiji knew that India is a poor state and it cannot afford to educate the millions. So Gandhi suggested education to be self supporting. The concept of “Karma Yoga” and dignity of labour will help in the intellectual development. So the child should pay labour partly by binding a gap between education and life drawing upon the cultural, social and vocational potentialities. It is a measure of social reconstruction.

4) Emphasis on mother tongue: Gandhi emphasized mother tongue as the medium of instruction. To him the English system of education hinders understanding and clarity of ideas. By mother tongue, the children can express their views clearly and understand others and this would build sound foundation of education.

5) Child centredness: Child-centredness is an important feature of Basic Education which means the children should be taught to the needs, interests, and capacities of children. So the curriculum and the method of teaching are to be developed to the capacities of learners. Different crafts and subjects to be included in the curriculum to meet individual differences.

6) Education based on non-violence: A unique feature of Gandhiji’s education philosophy was the application of the law of non-violence. He wanted to build a classless society and elimination of exploitation. By the scheme of non-violence and peace, he conquered the heart of brutal forces. So his education of philosophy is based on non-violence. He wanted to create a generation that should believe in non-violence.

Question 3:
What should be the aims, curriculum and methods of teaching of Basic
Education?
Answer:
M. K. Gandhi is called an idealist, a realist, a spiritual person in one. He advocated his philosophy of education and put stress on religious education. The main aims of this philosophy are as follows :

  • The utilitarian aim.
  • The cultural aim.
  • Harmonious development aim.
  • Complete living aim.
  • Character building aim.

1. The utilitarian aims : To fulfill this aim, the basic needs of human life like food, clothing and shelter and self-supporting to be imparted. The self-supporting aspects aimed at self-sufficient and education to meet one’s expenses. It is otherwise known as ‘Bread and Butter Aims ’ of education.

2. The cultural aims: Culture is essential to refine one’s personality.One should have the qualities of mind which should be reflected in one’s own conduct. Such aims helps in the transmission of culture.

3. Harmonious development aim: To Gandhi, education means “An all round draw ing out of the best in child and man, with body, mind and spirit”. To Gandhi, harmonious development means – innate and acquired powers development from social to intellectual. Basic education helps with all round development of personality of the individuals.

4. Complete living aims: To Gandhi, life is very complex. So he formulated a scheme of education which would fit the children to later life and a child to be prepared for complete living. He should learn how to support his living, social adjustment, occupation and self¬reliance.

5. Character building aims: Character building was the chief aim of basic education. To him character is the expression ofthe w’hole personality including the ethical and spiritual aspects. One should subordinate his own interest to the greater interest ofthe society, cooperate his fellow being about a new social order. Such a person is really a man of character. In his aims of education, Gandhi emphasis the building of character.

The individual character will influence the national character.
i)Curriculum: Gandhi emphasized on child centred curriculum. Education should be related to the environment of the child. He opposed English as the medium of instruction and mother tongue as the medium of instruction up to the level of matriculation. To him English hinders the clarity of thought and put a check on self-expression.My mother tongue, one can express his view correctly and understand others. It also helps in the development of nationalism and patriotism
He introduced craft as a part of curriculum and the whole process of education should be imparted through some handicrafts.
ii) Craft: Education should be given through the medium of some craft on productive work. So different handicrafts like weaving, spinning, carpentry, earthen pot building etc.
iii) Activity centred: The teaching of various subjects should be emphasized. Teaching of craft will be the center point and the teaching of all subjects should be related to craft.The co-related teaching methods are to be employed.
iv) Mother tongue: Mother tongue should be medium of instruction. It will help the children for clear expression and clear understanding, develop patriotism and nationalism.
v) Religious and moral education: For the development of personality, character religions and moral education is to be given. All should respect to all religions. Ethics of all religions is to be taught as a part of education. To Gandhi there is need of moral leaders in free India and building modem India.

CHSE Odisha Class 12 Foundations of Education Unit 1 Contribution of Educators Long Answer Questions

Question 4:
Discuss the essential features of Basic Education. Explain the gift of Basic education to education.
Answer:
The essential features of Basic education include:

  • Free and compulsory education.
  • Purposeful activity-centred education.
  • Emphasis on mother tongue.
  • Self-supporting education.
  • Primary importance for village.
  • New cooperative regime.
  • Dignity of labor.
  • Co-operative work.
  • Integrated teaching.
  • Educates body, mind, and spirit.

1. Free and compulsory education: Basic Education implies a free and compulsory education for all children between the age of 7 to 14 years. It will reduce the disparity among the children.

2. Purposeful activity centred education: Basic Education centers round some purposeful activity or useful and productive craft training which supports self supporting aims of education.

3. Mother tongue: The medium of instruction should be mother tongue of the child. By this the child can express his views fluently and understand others’ views. It also inculcates the spirit of nationalism and patriotism.

4. Self-supporting: Basic Education is aimed at self-supporting. It followed the principles of learning by doing. They earn from their craft work as well, so as to cover their expenses. Thus craft has both educational and economic value.

5. Primary importance for the village: Basic education was primarily devised for the village. Gandhiji say, “In discussing the question of primary education, I have neither to deliberately confirmed myself to the village, as it is to villages that the bulk of Indians population resides’. To tackle successfully the question of village is to solve the problem for the cities also.

6. New cooperative regime: Basic education aims at bringing about a new cooperative regime in place of the present in-human regime based on exploitation and violent forces.

7. Dignity of labor: Basic education curriculum inculcates the virtue of dignity of labor, a keen sense of discipline, and a great sense of responsibility. Labour-centred education reduces disparity among pupils. It helps with self-employment.

8. Cooperative work: In the scheme of Basic education both the teachers and pupils work for community development and social progress.

9. Integrated teaching: In Basic education, all the subjects are taught in an integrated way. All the instructions are co-related. It seeks to develop the child as a whole. The child is taught with co-related teaching methods of all subjects like math, general science, social sciences, language, drawing and paintings etc. It helps the harmonious development of the child.

10. Educates body, mind, and spirit: Basic education is meant to educate the body, mind and spirit with an unique relation among them. It seeks to develop the child as a whole.

Question 5:
Discuss the causes of downfall of Basic education.
Answer:
Inspite of the merits of Basic education, the scheme was criticised by the richer classes, educationists and suffer from a number of limitations. After the death of Gandhiji the scheme was given a death-blow. The most important reasons of the failure of Basic Education are as follows :

  • The Unclear Concept.
  • Emphasis on Idealistic view.
  • Emphasis on Economic aspects.
  • Compact Area approach. ‘
  • Absence of Text Books.
  • Lack of Trained Skilled Teachers and Textbooks.
  • Faculty timetable.
  • Costliness of Basic Education.
  • Opposition of Traditionalists.
  • Matriculation of Minus English.
  • Lack of Research.

1) The Unclear Concept: In that period most of the educationists the common people, education administrators as well were not clear about the concept of Basic Education. They were confused of craft education and mechanical education. The common people could understand nothing. In that period, there was no provision of propagation and no mass media system to highlight the program. So the concept of the scheme could not touch the common people and got failure.

2. Emphasis on Idealistic Approach: The scheme laid stress on some idealistic practices like manual work. Such scheme of education was not accepted by the British and the intellectuals because they educated people do not appreciate that their children could do any manual labour. They sent their children to public schools and English medium schools. So the confusion is created.

3. Emphasis on Economic Aspects: In Basic Education, too much emphasis was given on economic aspect. The craft centredness was not accepted by the intellectuals as well as educationists. The productivity activity of self supporting aspect exploits the child labour and craft work puts emphasis on economic aspect. The students become money minded. The guardians felt that their children were turned into laborers, so they opposed the basic ideals of craft.

4. Compact Area Approach: Basic schools were opened in some specific areas, especially in rural areas but not in town areas. The scheme was worked out in a limited area on an experimental basis. So compact area approach was a major cause of the failure of such education system.

5. Absence of Text Books: Basic scheme of education emphasized on craft education. It was a mechanical education. Text books were riot emphasized and no text book was prepared as there were no writers to prepare textbooks on craft training. It was another major causes of the downfall of Basic Education.

6. Lack of Qualified teachers: It was a new type of education like craft. The traditional teachers failed to understand the new pattern of education and the curriculum prepared by Dr. Jakir Hussain. Qualified trained teachers were not available as it was mechanical teaching. There was no provision of teachers’ training. So lack of qualified trained teachers, the Basic Scheme of Education led its downfall.

7. Faculty Time Table: In Basic Education much more was invested or devoted for craft work and other subjects were neglected. In a Basic School 2/3rd. of the time was utilized in craft work. On the timetable, academic subjects were taught after craft work. So academic subjects were neglected. Agricultural students become tired to their academic work. So the faulty timetable was an obstacle of spreading Basic Education.

8. Costliness of Basic Education: As Basic Education needed equipment, so more initial cost was required to purchase craft equipment. There were no funds to meet such expenses and the Govt, could not afford it so it led its downfall.

9. Opposition of Traditionalists: The dream of Gandhi to build a classless society was strongly opposed by the higher class people. So the traditionalists and conservatives were afraid that the new social order would upset their position and so they strongly opposed the system of education.

10. Matriculation Minus English Course: Gandhiji emphasized that English should not be taught to the students in matriculation stages. But the richer classes opposed this and did not prefer to admit their children in such a school. So the strength of the school reduced day by day.

11. Lack of Research: No research activities were encouraged and no research centers were set up. So lack of research, newer methods of teaching, and techniques the Basic Scheme of Education led its downfall.

Question 6:
Discuss the aims of education of Satyabadi School.
Or Explain Gopabandhu’s Educational thoughts.
Or Discuss the contribution of Gopabandhu to the present education.
Answer:
Gopabandhu believed in universal education. The organizers of national Education League opined that everyone has the right of being educated, just as the rays of sun and moon. One shared equally by the people. Pandit Nilakantha Das emphasized classless society education. The people of Odisha are poor and they cannot afford for the education of their children. So Gopabandhu proposed an education that should be ideal, forced, and inexpensive. In 1909 he set up a School at Satyabadi named as Open Air Schooling based on the ideals of Gopabandhu.

The aims, main tenents and educational thoughts of Gopabandhu are discussed below.
1. In-expensive Education: Gopbandhu was hilly aware of that India being a poor country and Odisha a poor province it cannot pay for education of the entire population. So the cost of education to be reduced. He experimented with the groove school on the lines of ancient Gurukul System with no school building and tuition fee payable by the students should be minimum. They should lead a simple and austre life in the school hostel.

2. Idealistic Education – Gopabandhu believed that it is not a costly school building but the idealistic and dedicated teachers who can make a good school were appointed. It is remarked that a school does not consist of only buildings, chairs, and tables, there must be well-educated, sincere and idealistic teachers. No education worthwhile can be imparted without good and efficient teachers.

3. Practical Education – Gopabandhu was cirtical about the prevailing system of education which does not equip the individual to meet the requirement of life. He wanted education to be practical which should make the students economically independent.
To him the present system of education failed to prepare our students for the struggle of life. So they should be taught crafts to maintain their livelihood and they should be taught physical exercise, industry and agriculture etc.

4. Religious and Moral Education: Gopabandhu believed in the all round development of the personality of an individual through education. The students must be taught craft skills in order to capable them to earn their living. There is need of civilized and cultured individuals. So there is need of religious and moral instructions for morality.

5. Social Service and National Integration: Gopabandhu did not stress on individuality. To him, individual is a part of society. So education would enable the individuate to perform the social functions as efficiently as successfully as possible. For him education is a preparation for a life of dedicated social service in the society or nation.Through this education, he wanted to bring about emotional and national integration. In the community dinner in his hostel, every day, high or low sit together and take meals.

6. Women’s Education – Gopabandhu was revolutionary in nature. He knew that in the backward and traditional society of Odisha,a great deal of courage is essential to advocate women’s education. To him, women are the wealth of the family as well as the wealth of the nation. They are the Goddess of family life. If women are educated, they will take care of their children.

7. Mother tongue as the Medium of Instruction – Gopabandhu emphasized on the importance of the mother tongue in the education of a child. It is essential to develop his mental powers. It is also essential to realize the intellectual cultural and spiritual aims of education So education should be imparted through the mother tongue. By mother tongue, the creative powers is to be developed.

Question 7:
Discuss the main features of Groove School ?
Answer:
The main basic principles in which the groove school grew up includes the following:

  • Open Air School.
  • Free Education.
  • Ideal Teachers.
  • All round development of Personality.
  • Teaching Craft Skills.
  • New Methods of Teaching.
  • Community dinner and Cultural programmes.
  • Emphasis on co-curricular activities.

Importance on Mother’s tongue.

1. Open Air School: Gopabandhu knew well that Indians cannot afford and spend the amount of money in constructing school building and to reduce the expenditure in education without reducing the educational standards the attempts been made opening a groove school on the lines of old Gurukul system Thus, it is an Open Air School similar to Shantiniketan.

2. Free Education: Education was free and minimum fee was charged. The attempts to set up school, an old Gurukul system and the students will lead a simple austere life.

3. Ideal Teachers: Gopabandhu put high premium on the quality of teachers. Gopabandhu aimed at ideal education and teachers should be ideal sacrificing in nature. The teachers of Satyabadi school had voluntarily given up the pleasures of life for the purpose of rendering service to the community.

4. All round development of Personality: Satyabadi system of education aimed at the development of all the aspects of the personality. He emphasized character building inculcation of social values, virtues qualities of good citizenship, patriotism, brotherhood and spirituality. For the development of good qualities various co-curricular activities, debates, excursions, physical exercises, games and prayer assemblies are essential.

5. Teaching Craft Skills: The system of education strongly opposed the system of education bookish and aimed at imparting education of art and craft skills. Then the children will be able to prepare for the future, learn the struggle for life. Craft education may enable to earn their livelihood.

6. New Method of Teaching: Satyabadi Vana Vidyalaya was a residential school and the teachers and students stay together, in the hostels. The Headmaster, asks the teachers to submit their class notes to him for supervision. The teachers and the Headmasters, sit together and discuss mutually the course. The programs like debate, excursion etc. are continued.

7. Community dinner and Cultural program: The elected Secretary (from the boarders) manage the hostel The school and hostel for self-discipline democratic management and ideal student life. The students and teachers take dinner together. It teaches them community living.

8. Emphasis on co-curricular activities: To bring an all around development of personalities of the students various types of co-curricular activities were arranged in the Satyabadi School, such as (i) Literary activities (ii) Debates and games (iii) Prayer assembly (iv) Physical exercises (v) Literary magazines etc. Debates are aimed at oratoral abilities of the students. Physical exercises brings about the development of character, discipline and virtues. Prayer assembly develops the discipline and moral instructions.

9. Importance of Mother tongue: Mother tongue emphasized on the medium of instruction. It helps in understanding and developing nationalism, and patriotism and the child can express his views clearly and understand others.

CHSE Odisha Class 12 Foundations of Education Unit 1 Contribution of Educators Long Answer Questions

Question 8:
Explain, the causes of downfall of Open Air Schooling or Satyabadi Vana Vidyalaya.
Answer:
Like the downfall of Basic Education of Gandhi, for some reasons Satyabadi Vana Vidyalaya led its downfall. The chief causes are:

  • Lack of local support and unclear concept.
  • Economic condition.
  • Lack of help of the Govt.
  • Participation of Gopabandhu in Indian National Movement.
  • The death of Utkalmani.

1. Lack of local support and unclear concept – Satyabadi Vana Vidyalaya was surrounded by conservative villages. Conservative people and Brahmin society. Such conservatives did not appreciate the idealistic education system of Gopabandhu. Pandit Nilakantha Das wanted to build a classless society education which was a stroke to the conservatives.

The conservatives opposed this and they do not like to read their children with other backward-class children. They wanted to continue the superstitions.Lack of local support the enrolment of children is reduced.To oppose Gopabandhu’s system of education in 1912 on March 22, the conservatives fired the school and the main property of school library was destroyed. Such an incident shook the strength of the school.

2. Non-cooperation of the Govt.: It was not a traditional education system nor followed the British system of education and opposed the older beliefs, superstitions and conservatism. It is filled with idealism, patriotism, nationalism and social service programs.It aimed at creating leader for the state. So the British opposed it. No Govt, grant lias come and the application for Govt. Recognition was canceled. The school was transferred under Calcutta University in 1916 and then to Patna University in 1917, but it could not get the Govt. help.

3. Economic Condition : The third cause of the downfall of Open Air Schooling was the economic condition of the school. In 1921 Vana Vidyalaya was transferred into a National School. But the Govt, grant only two hundred rupees per year was refused and cut off very relationship from Patna University. In 1923, it turned to a National College and become autonomous. But it did not exist long. It suffered from the financial crisis. The teachers demanded to merge the college with the University. For this Gopabandhu remained away from the college. But the colleagues failed to continue the college for which it led its downfall.

4. Participation in Non-cooperation Movement: In 1920, Utkalamani joined in the Non-cooperation movement. He invested all his time and resources in the Freedom struggle. He found no time and resources to invest in groove school. Thus, the school led its downfall

5. The Death of Utkalamani: The day before the World famous Car Festival on June 17, 1928, Gopabandhu died in an immature death. The glorious chapter of Odia’s history’ came to an end. The next generation did not give any importance to the institution and just five years after the death of Utkalamani, the other Satyabadi Panchasakhas died one after another, the school was neglected and led its downfall.

Question 9:
Discuss the educational philosophy of Sri Aurobindo.
Answer:
Sri Aurobindo dedicated his whole life for society and education to provide contribution to travel towards divine perfection and to express the power, harmony, beauty and joy of self-realization.By education, he means that which will offer the tools whereby one can live for the divine for the country for oneself and for others. His principle of the philosophy of education, the awareness of man as a spiritual being.

Integral Education – Aurovindo’s integral education means integral growth of the individual’s personality. The function of education is to study the mind of individuals, people, nature, the universe. He put more emphasis to study the mind.

The human mind consists of four layers. They are :
1. Chitta – the storehouse of memory.
2. Manas – the sixth sense like – sight, sound, taste, smell, touch.
3. Budhi – thought or intellect.
4. Truth – Satya
Integral education, attempts to the integral development of physical being, vital beings, psychic being and mental being about a transformation of man into a spiritual being.

Aurobindo’s philosophy of Education are:
1. Education of the Physical being: To Aurovindo beauty is the ideal of physical life such as (i) To discipline and control the physical function (ii) For harmonious development of the body and physical movements (iii) Rectification of defects (iv) To awaken the body consciousness one has to undertake physical exercises. The factors of spiritual discipline, service, bhakti, and yoga are essential physical education. Restlessness is the important aspect to control the body and to achieve. Concentration physical education also controls sex drives or impulses. Emphasis is given on games and sports which an renew physical and higher forms of energy, develop tolerance, self control, friendliness etc.

2. Education of the Vital Being : It helps in the development of character. Vital education emphasizes on the vital being of man by which the man be able to understand the inner and outer world. It develops self observation. Vital being means utilization of the sense organs which help us to receive knowledge. The senses like a sight hearing, small, touch, taste and mind should be trained. Vital education also aimed at the aesthetic personality development.

3. Education of the Mental Being: Mental being education emphasizes on mental science and concentration. The mother says to silence the mind, one has to take the help of classical yoga. By yoga, one can acquire mastery of the mind. So knowledge of the education of mental being which helps is the gradual liberation from ignorance.
Mental education has three-fold functions:
i)To gather old knowledge.
ii) To discover new knowledge.
iii) To develop the capacity use and apply the knowledge acquired.
Through the application of knowledge, the pupil develops cognition, ideas, intelligence and mental perception. For this man becomes the source of knowledge.

4. Education for Psyche Being: Psyche being is the psychological centre of mind. The function of education is to enable man to become conscious of the psychological centre which is key to an integral personality. Psyche education is to enable an individual to see his soul grow in freedom. It supports the vital, physical, and mental being. When an individual develops psyche consciousness, he understands life and himself.

To him the psyche being is a spiritual personality put forward by the soul in its evaluation. The business of education is to develop the capacity of psychological being towards a realization of potentialities. Psyche being is possible through yoga or tapasya of love. As a result of this yoga one can attain liberation from suffering.As a result four-fold approval like the physical, the mental, the psyche and love in the ii idi v ideal student, the man gets liberation from the material world, desires, ignorance and suffering.
A tota 1 spiritual education is the goal of education and spiritual transformation of man is the goal o f integral education.

Question 10:
Discuss the philosophical thoughts of Rousseau.
Answer:
Rousseau’s philosophical thoughts are related to Naturalism and Negative Education.

1) His Naturalism
a) God has made all humans good but when they come in contact with society they become spoiled. In order to change them again into good, we should bring them back to nature.
b) In the beginning of human civilization, man was happy and good, but now he is unhappy. If he goes back to nature, he will again be happy and good. Thus, a child be educated and developed according to his natural tendencies. Society and school has no role to play in the process.
c) He did not like old values and traditions of the society. According to him, social relations can be brought about by destroying these values.
d) There are three main forms of naturalism such as Social, Psychological and Physical. In his social naturalism, he devises education as a method to mold the society. He opined that we could not become a man and citizens at the same time. Out of two options, we should become a man only. Thus, the individuality of man is honored by him. Psychological naturalism meant that the child should be given chance to develop on the basis of his inner feeling and natural tendencies and experiences gained from contact with others are harmful and unnatural.By physical naturalism, Rousseau means that child should be given chance to come in contact with birds, animals, and other physical objects of nature and learn in the process. This learning will make him free from evils.
e) He opposes the organization of education in social foundations. Thus he opposed school/education in the formal sense and advocated an individual basis of education.
f) He opposed too all sorts of habit formation in the child. It is because this can make a child traditional.
Thus, Rousseau’s Naturalism is fully of many unnatural and impracticable ideas and he himself realized it but he put three ideas with such a force that is influenced not only the society of Europe but also the educational system of the period.

2) Negative Education
In the 17th. century, Europe, man was considered bad by nature. So efforts were made to change the nature of man by imparting religious education.
Rousseau went contrary to this believing infallibility of man and proposed the idea of Negative Education. By this education he means not teaching truth or virtues to a child but shielding his heart from evils and mind from errors. The feature of his negative education are given below:
a) Nothing against the interest, attitude on age of the child should be taught. He should be given full freedom to choose his own curriculum.
b) The education of a child should be based on his natural tendencies and stages of development by using different organs and senses of the child. Mind should be less taxed for the purpose. Mind should be inactive toll the child develops discretion power in him thus he emphasized, the training of senses by keeping the mind idle.
c) Child should be protected from outside environment to keep him alien to vices. In this way, there will not be any need to impart knowledge of virtues to the child. Virtues may be taught of the later stage of life.
d) The child should not be taught anything at all, especially from books. Small children should learn from nature itself.
e) Thus by Negative Education, Rousseau opposed not only the mental development of the individuals/child but he also opposed moral and spiritual development.

Question 11:
Discuss the different phases of education of Emile as supported by Rousseau. Curriculum, methods of teaching and discipline.
Answer:
Rousseau’s programme of education for Emile is devised into different phases and Rousseau had divided the whole programme of education curriculum on the basis of the development stages of human child.
(i) Infancy (from 00 to 5 years): At this stage instead of giving the child controlled information of various subjects it is better to pay attention to the development of child’s body and his sense organs. He should be allowed to play with whatever things he likes. The dresses should be made for free movement. His toys should be cheap ordinary and natural like leaves, plants flowers, stems etc. According to Rousseau Emile should be given a negative Education druing infancy.

(ii) Childhood (5 to 12 years): Rousseau opposed the use of textbooks during this period. The child should be given chance to leam everything through observation and experiences. These experiences develop sense organs, which will lead to the development of mind and power of reasoning. He should be allowed full freedom to use his sense, the sense organs, the eyes to be trained to measure height, weight, and distance.

(iii) Adolescence (12-15 years): During this period natural curiosity of the adult develops. So he should be taught natural science and languages, mathematics, music, painting and social services. He should use maps in learning geography.

(iv) Adulthood (15 – 20 years): The organs become active with a maturity of mind and intellect he should leam social and moral education like objects of social services.
His Discipline: Rousseau advocated complete freedom, left free to the environment.
Self discipline is learnt in the process of experiences. There is no scope ofgiving any punishment to the child but natural process of feed back in stills discipline in him.

Question 12:
Dsicuss the life philosophy of Rousseau. Give his educational aims and ‘Self Education’ and curriculum.
Answer:
Life Philosophy of Rousseau: Jean Jacques Rousseau (1712 -1778) lost his mother just after his birth and his father brought him up but he could not look after him. Rousseau fell to prey to all sorts of bad habits. He originally belonged to Geneva and the beauty of that place lured him to use it and it made him a careless man.
Rousseau got matured. He hated the society for its evils. Evil customs and artificial traditions and tried to retun it on the line of nationalism and wished everybody shun the evil society and live with nature.

Out of five books, “The progress of arts and science”, “New Heloise”, Confessions, ‘Social Contract’ and ‘Emile’ are unique and the last two books ‘Social Contract’ and ‘Emile’ brought great name and fame to him.His ideas of education can be seen in Emile. It is a novel whose hero is Emile and the heroine is Sofia. In his book, Rousseau keeps Emile away from society and culture and leaves him under the guidance of an ideal teacher in the natural environment and Emile is educated in an atmosphere of natural beauty. There are five chapters in the book. The first chapter describes education of Emile is in fancy, childhood, adolescence and adulthood and the last chapter deals with the education of Emile’s wife Sofia.

People reacted against his book “Emile very sharply. France and Switzerland banned it end it was put into the fire at many place in Europe consequently. Rousseau had to leave France for England in 1766.After 11 years of exile, he returned to France and wrote his last book “Confession”. Rousseau’s philosophical thoughts are related to Naturalism and Negative Education.

Educational Aims: Rousseau emphasized on the following aims of education, l) We are bom weak and we want strength. We are poor and we want help. Whatever we do, not have is to be given by education is the ultimate aim of education.

  • To establish harmony between man, object and nature.
  • Child attains pleasure by using his organs and senses and by applying his strength. So the aims of education is to develop his various innate powers by helping him in his natural activities.
  • Books are not end of education. They are only means and the child is the end. The aim of education is to develop the child to be fullest for a complete and happy life.

His Self-Education:
i) He opposes strongly the imposition of ideals and morals into the mind of the child from
outside. Children should learn these things through activities. It is because the children are more interested in activities rather than sitting idle and hearing lectures. At that stage, helps enough power of assimilate between construction and destruction. His only concern is to bring about change will form through any activity.
ii) Body can become strong through physical exericse and mind also become strong through self study. In self-education the child can proceed further according to his own physical and mental capacities.
iii) Only that knowledge gets retained for a longer period, which is learned from self-experiences. We should accept the experiences of others only after our own wisdom.
iv) Blind fellowship is not accepted at all. A child should not learn a thing because he has been asked to do so but he should learn oniyit in the process of his self study.
v) Special emphasis is to be given on the physical development of the child.
Curriculum
Rousseau was against the fixed curriculum, the child should be educated through activities and first-hand experiences.During infancy positive instructions to be imparted with good health training of senses and cultivation of natural habits. At the stage of childhood provision of in parting physical education through a set of gymnastics and the exercises training of senses.

At the stage of boyhood, the chief intellect is to be trained through teaching of good sense of physical senses, language, mathematics, manual works, social relations, music and drawing.At adolescence morality of the individual is to be trained through teaching of good education and by activity method and occupation. Moral education subjects are : history, religion, aesthetics, physical culture and sex education etc. are included in the curriculum at the adolescence stage.

CHSE Odisha Class 12 Foundations of Education Unit 1 Contribution of Educators Long Answer Questions

Question 13:
Discuss John Dewey’s contribution to educational thought and practice.
Answer:
John Dewey is one of the greatest educationists of the modem age. He has revolutionized the exponent of pragmatism.
Meaning of Education to John Dewey: John Dewey considered individuality as the aim of education. According to him, all education proceeds by the participation of the individual in social consciousness of the race. The educative process, according to John Dewey has two aspects – Psychological and Sociological because every individual is a psychological as well as social being. So no aspect can be neglected in the process of education.

  1.  Education as life: According to John Dewey education is a process of living. So the school experiences should have a resemblance with life outside the school and the school functions as a society in miniature form.
  2.  Education as Growth: Education is a continuous process that adds to child’s experience resulting in the growth and development of the child. It helps the child to grow to its full extent.
  3.  Education as Reconstruction of Experience: Every generation inherits certain experiences from its previous generation. These experiences are to be modified according to the changing situations through education.
  4. Education as a Social Process: Man is a social being and education socializes to human child. Right education helps the child make suitable adjustments with his social environment.John Dewey and Aims of Education: John Dewey is of the opinion that education process no aim beyond itself, it is its own end. There are no fixed aim of education to John Dewey.

Because, human life changes with the changes in time, place and situations and education should cater to the changing nature of human life. Education should therefore aim at cultivating a dynamic and adaptable mind in the child so that he can suitably adjust with his changing environment. Education should also create new value for the child. Education should aim at inculcating democratic values and attitudes in the child.

John Dewey and Curriculum: Curriculum according to John Dewey should reflect the child’s social life and social activities. It should be flexible, and changeable and it should take into consideration the child’s interests and educative experiences. As per example the curriculum at the primary stages should be based on the fourfold interests of the small child, interests in conservation and communication interests in inquiry interests in making change or construction and interest in artistic expression. Hence subjects like reading, writing, counting, handwork and drawing etc. are to be included at this stage.

The curriculum at higher students of education must have provisions for the environment and reorganization of past experiences. It just stimulates the learner to acquire new experiences and new ideas to they learned ones. John Dewey has also put emphasis on curriculum. This means each subject should be linked with the other and each should also related to the day life of the child.

John Dewey and Method of Teaching: John Dewey put emphasis on learning by doing. He stressed project method and this method is meant for the child. Earning was to be emphasized on teaching. The students should be free to carry on their whole planning and activity. Learning should be incidental and an outcome of the purposeful activity.

John Dewey and Discipline: John Dewey believed in the theory of free discipline and self-discipline. Discipline imposed from outside is directive with eyes of the John Dewey. Discipline should be social in character. The natural impulses of the child should be channelized in a socially desirable way. The main function of school discipline is to cultivate in the children’s social attitude, habits and ideal conduct through cooperative activity.

John Dewey and Role of the Teacher: In John Dewey’s system of education the child occupies the central position. The teacher is the friend, philosopher and guide of students. The teacher has to observe the pupil’s planning, encourage their activity and provide them the necessary opportunity and environment. John Dewey’s teacher is free to frame his own curriculum and carry on the administration ofhis own school.

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Odisha State Board BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 ଜ୍ୟାମିତିରେ ସାଦୃଶ୍ୟ Ex 1(b) Textbook Exercise Questions and Answers.

BSE Odisha Class 10 Maths Solutions Geometry Chapter 1 ଜ୍ୟାମିତିରେ ସାଦୃଶ୍ୟ Ex 1(b)

Question 1.
ଚିତ୍ରରେ △ABC ର \(\overline{\mathbf{BC}}\) ବାହୁ ଉପରିସ୍ଥ D ଏକ ବିନ୍ଦୁ, ଯେପରିକି \(\overline{\mathbf{AD}}\), ∠BAC ର ସମଦ୍ବିଖଣ୍ଡକ । ତଳେ ଥ‌ିବା ଅନୁପାତ ମାନଙ୍କ ମଧ୍ୟରୁ ଠିକ୍ ଅନୁପାତଟି ବାଛି ନିମ୍ନରେ ଥ‌ିବା ଶୂନ୍ୟସ୍ଥାନ ପୂରଣ କର ।
△ABD ଓ △ADC ର କ୍ଷେତ୍ରଫଳର ଅନୁପାତ …………………….
(AB: DC, BD: AC, AB : AC, AD : BC)
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 1

Question 2.
△ABC ର ∠ABC ର ପମଦୁଖପୃକ \(\overline{\mathbf{AC}}\) ବାକୁକ୍ଲି D ଦିନ୍ଦୁ6ର ଛେଦ ଦ6ର | AB = 4 ସେ.ମି. BC = 6 ସେ.ମି. ଏବଂ AC = 5 ସେ.ମି. ହେଲେ, AD ଓ CD ନିର୍ଣ୍ଣୟ କର ।
Solution:
△ABCର ∠ABCର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AC}}\) ।
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 2
⇒ \(\frac { AB }{ BC }\) = \(\frac { AD }{ DC }\)
⇒ \(\frac { AD }{ DC }\) = \(\frac { AB }{ BC }\) = \(\frac { 4 }{ 6 }\)
⇒ \(\frac { AD }{ DC }\) = \(\frac { 2 }{ 3 }\)
∴ AD = 2x ପେ.ମି. 6ହଲ, DC = 3x ପେ.ମି. |
AC AD + DC = 2x 6ପେ.ମି. + 3x ପେ.ମି. = 5 × ପେ.ମି.
ପ୍ରଶ୍ନନୁସାରେ 5x = 5 ⇒ x = 1
∴ AD = 2x ପେ.ମି. = 2 ପେ.ମି. ଓ DC = 3x ପେ.ମି. = 3 ପେ.ମି. |

BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 ଜ୍ୟାମିତିରେ ସାଦୃଶ୍ୟ Ex 1(b)

Question 3.
△ABC ର \(\overline{\mathbf{AB}}\), \(\overline{\mathbf{BC}}\) ଓ \(\overline{\mathbf{CA}}\) ବାହୁ ତ୍ରୟର ଦୈର୍ଘ୍ୟକୁ ଯଥାକ୍ରମେ c, a ଓ b ଏକକ ରୂପେ ସୂଚିତ କରାଯାଏ । ∠ACB ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AB}}\) କୁ M ବିନ୍ଦୁରେ ଛେଦକଲେ, ପ୍ରମାଣ କର ଯେ
(i) AM = \(\frac{b c}{a+b}\)
(ii) BM = \(\frac{c a}{a+b}\)
Solution:
△ABC 6ର ∠ACB ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{CM}}\) |
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 3
⇒ \(\frac { AC }{ BC }\) = \(\frac { AM }{ BM }\)
⇒ \(\frac { b }{ a }\) = \(\frac { AM }{ BM }\)
∴ AM = bx ଏକକ 6ଦୃ6କ, BM = ax ଏକକ
∴ c = AB = AM + BM = bx + ax = x (a + b) ⇒ x = \(\frac{c}{a+b}\)
∴ AM = bx = \(\frac{bc}{a+b}\) ଓ BM = ax = \(\frac{ac}{a+b}\) (ପ୍ରମାଣିତ)

Question 4.
(i) ଟିଦୃ6ର, △ABC ର \(\overline{\mathbf{AC}}\) ଦାକ୍ ପ୍ରତି ମଧ୍ୟମା \(\overline{\mathbf{BP}}\) | ∠BPC ଏର୍ବ ∠BPA ର ଅସ୍ତ୍ର୫ପମହି ଖଣ୍ଡକ ଯଥାକ୍ସେ \(\overline{\mathbf{BC}}\) ଓ \(\overline{\mathbf{AB}}\) କ୍ମ X ଓ y ବ୍ବ୍ର6ର 6ଚ୍ଛଦ କରତି | ପ୍ରମାଣ କର 6ସ \(\overleftrightarrow{\mathbf{X} \mathbf{Y}}\) || \(\overline{\mathbf{AC}}\) |
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 4
Solution:
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 5
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 6

Question 5.
ଚିତ୍ର ରେ △ABC ଉ \(\overline{\mathbf{BP}}\) ମଧ୍ୟମା | ∠ABC ର ସମଦୃଖଣ୍ଡକ \(\overleftrightarrow{\mathbf{P Y}}\) , \(\overline{\mathbf{AB}}\) କୁ Y ଦିନ୍ଦରେ 6ଚ୍ଛଦ କରେ | \(\overline{\mathbf{AC}}\) ସହି ସମାବର କରି Y ଦିନ୍ଦୁରେ \(\overleftrightarrow{\mathbf{YX}}\) ଅଙବ କରାଯାଇଚ୍ଚି , ଯେପରି ର।ତ୍ରା \(\overline{\mathbf{BC}}\) କୁ X ଦିନ୍ଦୁରେ ଛେଦ କଦୁଚ୍ଛ | ପ୍ରମାଣ କର ଯେ \(\overrightarrow{\mathbf{P X}}\) , ∠BPC ର ସମଦ୍ରିଖଣ୍ଡକ |
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 7
Solution:
ଦତ୍ତ : △ABC ର \(\overline{\mathbf{BP}}\) ଏକ ମଧ୍ୟମା | ∠APB ର ପ୍ରସଦ୍ଵିଖଶ୍ରକ \(\overleftrightarrow{\mathbf{P Y}}\) , \(\overline{\mathbf{AB}}\) କ Y ଦିନ୍ଦରେ ଛେଦକ6ର | \(\overline{\mathbf{AC}}\)ସହ ସମାନ୍ତର କରି Y ଦିନ୍ଦୁରେ \(\overleftrightarrow{\mathbf{YX}}\) ରଥନ କରାଯାଇଗ୍ଲି 6ଯପରି ତାହା \(\overline{\mathbf{BC}}\) କ୍ମି X ବିନ୍ଦୁଦକରୁଛି |
ପ୍ରାମାଣ୍ୟ : \(\overleftrightarrow{\mathbf{P X}}\) , ∠BPC ର ସମଦ୍ବିଖଣ୍ଡକ |
ପ୍ରମାଣ : △ABP ରେ ∠APB ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AB}}\) କୁ Y ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { BP }{ AP }\) = \(\frac { BY }{ AY }\)
△ABC 6ର \(\overline{\mathrm{XY}}\) || \(\overline{\mathrm{AC}}\) ⇒ \(\frac { BY }{ AY }\) = \(\frac { BX }{ CX }\)
∴ \(\frac { BP }{ AP }\) = \(\frac { BX }{ CX }\)
⇒ \(\frac { BP }{ CP }\) = \(\frac { BX }{ CX }\) (∵ AP = CP (ଦର))
⇒ \(\overrightarrow{\mathrm{PX}}\) , ∠BPC ର ପ୍ରସଦ୍ଵିଖଶ୍ରକ |

BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 ଜ୍ୟାମିତିରେ ସାଦୃଶ୍ୟ Ex 1(b)

Question 6.
△ABC ରେ ∠BAC ର ସମଦ୍ଵିଖଣ୍ଡକ, \(\overline{\mathbf{BC}}\) କୁ P ବିନ୍ଦୁରେ ଛେଦକରେ ଏବଂ ∠ABC ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AP}}\) କୁ ( ବିନ୍ଦୁରେ ଛେଦ କରେ । ପ୍ରମାଣ କର ଯେ \(\frac { AQ }{ QP }\) = \(\frac{\mathbf{A B}+\mathbf{A C}}{\mathbf{B C}}\) |
Solution:
ଦତ୍ତ : △ABC ରେ ∠BAC ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{BC}}\) କୁ P ବିନ୍ଦୁରେ ଛେଦକରେ । ∠ABC ର ସମଦ୍ଵିଖଣ୍ଡକ \(\overline{\mathbf{AP}}\) କୁ Q ବିନ୍ଦୁରେ ଛେଦକରେ ।
ପ୍ରାମାଣ୍ୟ : \(\frac { AQ }{ QP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BC}}\)
ପ୍ରମାଣ : △BAC ରେ ∠BAC ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{BC}}\) କୁ P ବିନ୍ଦୁରେ ଛେଦକରେ ।
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 8
⇒ \(\frac { AB }{ AC }\) = \(\frac { BP }{ CP }\) ⇒ \(\frac { AB }{ BP }\) = \(\frac { AC }{ CP }\) (ଏକାନ୍ତର ପ୍ରକ୍ରିୟା ଦ୍ବାରା )
⇒ \(\frac { AB }{ BP }\) = \(\frac { AC }{ CP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BP}+\mathrm{CP}}\) (କ୍ରମିକଯୋଗ ପ୍ରକ୍ରିୟା ଦ୍ଵାରା)
⇒ \(\frac { AB }{ BP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BC}}\) …(i)
ପୁନଶ୍ଚ △ABP ରେ ∠ABP ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AP}}\) କୁ Q ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { AB }{ BP }\) = \(\frac { AQ }{ QP }\) …(ii)
(i) ଓ (ii) କୁ \(\frac { AQ }{ QP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BC}}\) (ପ୍ରମାଣିତ)

Question 7.
ABCD ସାମାନ୍ତରିକ ଚିତ୍ରର ∠BAD ର ସମଦ୍ବିଖଣ୍ଡକ, \(\overline{\mathbf{BD}}\) କଣ୍ଠକୁ K ବିନ୍ଦୁରେ ଛେଦକରେ ଏବଂ ∠ABC ର ସମଦ୍ଵିଖଣ୍ଡକ, \(\overline{\mathbf{AC}}\) କଣ୍ଠକୁ L ବିନ୍ଦୁରେ ଛେଦ କରେ ।
ସମାଧାନ :\(\overrightarrow{\mathrm{LK}}\) || \(\overline{\mathbf{AB}}\) ।
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{LK}}\) || \(\overline{\mathbf{AB}}\)
ଅଙ୍କନ : \(\overrightarrow{\mathrm{AK}}\), \(\overline{\mathbf{DC}}\) କୁ M ବିନ୍ଦୁରେ ଛେଦକରୁ । K ବିନ୍ଦୁରେ \(\overline{\mathbf{AB}}\) ସହ ସମାନ୍ତର ଭାବେ ଅଙ୍କିତ ରେଖା \(\overline{\mathbf{AD}}\) କୁ N ବିନ୍ଦୁରେ ଛେଦକରୁ ।
ପ୍ରମାଣ : △BAD ରେ ∠DAB ର ସମଦ୍ଵିଖଣ୍ଡକ \(\overline{\mathbf{DB}}\) କୁ K ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { AD }{ AB }\) = \(\frac { DK }{ KB }\)
△DAB ରେ \(\overline{\mathbf{NK}}\) || \(\overline{\mathbf{AB}}\) |
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 9
⇒ \(\frac { DK }{ KB }\) = \(\frac { DN }{ AN }\)
△ ADM ରେ \(\overline{\mathbf{NK}}\) || \(\overline{\mathbf{DM}}\) ⇒ \(\frac { DN }{ AN }\) = \(\frac { KM }{ AK }\)
∴ \(\frac { AD }{ AB }\) = \(\frac { BC }{ AB }\) (∵ AD = BC)
△ ABC ରେ \(\overrightarrow{\mathrm{BL}}\) , ∠ABC ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { BC }{ AB }\) = \(\frac { CL }{ AL }\)
⇒ \(\frac { KM }{ AK }\) = \(\frac { CL }{ AL }\) (∵\(\frac { BC }{ AB }\) = \(\frac { AD }{ AB }\) = \(\frac { DK }{ KB }\) = \(\frac { DN }{ AN }\) = \(\frac { KM }{ AK }\) )
⇒ \(\overline{\mathbf{KL}}\) || \(\overline{\mathbf{MC}}\)
⇒ \(\overline{\mathbf{KL}}\) || \(\overline{\mathbf{AB}}\) (∵\(\overline{\mathbf{KL}}\) || \(\overline{\mathbf{AB}}\) ) (ପ୍ରମାଣିତ)

Question 8.
ABCD ଚହୁକୁଳର ∠DAB ଓ ∠DCB 6କାଣଦ୍ୱଯଉ ପମଦଖଣ୍ଡକ ପରପକ \(\overline{\mathbf{BD}}\) କଣ୍ଡ ରପରେ ଛେଦକରଚି | ପ୍ରାମାଣ କର ଯେ ∠ABC ଓ ∠ADC ର ପମ ଦିଖଣ୍ଡକଦୁଯ ପରସ୍ତକ୍ \(\overline{\mathbf{AC}}\) କଣ୍ଡ ରପ6ଭ 6ଚ୍ଚଦ କରି6ବା
Solution:
ଦର :ABCD ଚହୁକୁଳର ∠DAB ଓ ∠DCB 6କାଣଦ୍ୱଯଉ ପମଦଖଣ୍ଡକ \(\overline{\mathbf{AC}}\) କଣ୍ଡ ରପ6ଭ 6ଚ୍ଚଦ କରି6ବା
ପ୍ତମାତା : △BAD ରେ ∠DAB ର ସମଦିଖଣ୍ଡକ \(\overrightarrow{\mathrm{AE}}\) |
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 10
⇒ \(\frac { AB }{ AD }\) = \(\frac { BE }{ ED }\) …..(i)
ଚହୁକୁଳର △BAD ରେ ∠BCD ର ଛେଦକରଚି \(\overrightarrow{\mathrm{CE}}\) |
⇒ \(\frac { BC }{ CD }\) = \(\frac { BE }{ ED }\) ….(ii)
(i) ଓ (ii) ଦ୍ଦ \(\frac { AB }{ AD }\) = \(\frac { BC }{ CD }\)
⇒ \(\frac { AB }{ BC }\) = \(\frac { AD }{ CD }\) (ଏକାନ୍ତର ପ୍ରତଯାଦ୍ଧାରା)
ମରେକର ABC ର ସପଦଖଣୃକ AC କୁ F ଦିନ୍ଦୁରେ 6ଛଦକରେ |
⇒ \(\frac { AB }{ BC }\) = \(\frac { AF }{ FC }\) ⇒ \(\frac { AD }{ DC }\) = \(\frac { AF }{ FC }\) (∵\(\frac { AB }{ BC }\) = \(\frac { AD }{ DC }\))
⇒ \(\overline{\mathrm{DF}}\) , ADC ର ସପଦିଖଣ୍ଡଦ (ପ୍ରମାଣିତ)

Question 9.
△ABC ରେ ∠B ର ସମଦ୍ଵିଖଣ୍ଡକ, \(\overline{\mathrm{AC}}\) କୁ E ବିନ୍ଦୁରେ ଏବଂ ∠C ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ F ବିନ୍ଦୁରେ ଛେଦକରେ । \(\overline{\mathrm{FE}}\) || \(\overline{\mathrm{BC}}\) ହେଲେ ପ୍ରମାଣ କର ଯେ, △ABC ସମଦ୍ବିବାହୁ ।
ସମାଧାନ :
ଦତ୍ତ : △ABC ରେ ∠B ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AC}}\) କୁ E ବିନ୍ଦୁରେ ଓ ∠C ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ F ବିନ୍ଦୁରେ ଛେଦକରେ ଓ \(\overline{\mathrm{FE}}\) ||\(\overline{\mathrm{BC}}\) |
ପ୍ରାମାଣ୍ୟ : △ABC ସମଦ୍ବିବାହୁ |
ପ୍ରମାଣ : △ABC ରେ ∠B ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AC}}\) କୁ E ରେ ଛେଦକରେ ।
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 11
⇒ \(\frac { AC }{ BC }\) = \(\frac { AF }{ FB }\)
ସେହିପରି ∠Cର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ F ରେ ଛେଦ କରେ ।
⇒ \(\frac { AC }{ BC }\) = \(\frac { AF }{ FB }\)
\(\overline{\mathrm{FE}}\) || \(\overline{\mathrm{BC}}\) (ଦତ୍ତ)
⇒ \(\frac { AF }{ FB }\) = \(\frac { AE }{ EC }\) ⇒ \(\frac { AC }{ BC }\) = \(\frac { AB }{ BC }\)
⇒ AB = AC
⇒ △ABC ସପଦିଖଣ୍ଡଦ (ପ୍ରମାଣିତ)

BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 ଜ୍ୟାମିତିରେ ସାଦୃଶ୍ୟ Ex 1(b)

Question 10.
△ABC ରେ ∠A, ∠B ଓ ∠C ର ସମଦ୍ବିଖଣ୍ଡକ, \(\overline{\mathrm{BC}}\), \(\overline{\mathrm{CA}}\) ଓ \(\overline{\mathrm{AB}}\) କୁ ଯଥାକ୍ରମେ D, E ଓ F ବିନ୍ଦୁରେ ଛେଦକଲେ ପ୍ରମାଣ କର ଯେ \(\frac { BD }{ DC }\) . \(\frac { CE }{ EA }\) . \(\frac { AF }{ FB }\) = 1
Solution:
ଦତ୍ତ : △ABC ରେ ∠A, ∠B ଓ ∠C ର ସମଦ୍ଵିଖଣ୍ଡକ \(\overline{\mathrm{BC}}\), \(\overline{\mathrm{CA}}\) ଓ \(\overline{\mathrm{AB}}\) କୁ ଯଥାକ୍ରମେ D, E ଓ F ବିନ୍ଦୁରେ ଛେଦକଲେ |
ପ୍ରାମାଣ୍ୟ : \(\frac { BD }{ DC }\) . \(\frac { CE }{ EA }\) . \(\frac { AF }{ FB }\) = 1
ପ୍ରମାଣ : △ABC ରେ ∠A ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{BC}}\) କୁ D ରେ ଛେଦକରେ ।
BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 Img 12
⇒ \(\frac { BD }{ DC }\) = \(\frac { AB }{ AC }\)
ସେହିପରି ∠B ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AC}}\) କୁ E ରେ ଛେଦକରେ ।
⇒ \(\frac { CE }{ EA }\) = \(\frac { BC }{ AB }\)
∠Cର ସମଦ୍ୱିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ Fରେ ଛେଦକରେ ।
⇒ \(\frac { AF }{ FB }\) = \(\frac { AC }{ BC }\)
∴ \(\frac { BD }{ DC }\) × \(\frac { CE }{ EA }\) × \(\frac { AF }{ FB }\) = \(\frac { AB }{ AC }\) × \(\frac { BC }{ AB }\) × \(\frac { AC }{ BC }\) = 1 (ପ୍ରମାଣିତ)

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CHSE Odisha Class 12 English Grammar Modal Verbs

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Modal Verbs Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Modal Verbs

SECTION -1

Making requests (using can, could; may, will, would)
Read the sentences below carefully.
1. Suresh: Can you lend me your bicycle?
Mahesh: Of course, I’m not using it today.
2. Student: Could I borrow your dictionary, sir?
Teacher: Certainly. But it’s meant only for very advanced learners.
3. Shyam: Will you open the door, please?
Stranger: Sure.
4. Jatin: Would you mind repeating the last sentence, sir?
Speaker: Not at all. I said that…
5. Jina: May I ask a question, please?
Speaker: By all means.
6. Landlady: Will you please clean the kitchen?
Maid. Yes, ma’am. Right away.

The modal auxiliaries can, could, may, will, and would are used to make requests.
But we can well mark a slightly different way from the others.
1. The use of ‘can’ is informal, while could is more formal and polite. It suggests a more tentative attitude on the part of the speaker.
2. ‘May’ is used rather in a formal way to express a request.
3. ‘Will’ is also used to make requests when we don’t need to be particularly formal or polite.
4. ‘Would’ or would you mind is used for more polite requests or formal (with the 2nd person).

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 1
Make a request to suit each of the situations suggested below, using the word supplied in brackets. In case no word has been suggested, you are free to choose your own words to make the request.
(a) You need some money. Ask a friend to lend you some. (can)
_________________________________
(b) You want a speaker in a seminar to explain something. Ask him to do so. (could/ would)
_________________________________
(c) You want your room key from the receptionist in a hotel. Ask the receptionist to give you the key. (can/may)
_________________________________
(d) You want a visitor to wait a minute while you get ready. (would)
_________________________________
(e) You are carrying a heavy bag. Ask someone to open the door for you. (could)
_________________________________
(f) You are on the phone. You want to speak to the chairman. (may)
_________________________________
(g) You want someone to tell you how to reach the railway station.
_________________________________
(h) You are buying a pair of shoes and want a receipt.
_________________________________
(i) You are working and want everybody to be quiet for some time.
_________________________________
(j) You need something to eat. Ask your mother.
_________________________________
(k) You are on a train and you would like to borrow a newspaper from another passenger, who has just finished reading it.
_________________________________
Answer:
(a) Can you lend me some money?
(b) Could you please explain something?
Would you explain something, please?
(c) Can you please give me the room key?
May I get the room key, please?
(d) Would you wait for a minute, please?
(e) Could you please open the door for me?
(f) May I talk to the chairman, please?
(g) Could you please tell me how to reach the railway station?
(h) Would you give me the receipt, please?
(Or) Could you please give me the receipt?
(i) Could you be silent for some time, please?
Would you mind keeping silent for some time?
(j) Can you give me something to eat?
(k) Would you mind giving me the newspaper for some time?

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 2
Monisha is ill in bed and has to request her friend to do things for her. Use can, will, could or would for the requests that she must make. (More than one answer may be possible.)
(a) Monisha wants some books to read. She would like her friend to get some.
_________________________________
(b) Monisha doesn’t want to be disturbed by visitors.
_________________________________
(c) Monisha wants her friend to write a letter for her.
_________________________________
(d) Monisha wants some vegetable soup for lunch.
_________________________________
(e) Monisha wants her friend to fetch the mobile phone, which is in the next room.
_________________________________
(f) Monisha wants her friend not to go out and leave her alone.
_________________________________
(g) Monisha wants her friend to wash her clothes.
_________________________________
Answer:
(a) Can you lend me some books, please?
(b) Would you mind stop talking?
(c) Can you please write a letter for me?
(d) Could you/Can you provide me some vegetable soup for lunch, please?
(e) Can you get me the mobile phone from the next room, please?
(f) Would you stay for some time here, please?
(g) Can you please wash my clothes?

Activity – 3
Seema is staying in Leena’s home as a guest, and Leena has to request Seema to do a few things for her, which she is not able to do herself, for some reason or the other. Here is an example.
Seema, could you please clean the dishes after dinner? I’ve got to go to the market to buy a few things.
Can you make a few more requests to Seema on behalf of Leena, using the clues below? You also have to provide a reason for each request. (You should be specially polite while making more unusual requests.)
(a) switch off the lights
_________________________________
(b) make some tea
_________________________________
(c) water the plants in the garden
_________________________________
(d) feed the dog
_________________________________
(e) take the rubbish out of the dustbin
_________________________________
(f) take care of the neighbor’s children
_________________________________
(g) cook dinner
_________________________________
Answer:
(a) Could you please switch off the lights? I have to sweep the room.
(b) Could you please make me some tea?
I have got to wash my dresses.
(c) Would you please water the plants in the garden? I’ve to nurse my grandfather.
(d) Would you mind feeding the dog? I have got to do shopping.
I have to wash the utensils.
(e) Could you take the rubbish out of the dustbin, please?
I have to wash the utensils.
(f) Could you take care of the neighbor’s children, please? I have to have my bath.
(g) Could you please cook dinner?
I’ve, some sums to work out.

CHSE Odisha Class 12 English Grammar Modal Verbs

SECTION – 2

Asking for and granting permission
(using can, could, may, would)
Look at the examples below.
(a) Tarun: Can I use your typewriter to type out an application?
Friend: Yes, of course, you can.
(b) Tapas: Could I use the telephone?
Receptionist: Yes, sir. But this one is only for local calls.
(c) Journalist: Mr. Prime Minister, may I ask what you plan to do for unemployed engineers?
Prime Minister: New jobs are being created for them.
(d) Shefali: Would you mind if I sat here?
Stranger: No, not at all.
Can is used for permission usually in an informal style. When we talk to our intimate/ private men and women, we use ‘can’ for permission, and ‘could is used for permission when we are not sure whether the permission will be granted. It is usually used in ‘formal’ situations (i.e., for unknown people). Do remember this ‘could’ modal verb’ is never used to give permission to someone.
‘May and Would you mind’ are usually used for permission in a formal style. The speaker is even less sure of getting permission or feels that permission is likely to be refused.

Activity – 4
Ask for permission using can, could, or may. (More than one answer is possible.)
(a) You are at a seminar where someone is speaking. You want to ask the speaker a question.
Excuse me: _________________________________
(b) You are late for your English class. You want the teacher’s permission to get in.
_________________________________
(c) You are interviewing an actor. You would like to ask him something about his personal life.
_________________________________
(d) Yon wants to stay in the hostel. Ask the hostel warden for permission.
_________________________________
(e) You want to join the cricket team of your college. Ask the teacher in charge of the games.
_________________________________
(f) You have been invited to dinner by someone you do not know very well. You would like to ask for another piece of chicken.
_________________________________
(g) Your friend has a book that you want to read. Ask him/her.
_________________________________
Answer:
(a) You are at a seminar where someone is speaking. You want to ask the speaker a question.
Excuse me, could I ask you a question?
(b) You are late for your English class. You want the teacher’s permission to get in. Could, I get into the class? Or, May I come in?
(c) You are interviewing an actor. You would like to ask him something about his personal life.
Would you mind telling me a few words on your personal life?
Or, May I ask a few questions on your personal life?
(d) You want to stay in the hostel. Ask the hostel warden for permission.
Could you allow/grant me to stay in the hostel?
(e) You want to join the cricket team of your college. Ask the teacher in charge of the games.
Could I join the cricket team this year?
(f) You have been invited to dinner by someone you do not know very well. You would like to ask for another piece of chicken.
Could you give me one more piece of chicken?
(g) Your friend has a book that you want to read. Ask him/her.
Can you lend me your book for a night?

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 5
Imagine that you are a guest at the places mentioned below. Use can (informal), could (semi-formal) or may (formal) to ask for permission to do a different thing at each place. (One has been done for you.) At your grandparents home Can I use the phone, grandfather?
(a) At your teacher’s home.
_________________________________
(b) At your neighbor’s home.
_________________________________
(c) At the house of a favorite uncle.
_________________________________
(d) At the house of a close friend.
_________________________________
(e) At the house of someone you are visiting for the first time.
_________________________________
(f) At the house of a friend of your elder brother.
_________________________________
(g) At a distant relative’s home
_________________________________
Answer:
(a) Could I use your bicycle?
(b) Can I use your comb?
(c) Can I have your photograph?
(d) Can I ride your scooter?
(e) Could I use your dictionary?
(f) Could I use your pen?
(g) Could I / May I switch on the TV?

Activity – 6
Say whether the sentences below are used to ask for permission or to make a request or whether they are used in formal or informal situations.
(a) Mr. Mohanty, would you please tell all the teachers to come for a meeting in my office at 3 o’clock?
(b) Can you put this parcel on the table, please?
(c) May I ask you a question about this job, sir?
(d) Would you mind sitting on that chair?
(e) Could you pass the salt, please?
(f) Can my friend stay here too?
(g) May I wait in the corridor outside?
Answer:
(a) Formal request
(b) Informal request
(c) Formal request
(d) More formal request
(e) Formal request
(f) Informal permission
(g) Formal permission

CHSE Odisha Class 12 English Grammar Modal Verbs

SECTION – 3

Making an offer to help (using will, would, shall, can, could)
(a) Rina: I want to take this bag with me.
Chhabi: I will (can) carry it for you.
Rina: Oh, thanks.
(b) Tarak: 1 must leave now.
Puma: Shall (Can) I get a taxi for you?
Tarak: Yes, please.
(c) Host: Would you like some more chicken?
Guest: Yes, please. Thank you.
(d) Pinaki : (to his friend’s friend) Could I buy the tickets for you?
Friends friend: Thank you very much.

Will, shall, and can are used in informal English to offer help to someone. will and shall are commonly abbreviated to ‘il (ill, We’ll, etc.) Will is used only in statements (e.g., I’ll carry your bag) but shall and can are used in questions as well as statements (e.g., Shall I carry your bag ? Can I carry your bag ? or I shall carry your bag / I can carn your bag). Could and would are used in questions as well as statements to offer help, in more formal situations. (e.g., could j carry your bag? ¡ could carry your bag!
Would you like me to carry your bag? I would be happy to carry your bag, etc.).

Activity – 7
Make offers to suit the following situations.
(a) Your friend accidentally drops his pen on the floor.
_________________________________
(b) An old man wants you to make room for him to sit down.
_________________________________
(c) A patient is sweating profusely and the windows are closed.
_________________________________
(d) An old man is carrying a heavy suitcase and gasping for breath.
_________________________________
(e) Your principal wants to get some medicines from a pharmacy.
_________________________________
(f) A stranger wants to go to a particular place and you are on a motorbike.
_________________________________
(g) Your friend does not have enough money to buy a book he needs.
_________________________________
(h) Your mother is not able to cook as she is unwell.
_________________________________
(i) Your sister is not able to work out a sum.
_________________________________
(j) Your younger brother is trying to reach a book on the top shelf of a cupboard.
_________________________________
Answer:
(a) Shall I/Can I lift it from the floor?
(Or) I’ll lift it form the floor.
(b) Would/Could I give you a seat here?
(c) Could/Would I open the windows for you?
(d) Could I carry the suitcase for you?
(e) Would / Could I bring some medicines for you, sir?
(f) Could I give you a lift?
(g) Shall / Can I lend you some money?
(h) I’ll cook for you.
(Or) Shall / Can I cook for you?
(i) Shall/Can I work out the sum for you?
(j) I’ll (will) get the book for you.
(Or) Shall/Can I get the book for you?

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity-8
Study the offers below and say which ones are made in a formal situation in which each one could have been made.
(a) Shall I call the doctor for you?
_________________________________
(b) Would you like me to call the police?
_________________________________
(c) Shall I switch off the light?
_________________________________
(d) I can lend you two hundred rupees if you like.
_________________________________
(e) I’ll help you make the bed.
_________________________________
(f) Could I wait for you at the gate?
_________________________________
Answer:
(a) Shall I call the doctor for you?
Yes, I’m unwell, (formal)
(b) Would you like me to call the police?
Yes, I have to see the man stabbed.
(c) Shall I switch off the light?
Yes, I am awful tired now. (formal)
(d) I can lend you two hundred rupees if you like.
I’m badly in need of some money now. Oh, thanks.
(e) I’ll help you make the bed.
It’s very kind of you. I’m running a temperature now. (formal)
(f) Could I wait for you at the gate?
Yes, you may come and receive my other friends. (formal)

SECTION – 4

Making a suggestion (using shall, can, could)
(a) Pramod: It’s a lovely day. Shall we go for a walk?
Prashant: Yes, let’s do that.
(b) Nilima: Sisir is becoming more and more difficult to handle.
Manisha: We can talk to him if you like.
Nilima : No, I’ll manage without him.
(c) Girija: We need Sima’s room for the guest.
But she has gone home.
Gauri: We could go to her village tomorrow and collect the key.
In the sentences above, different ways of making suggestions have been shown.
The commonly used words are: Shall we /Can we /Could we (in questions), or You can /We can / We could….. (in statements), used together with if you like/want.
Suggestions can also be made by using let us (let’s), why don’t you/ we…. ? or how / what about…. ? Let’s and why don’t you/we…. ? are followed by the infinitive without to (e.g. Let’s stop here; why don’t you ask him ?, while How/What about….. ? are followed by an ‘-ing’ form (e.g., How about stopping here and eating lunch ?)

Activity – 9
Make suggestions to suit the following situations. (More than one answer is possible.)
(a) You think, your friend and you should go for a walk.
_________________________________
(b) You would like to have dinner at a restaurant with your neighbor.
_________________________________
(c) You feel like going to the park with your mother.
_________________________________
(d) You would like your father to take you to an uncle’s house.
_________________________________
(e) You have met somebody for the first time at a friend’s house. He is watching a film on television, but you would like to watch a cricket match, on a different channel.
_________________________________
(f) You feel like going to the theatre with some friends.
_________________________________
(g) It is 11.00 p.m. Your roommate in the hostel is reading a book, but you would like to sleep.
_________________________________
Answer:
(a) Let’s go for a walk.
Or, Can/Shall we go for a walk?
(b) Shall/Can we have dinner at a restaurant?
(c) Why don’t we got to the park now?
(d) Why don’t you take me to my uncle’s house?
(e) Could you change this channel? Let us see the cricket match in D.D. Sports.
(f) Let’s go to the theatre now.
Or, Why don’t we got to the theatre as we have some free moments now?
(g) Could you switch off the light? Let’s go to bed.

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 10
Your friends and you are putting up a cultural show in your college. Make suggestions about the arrangements for the show, using the hints below. Study the example below and write your sentences.
(i) the place where the show is to be put up
(ii) decorating the stage
(iii) fixing the lights
(iv) getting singers and musicians to perform
(v) setting up the sound system
(vi) the guests to be invited
(vii) the refreshments to be served
Answer:
Example: We can invite the Chief Minister to be the Chief Guest.
(i) Shall we select/choose the old auditorium for the show?
(ii) Why don’t we decorate the stage by ourselves?
(iii) We shall invite the electrician for fixing the lights.
(iv) Let’s invite Akshay Mohanty and party for the musical show.
(v) What about setting up the sound system?
(vi) Why don’t we invite the Chief Minister and the Minister for Mass Education to be the guests?
(vii) The volunteers shall serve refreshments for the guests.

Activity – 11
Which of the following offer and which are suggestions? Say whether they are formal or informal.
(a) I can pay for your ticket if you like.
(b) What shall I do in case I don’t find Ram at home?
(c) Would you like them to wait for you?
(d) We could leave it until later.
(e) I can lend you the book.
(f) Could we paint this wall for you?
Answer:
(a) offer informal
(b) offer informal
(c) offer formal
(d) suggestion informal
(e) offer informal
(f) offer informal

CHSE Odisha Class 12 English Grammar Modal Verbs

SECTION – 5

1. Expressing ability to do something (using can be able to)
Study the following dialogues.
(a) Interviewer: Can you type?
Candidate: Yes sir. I can also take dictation in shorthand.
Interviewer: Will you be able to talk to our foreign clients?
Candidate: Yes sir. I can speak German and Italian.
(b) Teacher: Who can solve this problem?
Student: I can.
‘Can’ the modal in the above conversation is used to mean ‘ability ’ in general. ‘Be + able to’ is also used to mean the same meaning ‘ability’ to do something. ‘Can’ is informal/usual and ‘be + able to’ is usually formal.

Activity – 12
Complete the sentences below using can or be able to. (In some of the sentences, it will not be possible to use can.)
(a) Ask Karim about your friend’s condition. He might — tell you something.
(b) Ravi was bom and educated in Hyderabad. He — speaks Telugu.
(c) My friend can’t understand my problem. She’s never — understand it.
(d) I can’t lend you money but I — get the book for you.
(e) Meera — read Tamil but she doesn’t have any Tamil books.
(f) I haven’t — buy any books lately.
(g) We — travel a lot but we can’t do it now.
(h) Meet your teacher tomorrow. He — explain the question to you.
Answer:
(a) Ask Karim about your friend’s condition. He might be able to tell you something.
(b) Ravi was born and educated in Hyderabad. He can speak Telugu.
(c) My friend can’t understand my problem. She has never been able to understand it.
(d) I can’t lend you money but I will be able to get the book for you.
(e) Meera can read Tamil but she doesn’t have any Tamil books.
(f) I haven’t been able to buy any books lately.
(g) We used to be able to travel a lot but we can’t do it now.
(h) Meet your teacher tomorrow. He will be able to explain the question to you.

Activity – 13
List five things that you can do.
1. _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
List five things that you can’t do.
1. _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
Answer:
List five things that you can do.
1. I can lift this heavy box.
2. I will be able to get the first division.
3. I can speak and write in three languages.
4. I can give the answer to that question.
5. I will be able to swim in the river.

List five things that you can’t do.
1. I can’t lift an elephant.
2. I won’t be able to swim in the river.
3. I can’t read Greek.
4. I won’t be able to run 5 km at a stretch.
5. I won’t be able to get a medal in swimming

Activity – 14
A new student has joined your class. As the Secretary of the College Union, you would like to know which activities your new classmate would be able to take part in. Frame at least five questions that you might want to ask him and provide the answers that might be given.
Q. Can you draw and paint?
A. Yes, I can / No, I can’t.
1. Q. _________________________________
A. _________________________________
2. Q. _________________________________
A. _________________________________
3. Q. _________________________________
A. _________________________________
4. Q. _________________________________
A. _________________________________
5. Q. _________________________________
A. _________________________________
Answer:
Question 1.
Will you be able to contact the guests?
Answer:
Yes, I can.

Question 2.
Can you speak Hindi fluently?
Answer:
Yes, I can.

Question 3.
Will you be able to do shopping?
Answer:
Yes, I can do the shopping.

CHSE Odisha Class 12 English Grammar Modal Verbs

Question 4.
Will you be able to take care of the guests?
Answer:
Yes, I can.

Question 5.
Will you be able to see the seat arrangements?
Answer:
Yes, I can.

2. General ability versus the ability to do something in a particular situation. Look at the following sentences.

  • Mohan could speak Assamese when he was a boy.
  • When I was in London I could visit the museum every day.
  • I had only a brief meeting with the Principal, but I was able to explain my difficulties to him.

In Sentence 1, could is used to refer to the general ability to do something that somebody possessed (in the past), while in Sentence 2, could indicate that the opportunity to do something was available. In Sentence 3, was able to indicate the ability, or the opportunity, to perform an action in a particular situation. Could is not used in such a context. Sometimes could is the past of ‘can’. We use ‘could’ to say that someone had the general ability to do something. But ‘was/were able to’ is used to indicate the past ‘ability + performance’ (result) which means ‘managed to do something in one particular situation.

Activity – 15
Use could or was/were able to in the sentences below. Use a negative if necessary. More than one answer is possible.
(a) The author of the book learned to write very early in life. He — write short stories when he was at school.
(b) My scooter didn’t start. Luckily I — borrowed a bicycle and got there in time for the interview.
(c) It was dark. We — see a thing.
(d) The children were warned that a fire had started, and they — move their belongings in time.
(e) I — meet my friend as the bus had left.
(f) The people in the neighboring village were having a party last night and you — have joined them.
(g) My friend ran after the bus and — get on.
(h) The freedom fighters had to live in the jungles for months. They — survive without food for several days.
Answer:
(a) The author of this book learned to write very early in life. He was able to write short stories when he was at school.
(b) My scooter didn’t start. Luckily I was able to borrow a bicycle and got there in time for the interview.
(c) It was dark. We couldn’t see a thing.
(d) The children were warned that a fire had started, and they were able to move their belongings in time.
(e) I could not meet my friend as the bus had left.
(f) The people in the neighboring village were having a party last night and you could have joined them.
(g) My friend ran after the bus and was able to get on.
(h) The freedom fighters had to live in the jungles for months. They were able to survive without food for several days.

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 16
Saurabh is 40. Sometimes he feels that he has wasted his life. Read about Saurabh and replace some of the words with could have …, as shown in the example below.
Example: When Saurabh was 15 he had a chance to go abroad, but he decided not to go.
Ans. When Saurabh was 15 he could have gone abroad.
(a) Saurabh got a scholarship to study in a reputed public school. But he didn’t go.
_________________________________
(b) He was a good speaker, but he decided not to participate in debates.
_________________________________
(c) He had the opportunity to learn music under a famous teacher, but he decided against it.
_________________________________
(d) He was intelligent enough to come out first in the examination, but he did not try.
_________________________________
(e) He had the opportunity to start a business, but he did not want to.
_________________________________
(f) Everyone thought he had the creativity to write novels, but he never tried.
_________________________________
Answer:
(a) Saurabh could have studied in a reputed public school when he was young.
(b) He could have participated in debates when he was in school.
(c) He could have learned music under a famous teacher when he was 20 years old.
(d) He could have come out first in the examination if he had studied sincerely.
(e) He could have started a business when he was 30 years old.
(f) When he was 25 years old, he could have written novels.

Activity – 17
Use can, can’t, could, couldn’t was/were able to, where required. (Alternative answers are possible.)
(a) She — even speak properly when she was a girl, but now she’s a famous singer.
(b) Did you see anybody in the park? No, I — find anybody.
(c) An eagle — fly for hours.
(d) When my sister was just 7, she — speak Hindi much more fluently than she — now.
(e) On the fifth day the rescuers saw the children and — reach them without too much trouble.
(f) After weeks of training, I — climb some of the coconut trees.
Answer:
(a) She could not even speak properly when she was a girl, but now she’s a famous singer.
(b) Did you see anybody in the park? No, I could not find anybody.
(c) An eagle can fly for hours.
(d) When my sister was just 7, she was able to speak Hindi much more fluently than she can now.
(e) On the fifth day the rescuers saw the children and were able to reach them without too much trouble.
(f) After weeks of training, I was able to climb some of the coconut trees.

CHSE Odisha Class 12 English Grammar Modal Verbs

SECTION – 6

Indicating possibility (using may, can)
(a) This house is too small. We may sell it and buy a bigger one.
(b) That box is too heavy for you. You may drop it.
(c) Camels can survive for weeks in the desert, without water.
(d) Smoking can cause cancer.
‘May’ is used to express a specific possibility in the present or future. It can refer to a single occasion. But ‘can ’ is used to express a general theoretical possibility.

Activity – 18
Use can or may, as required, in the following sentences.
(a) The government — hike the bus fares next month.
(b) The villagers — convert this building into a hospital if everyone agrees.
(c) This medicine — cure any disease.
(d) My friends — put on a play here again next year.
(e) We’re going to do something different this year. We — decide to hire a professional drama group.
(f) Your boss is impressed with your work. You — get a promotion soon.
(g) The presence of lead particles in the air — cause brain damage in children.
(h) The machine has broken down and — takes some time to repair.
Answer:
(a) The government may hike the bus fares next month.
(b) The villagers may convert this building into a hospital if everyone agrees.
(c) This medicine can cure any disease.
(d) My friends may put on a play here again next year.
(e) We’re going to do something different this year. We may decide to hire a professional drama group.
(f) Your boss is impressed with your work. You may get a promotion soon.
(g) The presence of lead particles in the air can cause brain damage in children.
(h) The machine has broken down and may take some time to repair.

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 19
A group of engineers has come up with a number of unusual products, for use at home. These products are :
1. A battery-operated fan.
2. A portable water heater.
3. Writing paper that glows in the dark.
4. Shirts made of edible material.
5. Shoes with a built-in alarm clock.
6. A bicycle that can float.
Think of some situations in which these products could prove to be very useful and frame sentences suggesting (to prospective customers) some possible uses for the products. One example is given.
Example
1. You can use the battery-operated fan to cool yourself when you are sitting in your garden.
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
6. _________________________________
Answer:
2. You can use the portable water heater when you go outside during chilly winter.
3. You can use writing paper that glows in the dark when there is no light.
4. You can use shirts made of edible material if you need.
5. You can use shoes with a built-in alarm clock to make use of the time properly.
6. You can use a bicycle that can float when you want to cross a flooded river.

SECTION – 7

Indicating present or future possibility (using may, might or could)
Look at the following sentences.
(a) Where’s Madhuri? She may/might / could be in the garden.
(b) There’s someone at the gate. It may / might / could be the postman.
(c) They’re not cooking dinner. They may / might / could be planning to go out tonight.
May, might, and could are used here to talk about present or future possibilities. Might is normally a little less sure than may, and could is less sure than may or might. Note that we can’t use can in the above examples. Can you say why? (Hint: Refer to the difference between can and may.)
‘May, might could’ all three models are used in sentences for possibility. There is still a little difference between them. May is a bit stronger than might or could. ‘Might’ is a little less sure than ‘may’ and ‘could’ is less sure than ‘may or might’.

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 20
Rewrite the following sentences using ‘might’ or ‘could’.
(a) It is possible that she is cheating you.
_________________________________
(b) It is possible that they’ll come in the evening.
_________________________________
(c) It is possible that he is planning to sell the car.
_________________________________
(d) It is possible that she is telling the truth.
_________________________________
(e) This statement possibly contradicts his earlier statement.
_________________________________
(f) It is possible that one of them is a spy.
_________________________________
Answer:
(a) She might cheat me.
(b) They could come in the evening.
(c) He might sell the car.
(d) She might tell the truth.
(e) He might contradict his earlier statement.
(f) He might be a spy.

Activity – 21
Use may, might or could, together with the appropriate forms of the verbs in brackets.
1. Who is the girl Madhu is talking to? I’m not sure. She — (be) her sister.
2. Why are the boys shouting? I don’t know. They — (play).
3. Where is Manisha? I have no idea. She — (study) in the library.
4. Who is that man with Vijay? I’m not sure. It — (be) his uncle.
5. Shall I tell the Minister about you? You’d better not. He — (think) I want to ask him for a favor.
Answer:
1. Who is the girl Madhu is talking to? I’m not sure. She might be her sister.
2. Why are the boys shouting? I don’t know. The might he plane.
3. Where is Manisha? I have no idea. She might be studying in the library.
4. Who is that man with Vijay? I’m not sure. It might be his uncle.
5. Shall I tell the Minister about you? You’d better not. He may think I want to ask him for a favor.

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 22
You are going for a walk, and you suddenly see a mysterious flying object, high up in the sky. Make five guesses about what the object could be.
1. _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
Answers
1. It might be a skylark.
2. It may be a balloon.
3. It might be a parachute.
4. It could be the wing of a damaged airplane.
5. It might be a soldier falling from an aircraft.

SECTION – 8

Referring to possibility in the past (using may, might, or could)
Look at the examples below.
(a) She was not in the hostel yesterday. She might / could have gone home.
(b) A: Do you think he saw you?
B: No, he was too far away. He couldn’t have seen me.
(c) You were stupid to throw stones at the dog. It might have attacked you.
We use may/might/could, together with some verbs in the present perfect form, to talk about the possibility in the past.

Activity – 23
Complete the sentences below, expressing possibility in the past.
(a) The other teams weren’t good, so our team — (win). „
(b) You know where the library is, don’t you? You — (pass) it on your way here.
(c) Why didn’t your friend answer the phone? He — (not/ hear) it ringing.
(d) The light’s on. They — (forget) to switch it off.
(e) I did not hear the child’s voice, and I thought he — (fall asleep).
(f) Our teacher is not at home. He — (go) to meet a friend.
(g) How did you get that stain on your saree? I’m not sure. The baby — (drop) food on it.
(h) A: I can’t find my umbrella. Have you seen it?
B: No. You — (leave) in the restaurant.
Answer:
(a) The other teams weren’t good, so our team might have won.
(b) You know where the library is, don’t you? You might have passed it on your way here.
(c) Why didn’t your friend answer the phone? He could/might not have heard it ringing.
(d) The light’s on. They might have forgotten to switch it off.
(e) I did not hear the child’s voice, and I thought he could/might have fallen asleep.
(f) Our teacher is not at home. He could have gone to meet a friend.
(g) How did you get that stain on your saree? I’m not sure. The baby might/could have dropped food on it.
(h) A: I can’t find my umbrella. Have you seen it?
B: No. You might/could have left in the restaurant.

CHSE Odisha Class 12 English Grammar Modal Verbs

SECTION – 9

Making a deduction (using must have/can’t have)
Look at the following example.
The old man has not had anything to eat for the last two days. He must be starving.
The speaker is deducing something (starving). She / He takes the help of logical analysis or the basis of evidence that is available. She / He is very much sure that what he/she says is correct. So in the above example, ‘must’ is used for deduction. Can’t: In negative sentences for logical analysis/conclusion ‘can’t’ is used. The speaker is very sure about some negative conclusion that she/he has reached. The use of ‘must have ’ and ‘can’t have ’ shows that the speaker has made a deduction about something that happened in the past.
Example
1. Ramesh has done very well in the examination. He must have worked really hard.
2. The library was closed all day yesterday. You can’t have been there yesterday.

Activity – 24
Answer the questions in Column A, using must or can’t, and choosing a suitable reason from Column B. (One answer has been provided.)
Modal Verbs
Example: (She can’t be ill. She has gone swimming.)
Answer:
2. They must be sleeping. Their bedroom lights are off.
3. He must be happy. He has just got a job.
4. He can’t be a Bengali. He speaks Telugu.
5. The shopkeeper can’t be honest. He charged more than the price.
6. These boys must be naughty. They play tricks on everyone.
7. She can’t be married. She is too young.

Activity – 25
Consider the situations below and use the words in brackets to frame sentences with ‘/must have’ and ‘can’t have
(a) Satish got the first division in the exam. (He / works hard)
_________________________________
(b) Someone saw Sudha in the college library at 8.00 a.m. yesterday. (She / stays / in bed / all morning)
_________________________________
(c) The traffic lights were red and the car stopped, (the driver/see / the red light)
_________________________________
(d) He knows a lot about teaching. ( He / a teacher when he was young)
_________________________________
(e) Girish knew exactly what to do. (He / learns / the skills / very carefully)
_________________________________
(f) My friend knew everything about our plan. (He / listens / to our conversation)
_________________________________
(g) Janaki walked past me without speaking. (She / see / me)
_________________________________
(h) There are five stitches on her head. (She / have / an accident)
_________________________________
Answer:
(a) He must have worked hard.
(b) She can’t have stayed in bed all morning.
(c) The driver must have seen the red light.
(d) He must have been a teacher when he was young.
(e) He must have learnt the skills very carefully.
(f) He must have listened to our conversation.
(g) She can’t have seen me.
(h) She must have had an accident.

CHSE Odisha Class 12 English Grammar Modal Verbs

SECTION – 10

Offering advice (using should, ought to, had better, be supposed to)
(a) If your toothache is not getting better, you should see a dentist.
(b) They really looked after you well. You ought to write a letter of thanks.
(c) Your roommates are complaining. You had better turn the music down.
Should and ought to are used to ask for as well as give advice. Ought to is preferred when the advice is given by someone in authority.
‘Had better’ (generally abbreviated to better) indicates a strong recommendation, made for a particular situation.
Should have … and ought to have … are used to show that someone did not do something (in the past) which was advisable.
Look at the examples below.
1. I should have bought that book yesterday, but I didn’t have the money.
2. Haven’t you been to see your doctor? You ought to have seen him yesterday

Activity – 26
Complete the sentences in the “Advice” column, using ‘should’ or ‘ought to’.
Modal Verbs 1
Answer:
i. I should have bought a new pen yesterday, but I didn’t have money.
ii. I should have looked for other books, but I didn’t have free moments.
iii. I should have given some money to the poor, but I didn’t get the key of my drawer.
iv. They ought to have asked their teacher as they did not solve it themselves.
v. I should have gone and collected the glasses from the shop.
vi. I should have taken some days off.

Activity – 27
Produce sentences indicating what the speaker should (not) / ought to have done in given situations.
(a) I’m in trouble because I didn’t wish my boss “Good morning”!
(b) The pen he used to write the examination was not good enough.
(c) Nirmal did not meet Seeta until it was too late.
(d) I’m sorry that he didn’t take your advice.
(e) Smita had to go to the bank opposite the college, but she hired a taxi.
(f) I sent a messenger three days ago, but he has not arrived yet.
(g) She left her books in the canteen. She didn’t find them when she went back.
Answer:
(a) I’m in trouble because I didn’t wish my boss “Good morning”!
I should have wished my boss “Good morning.”
(b) The pen he used to write the examination was not good enough.
He ought to have used a good pen to write the examination.
(c) Nirmal did not meet Seeta until it was too late.
Nirmal should have met Seeta in time.
(d) I’m sorry that he didn’t take your advice. He ought to have taken your advice.
(e) Smita had to go to the bank opposite the college, but she hired a taxi. Smita should not have hired a taxi.
(I) I sent a messenger three days ago, but he has not arrived yet. He should have arrived by this time.
(g) She left her books in the canteen. She didn’t find them when she went back. She should have been very careful.

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 28
What advice would you offer someone in a difficult or dangerous situation, such as an Are, flood, cyclone, a roof falling in, or a wild animal running loose in the city?
Think of at least 7 such situations and form sentences to offer advice, using either had better or had better not.
Example (a fire) You’d better phone the fire brigade.
1. (a burglary) You’d better not _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
6. _________________________________
7. _________________________________
Answer:
1. You’d better not fight against them.
2. (a flood) You’d better take shelter on a hill.
3. (cyclone) You’d better leave that old house.
4. (a wild animal running loose) You’d better not open the door.
5. You’d better telephone the police about the wild animal.
6. (a roof falling in) You’d better leave the house with your family members.
7. (afire) You’d better make lose your cattle.

SECTION – 11

Expressing obligation or necessity (using must have to / had to, got to)
(a) I’ve got terrible pain in my back. I must go and see the doctor.
(b) I have got an appointment. I have to go and see the doctor at 9.00 tomorrow morning.
(c) Our teacher had given us fifty sums to work out. So I had to work late yesterday.
(d) My friend must be waiting for me. I’ve got to hurry.
‘Must’ is used for an internal obligation or when authority comes from the speaker. ‘Have to ’ is normally used for outside direction/obligation or when the authority comes from someone other than the speaker.
We use ‘had to’ when talking about past obligations or necessity. ‘Have got’ is sometimes used instead or ‘have to’ to talk about obligation or necessity but it is more informal.

Activity – 29
Complete the sentences using must or some form of have to. (In some cases, more than one answer is possible.)
(a) I really — find something cheaper. This is too expensive.
(b) A. — you — get a visa to go to Nepal?
B. No, you don’t but you — get one for Pakistan.
(c) You — fill in this form first. You can’t do anything until it is completed.
(d) Sudhir: I’ll meet you at the airport at 9 o’clock then.
Kamal: What! We — check in by 7.30.
(e) Jiban: This medicine tastes horrible. I’m going to take it only once a day.
Jiten: Now, don’t be silly. The doctor says you — take it 3 times a day.
Jiban: All right, I’ll take the medicine after meals.
Jiten: No, you — take the medicine before meals.
(f) You — remember to brush your teeth. If you don’t, you’ll have to go to the dentist.
(g) I — stay in bed yesterday because I wasn’t very well.
(h) I couldn’t go to the party last night because I — look after my youngest sister, who was ill.
Answer:
(a) I really must find something cheaper. This is too expensive.
(b) A: Have you got to get a visa to go to Nepal?
B: No, you don’t, but you have to get one for Pakistan.
(c) You have to fill in this form first. You can’t do anything until it is completed.
(d) Sudhir: I’ll meet you at the airport at 9 o’clock then.
Kamal: What! We have to check in by 7.30.
(e) Jiban: I’ve never tasted such horrible medicine. I’m going to take it only once a day.
Jiten: Now, don’t be silly. The doctor says you have to take it 3 times a day.
Jiban: All right, I’ll take the medicine after meals.
Jiten: No, you have to take the medicine before meals.
(f) You must remember to brush your teeth. If you don’t, you’ll have to go to the dentist.
(g) I had to stay in bed yesterday because I wasn’t very well.
(h) I couldn’t go to the party last night because I had to look after my youngest sister.

CHSE Odisha Class 12 English Grammar Modal Verbs

SECTION – 12

Expressing prohibition (using mustn’t, needn’t, don’t have to)
(a) You mustn’t jump over that wall. You’ll break your legs.
(b) You mustn’t drive that car. The brakes don’t work.
(c) Tomorrow is a holiday. You needn’t get up early.
(d) They needn’t buy the book. They can get it in the library.
(e) We don’t have to / need to go to a hotel. My mother can cook for us. ‘Mustn’t’ is usually used for prohibition or it is forbidden to do something.
But needn ’t is used for absence or obligation/necessity. Doesn ’t/ don’t have to, doesn’t / don’t need to’ are used when it is not necessary to do something.

Activity – 30
Choose the correct modal.
(a) They’ve been late for class three times this week. They mustn ’t/ needn’t be late again.
(b He mustn’t / needn’t tell our teacher about the meeting. Sudha has already told him.
(c) You mustn’t / don’t have to make any noise going into the house.
It’s very late and everybody is asleep.
(d) I mustn’t / don’t have to hurry. I’ve got plenty of time.
(e) You mustn’t / needn’t open the door before the bus stops. You could fall out.
(f) You don’t have to / mustn’t wash that shirt. It isn’t dirty.
(g) Sima needn’t/ mustn’t finish her essay today. She’s got to hand it in by next Friday.
(h) You needn’t / mustn’t wear your best clothes. You can wear what you like.
Answer:
(a) The mustn’t be late again.
(b) He needn’t tell our teacher about the meeting. Sudha has already told him.
(c) You mustn’t make any noise going into the house. It’s very late and everybody is asleep.
(d) I don’t have to hurry. I’ve got plenty of time.
(e) You mustn’t open the door before the bus stops. You could fall out.
(f) You don’t have to wash that shirt. It isn’t dirty.
(g) Sima needn’t finish her essay today.
She’s got to hand it in by next Friday.
(h) You needn’t wear your best clothes. You can wear what you like.

CHSE Odisha Class 12 English Grammar Modal Verbs

Activity – 31
List five things which a visitor to a zoo must not do.
1. (A) Visitors to a zoo mustn’t…..
2. (S)he…
3. _________________________________
4. _________________________________
5. _________________________________
6. _________________________________
7. _________________________________
8. _________________________________
Answer:
1. He mustn’t tease the wild animals.
2. He mustn ’t row boats himself in the lake without a guide.
3. He mustn’t throw stones at the birds.
4. He mustn’t give food to any animals there.
5. He mustn’t put his fingers inside a cage.
6. He mustn’t disfigure the walls.
7. He mustn’t go near the crocodiles.
8. He mustn’t terrify the small animals.

Activity – 32
You went on a picnic to some far-away place with a group of friends. As you did not know what things would be available there, you made elaborate preparations. Now, after your return, you are narrating your experiences to another group of friends, who would also like to go on a picnic to the same spot.
Tell your friends which of the arrangements made by you were necessary, and which of them were either unnecessary or proved to be unnecessary. Use had to, needed to, didn’t need to, didn’t have to, and need not have to talk about the arrangements which were either necessary or unnecessary.
Here are some of the arrangements that were made.
1. hiring a bus
2. buying fire-wood for cooking
3. carrying water for drinking and cooking
4. carrying food materials: rice daal, vegetables, meat
5. finding a place to cook in
6. finding a place to serve the food
7. going to places of interest nearby
8. thinking of ways to keep yourself entertained
9. washing utensils after the meal
10. making arrangements for the return journey.
Answer:
1. We had to hire a bus for the picnic.
2. We needn’t have to / didn’t have to buy firewood for cooking as it as plentily available there.
3. We didn’t have to carry water for drinking and cooking.
4. We had to carry food materials: rice, daal, vegetables, and meat.
5. We needed to / had to find a place to cook in.
6. We needed to find a place to serve the food.
7. We needn’t have to go to places of interest nearby.
8. We had to think of ways to keep ourselves entertained.
9. We needed to wash the utensils after the meal.
10. We needn’t have to make arrangements for the return journey as we had already arranged before.

CHSE Odisha Class 12 English Grammar Modal Verbs

Multiple-Choice Questions (MCQs) with Answers

Question 1.
Rain has stopped; you ___________ carry an umbrella with you.
(A) mustn’t
(B) ought not
(C) needn’t
(D) won’t
Answer:
(C) needn’t

Question 2.
A judge ___________ be upright.
(A) shall
(B) will
(C) must
(D) could
Answer:
(C) must

Question 3.
He ___________be at least thirty years old.
(A) can
(B) should
(C) will
(D) must
Answer:
(D) must

Question 4.
Shut the window, ___________?
(A) will you
(B) would you
(C) could you
(D) none of these
Answer:
(B) would you

CHSE Odisha Class 12 English Grammar Modal Verbs

Question 5.
___________ you open the door, please?
(A) Shall
(B) Will
(C) Can
(D) May
Answer:
(B) Will

Question 6.
You do ___________as you are told.
(A) will
(B) can
(C) must
(D) shall
Answer:
(D) shall

Question 7.
I ___________ try if you wish.
(A) shall
(B) will
(C) should
(D) would
Answer:
(B) will

Question 8.
_____ you rather have tea or coffee?
(A) Should
(B) Will
(C) Would
(D) Can
Answer:
(C) Would

Question 9.
He _____ prefers to have coffee.
(A) will
(B) can
(C) would
(D) none of these
Answer:
(C) would

Question 10.
We _____ disobey our parents.
(A) needn’t
(B) mustn’t
(C) can’t
(D) wouldn’t
Answer:
(B) mustn’t

Question 11.
I ____ do it now.
(A) could
(B) should
(C) can
(D) might
Answer:
(C) can

CHSE Odisha Class 12 English Grammar Modal Verbs

Question 12.
They worked hard and they succeed.
(A) may
(B) could
(C) might
(D) should
Answer:
(C) might

Question 13.
Let’s go for cricket, _____ we?
(A) should
(B) could
(C) would
(D) shall
Answer:
(D) shall

Question 14.
It _____ rain tonight.
(A) can
(B) could
(C) should
(D) may
Answer:
(D) may

Question 15.
I ___________ do it long ago.
(A) could
(B) might
(C) should
(D) would
Answer:
(A) could

Question l6.
He is so weak that he _____ walks.
(A) will not
(B) would not
(C) cannot
(D) may not
Answer:
(C) cannot

Question 17.
You ____ go now.
(A) can
(B) could
(C) ought
(D) none of these
Answer:
(A) can

Question 18.
_____ I use your telephone directory?
(A) May
(B) Can
(C) Shall
(D) both (A) and (B)
Answer:
(D) both (A) and (B)

CHSE Odisha Class 12 English Grammar Modal Verbs

Question 19.
If you do this, you _____ be punished.
(A) will
(B) would
(C) shall
(D) can
Answer:
(A) will

Question 20.
I ____ do as you did.
(A) could
(B) should
(C) can
(D) would
Answer:
(D) would

Question 21.
Take heed less you ____ fall.
(A) would
(B) should
(C) might
(D) could
Answer:
(B) should

Question 22.
I _____ have my work here.
(A) must
(B) may
(C) can
(D) none of these
Answer:
(A) must

Question 23.
You _____ if the Court had instructed you to do so.
(A) shall have attended
(B) would have to attend
(C) would have had to attend
(D) would attend
Answer:
(C) would have had to attend

Question 24.
Tell my mother that she _____ telephone me at work for I will be home by seven o’clock this evening.
(A) needs not to
(B) need not to
(C) has no need
(D) need not
Answer:
(D) need not

Question 25.
The fire spread through the building quickly but everybody ___________.
(A) was able to escape
(B) managed to escape
(C) could escape
(D) both (A) and (B)
Answer:
(D) both (A) and (B)

Question 26.
The phone is ringing. It ___________be Tim.
(A) might
(B) can
(C) could
(D) both (A) and (C)
Answer:
(D) both (A) and (C)

Question 27.
Why did you stay at a hotel when you went to New York? You _____ with Barbara.
(A) can stay
(B) could stay
(C) could have stayed
(D) none of these
Answer:
(C) could have stayed

CHSE Odisha Class 12 English Grammar Modal Verbs

Question 28.
I’ve lost one of my gloves. I ___________ it somewhere.
(A) must drop
(B) must have dropped
(C) must be dropping
(D) must have been dropping
Answer:
(B) must have dropped

Question 29.
Take an umbrella with you when you go out, It _____ rain later.
(A) may
(B) might
(C) can
(D) could
Answer:
(A) may

Question 30.
What was wrong with you? Why ___________ go to the hospital?
(A) had you to
(B) did you have to
(C) must you
(D) none of these
Answer:
(B) did you have to

Question 31.
There’s plenty of time. You ___________ hurry.
(A) don’t have to
(B) mustn’t
(C) needn’t
(D) none of these
Answer:
(A) don’t have to

Question 32.
It was a great party last night. You _____ come. Why didn’t you?
(A) must have
(B) should have
(C) ought to have
(D) had to
Answer:
(B) should have

Question 33.
Jane ______ a car.
(A) suggested that I buy
(B) suggested that I should buy
(C) suggested me to buy
(D) none of these
Answer:
(A) suggested that I buy

Question 34.
I think all drivers _____ seat belts.
(A) should wear
(B) had better wear
(C) had better to wear
(D) none of these
Answer:
(A) should wear

CHSE Odisha Class 12 English Grammar Modal Verbs

Question 35.
It’s late. It’s time ___________ home.
(A) we go
(B) we must go
(C) we should go
(D) we went
Answer:
(D) we went

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 2 The Present Perfect

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 2 The Present Perfect Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 2 The Present Perfect

SECTION- 1:
Examine the use of the Present Perfect in the following sentences.
(a) A: Where’s your T.V. set? I don’t see it.
B: I have sold it.
(b) A: Why are you looking so happy?
B: I have just got a job.
In the above examples, the speaker ‘B’ talks about some events beginning in the past and lasting up to the present moment (or still continuing). Though the event started in the past, it is connected to the present moment of speaking. In this sense, we used the Present Perfect Tense.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 2 The Present Perfect

Activity — 9
Complete the sentences marked B. Use the verb in brackets, together with ‘just/already/yet’.
A: What does your wife think of your plan?
B : I __________(not tell) her yet.
A: Would you like something to eat?
B : No, thanks I __________(just/eat).
A: Is your brother here yet?
B : Yes, he __________(just/arrive).
A: What’s on TV today?
B: I don’t know. I __________(not see) the programme yet.
A: Do you know where Bidhu lives?
B : Yes, he __________(just/move) to Satyanagar.
A: Are your friends coming to the circus with us?
B : No, they __________(already/see) it.
A: When is Prakash leaving?
B : He __________(already/leave).
Answer:
1. A: What does your wife think of your plan?
B: I have not told her yet.
A: Would you like something to eat?
B: No, thanks I have just eaten.
A: Is your brother here yet?
B: Yes, he has just arrived.
A: What’s on TV today?
B: I don’t know. I have not seen the program yet.
A: Do you know where Bidhu lives?
B: Yes, he has just moved to Satyanagar.
A: Are your friends coming to the circus with us?
B: No, they have already seen it.
A: When is Prakash leaving?
B: He has already left.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 2 The Present Perfect

Activity – 10
Study the situations suggested below and makeup sentences with “yet”, “already” or “just”.
1. You are going to Koraput next Sunday. You phone your travel agent to buy a ticket for you.
Later your father says. ‘Shall I get the ticket for you ?”
You: No, (buy) ___________________________________.
2. Alok goes to the Post Office but returns after a while. His friend asks you if he is still at the Post Office.
You: No, (come back) ___________________________________.
3. You know that one of your classmates is looking for a house. When you meet him, you want to know if he has been successful.
You: ___________________________________.
4. You visit a friend’s house after lunch. He asks if you would like something to eat.
You: ___________________________________.
5. You are doing your homework. Your brother thinks that you have finished and turns the light off. What would you tell him?
You: ___________________________________.
6. Amar goes out. Ten minutes later his friend comes and asks you if he can meet Amar.
You: ___________________________________.
Answer:
1. No, I have already bought it from a travel agent.
2. No, he has already come back.
3. Have you got a house yet?
4. Have you had your lunch yet?
5. I have not finished my homework yet.
6. Amar has iust gone out

Activity – 11
Below is a list of things that your parents have asked you to do today. You have checked the things you’ve done so far. Talk about the things you’ve already done and the things you haven’t done yet. (Two have been done for you as examples.)
1. do the washing up
2. do your homework ✓
3. wash the scooter
4. write to the brother
5. read today’s newspapers ✓
6. defrost the fridge
7. buy some fruits ✓
8. watch the news on TV
9. clean the windows ✓
10. water the plants
11. empty the dustbins ✓
12. phone uncle
Answer:
1. I haven’t done the washing up yet.
2. I have already done my homework.
3. I have not washed the scooter yet.
4. I have not written to my brother yet.
5. I have already read today’s newspaper.
6. I have not de-frosted the fridge yet.
7. I have already bought some fruit.
8. I have not watched the news on TV.
9. I have already cleaned the windows.
10. I haven’t watered the plants yet.
11. I have not emptied the dustbin yet.
12. I have not phoned my uncle yet.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 2 The Present Perfect

Activity – 12
Anil, Anima, Mohan and Anand are talking about the places they have visited. Fill in the spaces using the information in the chart below.

Kolkata Koraput Puri Sambalpur Shillong
Anil Yes No No Yes No
Anima Yes No Yes Yes No
Mohan No No Yes No No
Anand Yes No Yes Yes No

1. Anil __________been to Kolkata, but Mohan ___________.
2. Three people __________ been to Puri.
3. Only one person __________been to Sambalpur.
4. Mohan is the only one who __________ visited only one place.
5. Nobody __________ been to Shillong.
6. Two people __________ been to three places.
7. Anima and Mohan __________ both been to Puri, but neither __________ been to Koraput.
Answer:
1. Anil has been to Calcutta, but Mohan hasn ’t.
2. Three people have been to Puri.
3. Only one person hasn’t been to Sambalpur.
4. Mohan is the only one who has visited only one place.
5. Nobody has been to Shillong.
6. Two people have been to three places.
7. Anima and Mohan have both been to Puri, but neither haven’t been to Koraput.

Note:
Look at the difference between ‘have /has been ’ and ‘have/has gone ‘Has /have been’ means went and returned. But ‘has gone/have gone means went and not returned. The Present Perfect form of ‘go’ (has/have gone) is not used when the subject of the sentence is 7, we or you.’ The Present Perfect is used to refer to some happening in the past, for which the time of action is not given.

SECTION – 2
Look at the sentences below.
1. Hari didn’t have a beard six months ago. He has a beard now. He has grown a beard.
2. Malati was very shy. She is smart now. She has become smart.
3. She was a little baby when I last saw her. She is a young girl now. She has grown up.
When a change has taken place between now and sometime before now, we use the Present Perfect Tense.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 2 The Present Perfect

Activity – 13
Study the situations below and make up appropriate sentences using the verbs suggested.
1. Yesterday my sister bought a pen. She can’t find it now. (lose)
______________________________________________.
2. The children were playing here some time ago. Now they are not seen, (leave)
______________________________________________.
3. My friend weighed 50 kilograms. Now he weighs 70. (gain weight)
______________________________________________.
4. The man met with an accident. Now he is not able to speak, (loses voice)
______________________________________________.
5. It was raining in the morning. Now the sky is clear. (stop)
______________________________________________.
6. The tiger attacked the man. He is dead now. (kill)
______________________________________________.
7. He had some paper with him. Now he does not have any to write on. (run out)
______________________________________________.
8. My teacher got a job in a bank. He is not coming to school anymore, (resign)
______________________________________________.
Answer:
1. She has lost it somewhere.
2. They have already left.
3. He has gained weight.
4. He has lost voice in the accident.
5. The rain has already stopped.
6. The tiger has already killed the man.
7. He has already run out of paper.
8. He has already resigned from school.

SECTION – 3
Present Perfect is often used with the following time expressions.

lately until now ever for five years
not yet never always over the last eight years
recently just so far in the past Iwo years
in recent years already since 1990

Do remember that the expressions like “last year, ago, yesterday” etc. cannot be used in the Present Perfect.

Activity – 14
Rewrite the following sentences putting the words in brackets in the right place. The first one has been done for you.
1. My teacher has wanted to be a writer. (never)
Ans. My teacher has never wanted to be a writer.
2. I’ve found him helpful, (always)
______________________________________________.
3. People have misunderstood him. (often)
______________________________________________.
4. I’ve had lunch. (just)
______________________________________________.
5. Has he been to Puri? (ever)
______________________________________________.
6. Don’t panic. The police have arrested the culprit, (already)
______________________________________________.
Answer:
2. I’ve always found him helpful.
3. People have often misunderstood him.
4. I’ve Just had lunch.
5. Has he ever been to Puri?
6. Don’t panic. The police have already arrested the culprit.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 2 The Present Perfect

Activity – 15
Imagine that you suddenly run into an old friend whom you have not met for the last five years. But he has changed so much that you can hardly recognize him. Describe the changes that have taken place in your friend.

Unit-2

a) _______________________________
b) _______________________________
c) _______________________________
d) _______________________________
e) _______________________________
Answer:
1. He has grown into a young man.
2. He has become strong and healthy.
3. He has grown fair and tall.
4. He has made himself smart and confident.
5. He has grown a thick beard.

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BSE Odisha 6th Class English Solutions Follow-Up Lesson 3 My Story is Said

Odisha State Board BSE Odisha 6th Class English Solutions Follow-Up Lesson 3 My Story is Said Textbook Exercise Questions and Answers.

BSE Odisha Class 6 English Solutions Follow-Up Lesson 3 My Story is Said

BSE Odisha 6th Class English Follow-Up Lesson 3 My Story is Said Text Book Questions and Answers

Session 1 (ସୋପାନ- ୧):
I. Pre-Reading (ପଢ଼ିବା ପୂର୍ବରୁ):

→ Socialisation (ସାମାଜିକୀକରଣ):
→ You can think of a pre-reading activity by linking this with the main lesson or from the picture.
(ତୁମେ ଏକ ପଢ଼ିବା ପୂର୍ବବର୍ତ୍ତୀ କାର୍ଯ୍ୟ ବିଷୟରେ ଚିନ୍ତା କରିପାର – ହୁଏତ ଏହାକୁ ମୁଖ୍ୟ ବିଷୟ ସହ ସଂଯୁକ୍ତ କରି କିମ୍ବା ଛବିରୁ ।)

II. While-Reading (ପଢ଼ିବା ସମୟରେ):

  • Follow the steps of the main lesson.
    (ମୁଖ୍ୟ ପାଠର ସୋପାନଗୁଡ଼ିକୁ ଅନୁସରଣ କର ।)
  • Read the following chain poem translated from Odia. This poem is generally sung when a story ends.
    (ଓଡ଼ିଆରୁ ଅନୁବାଦ ହୋଇଥିବା ନିମ୍ନଲିଖ୍ ଶିକୁଳି କବିତାଟିକୁ ପଢ଼ । ଏହି କବିତାଟି ସାଧାରଣତଃ ବୋଲାଯାଏ ଯେତେବେଳେ ଗୋଟିଏ ଗପ ଶେଷ ହୋଇଯାଏ ।)

BSE Odisha 6th Class English Solutions Follow-Up Lesson 3 My Story is Said

TEXT (ବିଷୟବସ୍ତୁ):
lesson 3
1. My story is said
The flowering plant is dead.

2. O flowering plant! why did you die ?
The black cow ate me up and made me lie.

3. O black cow! why did the plant you eat?
Because the cowherd did not well me treat.

4. O cowherd! why didn’t you well the cow treat to eat?
The daughter-in-law did not give me food.

5. O daughter-in-law ! why didn’t you give food, why?
Because my little baby did cry.
lesson 3
6. O little baby! why did you cry?
The ant bit me, that is why.

7. O ant! why did you bite the little child?
Under the soil I hide
And bite soft flesh when I do find.

କବିତାର ଓଡ଼ିଆ ଉଚ୍ଚାରଣ:
1. ମାଇଁ ଷ୍ଟୋରି ଇଜ୍ ସେଡ୍
ଦି ଫ୍ଲାୱାରିଙ୍ଗ୍ ପ୍ଲାଣ୍ଟ୍ ଇଜ୍ ଡେଡ୍ ।

2. ଓ ଫ୍ଲାୱାରିଙ୍ଗ୍ ପ୍ଲାଣ୍ଟ ! ହୁଏ ଡିଡ଼୍ ଇୟୁ ଡାଏ ?
ଦି ବ୍ଲାକ୍ କାଓ ଏଟ୍ ମି ଅପ୍ ଆଣ୍ଡ ମେଡ଼୍ ମି ଲାଏ ।

3. ଓ ବ୍ଲାକ୍ କାଓ ! ହ୍ଵାଏ ଡିଡ୍ ଦ’ ପ୍ଲାଣ୍ଟ୍‌ ଇୟୁ ଇଟ୍ ?
ବିକଜ୍ ଦ’ କାଓହଡ଼୍ ଡିଡ଼୍ ନଟ୍ ୱେଲ୍ ମି ଟ୍ରିଟ୍ ।

4. ଓ କାଓହଡ଼ ! ହ୍ବାଏ ଡିଡ଼ିଣ୍ଟ୍ ଇୟୁ ୱେଲ୍‌ ଦ’ କାଓ ଟ୍ରିଟ୍ ଟୁ ଇଟ୍ ?
ଦି ଡଟର୍-ଇନ୍-ଲ୍ ଡିଡ୍ ନଟ୍ ଗିଭ୍ ମି ଫୁଡ୍ ।

5. ଓ ଡଟର୍‌-ଇନ୍-ଲ୍ ! ହ୍ବାଏ ଡିଡ଼ିଣ୍ଟ୍‌ ଇୟୁ ଗିଭ୍ ଫୁଡ୍, ଦ୍ଵାଏ ?
ବିକଜ୍ ମାଇଁ ଲିଟିଲ୍ ବେବି ଡିଡ଼୍ କ୍ରାଏ ।

6. ଓ ଲିଟିଲ୍ ବେବି ! ହୁଏ ଡିଡ଼୍ ଇୟୁ କ୍ରାଏ ?
ଦି ଆଣ୍ଡ୍ ବିଟ୍ ମି, ଦ୍ୟାଟ୍ ଇଜ୍ ହୁଏ ।

7. ଓ ଆଣ୍ଡ୍ ! ହୁଏ ଡିଡ୍ ଇୟୁ ବାଇଟ୍ ଦ’ ଲିଟିଲ୍ ଚାଇଲ୍‌ଡ୍ ?
ଅଣ୍ଡର୍ ଦ’ ସିଏଲ୍ ଆଇ ହାଇଡ଼୍
ଆଣ୍ଡ୍ ବାଇଟ୍ ସଫ୍ଟ ପ୍ଲେସ୍ ସ୍ପେନ୍ ଆଈ ଡୁ ଫାଇଣ୍ଡ୍ ।

BSE Odisha 6th Class English Solutions Follow-Up Lesson 3 My Story is Said

କବିତାର ସାରକଥା | ଓଡ଼ିଆ ଅନୁବାଦ:
୧।  ମୋ ଗପଟି କୁହା ସରିଲା
ଫୁଲଗଛଟି ମରିଗଲା ।

୨। ହେ ଫୁଲଗଛ ! ତୁ କାହିଁକି ମରିଗଲୁ ?
କାଳୀଗାଈଟା ମୋତେ ଖାଇଦେଲା ଏବଂ ମୋତେ ତଳେ ପକାଇ ଦେଲା ।

୩ । ହେ କାଳୀଗାଈ ! ଫୁଲଗଛଟିକୁ ତୁ କାହିଁକି ଖାଇଦେଲୁ ?
କାରଣ ଗାଈ ଜଗୁଆଳିଟା ମୋ’ର ଖାଇବା ପିଇବା ବୁଝିଲା ନାହିଁ ।

୪ । ହେ ଗାଈ ଜଗୁଆଳି ! ତୁ କାହିଁକି ଗାଈର ଭଲ ଯତ୍ନ ନେଲୁ ନାହିଁ ଓ ତାକୁ ଖାଇବାକୁ ଦେଲୁନି ?
ବୋହୂଟା ମୋତେ ଖାଦ୍ୟ ଦେଲା ନାହିଁ ।

୫ । ହେ ବୋହୂ ! ତୁ କାହିଁକି ଖାଦ୍ୟ ଦେଲୁନି, କାହିଁକି ?
କାରଣ ମୋ ଛୋଟ ଛୁଆଟି କାନ୍ଦିଲା ।

୬ । ହେ ଛୋଟ ଛୁଆ ! ତୁ କାହିଁକି କାନ୍ଦିଲୁ ?
ପିମ୍ପୁଡ଼ିଟା ମୋତେ କାମୁଡ଼ି ଦେଲା, ସେଇଥପାଇଁ।

୭ | ହେ ପିମ୍ପୁଡ଼ି ! ତୁ କାହିଁକି ଛୋଟ ଛୁଆଟିକୁ କାମୁଡ଼ି ଦେଲୁ ?
ମୁଁ ମାଟିତଳେ ଲୁଚିଥାଏ
ଏବଂ ଯେତେବେଳେ ମୁଁ ନରମ ମାଂସ ପାଏ କାମୁଡ଼ିଦିଏ ।

Session – 2 (ସୋପାନ – ୨):
III. Post-Reading (ପଢ଼ିସାରିବା ପରେ):

1. Writing (ଲେଖୁ ):
(a) Answer the following questions.
(ନିମ୍ନଲିଖୂତ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଦିଅ ।)

(i) What language is this poem from ?
(କେଉଁ ଭାଷାରୁ ଏହି କବିତାଟି ଆସିଛି ?)
Answer:
This poem is from the Odia language.

(ii) When is this song normally sung?
(ସାଧାରଣତଃ କେତେବେଳେ ଏହି ଗୀତଟି ବୋଲାଯାଏ ? )
Answer:
This song is normally sung when a story ends.

(iii) Why was the flowering plant dead?
(କାହିଁକି ଫୁଲଗଛଟି ମରିଗଲା ?)
The ____________________________________dead because
_________________________________________
_________________________________________
Answer:
The flowering plant was dead because the black cow ate it up and made it lie.

BSE Odisha 6th Class English Solutions Follow-Up Lesson 3 My Story is Said

(iv) Why did the cow eat up the flowering plant?
(ଗାଈ କାହିଁକି ଫୁଲଚାରାଟିକୁ ଖାଇଦେଲା ?)
Ans. The cow ate up the flowering plant because the cowherd did not treat the cow well.

Word Note (ଶବ୍ଦାର୍ଥ):
(The words/phrases have been defined mostly on contextual meanings.)
(ଶବ୍ଦ । ଖଣ୍ଡବାକ୍ୟଗୁଡ଼ିକ ଅଧିକାଂଶତଃ ପ୍ରସଙ୍ଗଗତ ଅର୍ଥ ଉପରେ ନିର୍ଭର କରି ବ୍ୟାଖ୍ୟା କରାଯାଇଛି।)

battle — fight, ଯୁଦ୍ଧ
bite — cut with teeth, କାମୁଡିବା
cowherd — one who looks after cows, ଗାଈ ଜଗୁଆଳି
kingdom — country ruled by a king, ରାଜ୍ୟ
look after — take care of, ଯତ୍ନ ନେବା, ଦେଖାଶୁଣା କରିବା
nail — metal nail for fixing horse-shoe, ଲୁହାକଣ୍ଟା
rider — (here) the person who rides a horse, ଆରୋହୀ |
shoe nail — horse shoe nail, ଘୋଡ଼ା ନାଲ
treat — caring, feeding, ଯତ୍ନ ନେବା, ଖାଇବା ପିଇବା ବୁଝିବା
daughter-in-law — the wife of the son, ବୋହୂ ବା ବଧୂ
hide — ଲୁଚାନ୍ତୁ |
bite — କାମୁଡିବା
soft — ନରମ
flesh — ମାଂସ
lie — ମିଛ କହିବା
die — ମର
dead — ମୃତ
bit — ବିଟ୍
lost — ହଜିଯାଇଛି |

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 7 Future Time Reference Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 7 Future Time Reference

SECTION – 1

The Present Progressive is used for future reference
A: What are you doing tomorrow evening?
B: I’m going to the town hall. My friends are coming. We are putting up a show for the handicapped. We are also meeting the Minister for some funds. Are you going somewhere tomorrow evening?
A: Yes, I’m going to the library. I thought I could ask you to come along.
In the dialogue above you can only see the use of more number of Present Progressive constructions/sentences.

Here are a few questions for you to answer.
1. Which period of time does the use of the Present Progressive refer to: time which is past, time which is present, or future time?
2. Are ‘A’ and ‘B’ talking about actions that they have already planned and arranged to do?
3. Is the arrangement personal (made by either A or B) or is official (made by someone else, who is in a position of authority)?
Answer:
1. The time in all the Present Progressive sentences refers to a future time (futurity).
2. Yes. In the dialogue between A and B, we see the actions have already been planned/arranged.
3. The arrangements are personal. No official planning/arrangements.
The above sentences (Present Progressive form) are based on a personal plan or decision or need or requirement. So now we can say these sentences are based on the ‘internal evidence’ of the speaker or writer.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Activity – 26
Surabhi, who is 16, wants to go on an excursion with her friends and teachers. . Her mother is worried and has a lot of questions to ask about the arrangements. Look at the hints supplied and complete the dialogue between them, using the appropriate forms of the verbs.
Mother: Who / you / go / with?
______________________
Surabhi: friends/teachers
______________________
Mother: Where / you / go?
______________________
Surabhi: Darjeeling
______________________
Mother: When / go / there?
______________________
Surabhi: next Monday
______________________
Mother: How / you / get there?
______________________
Surabhi: by bus?
______________________
Mother: Where / you / stay?
______________________
Mother: a hotel.
______________________
Answer:
Mother: Who are you going with?
Surabhi: I’m going with my friends and teachers.
Mother: Where are you going?
Surabhi: I’m (We are) going to Darjeeling.
Mother: When are you going there?
Surabhi: I’m (We are) going there next Monday.
Mother: How are you getting there?
Surabhi: I’m (We are) getting there by bus.
Mother: Where are you staying?
Surabhi: I’m (We are) staying in a hotel.
Mother: What are you doing the next Tuesday there?
Surabhi: I’m visiting a cinema with my cousin.
Mother: When are you coming back?
Surabhi: I’m (We are) coming back next Sunday.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Activity – 27
Bindu maintains a diary in which she writes down a list of the things that she plans to do during the week ahead. Here is an outline of the entries in her diary for the next week. Complete the entries, using the hints given below. Use the Present Progressive.
Monday: meet music teacher.
______________________
Tuesday: go to the cinema with cousin
______________________
Wednesday: play badminton
______________________
Thursday: see off Maya at the station.
______________________
Friday: throw a party for friends.
______________________
Saturday: visit a dentist in the evening.
______________________
Sunday: rest.
______________________
Answer:
Monday: Bindu is meeting her music teacher on Monday.
Tuesday: She is going to the cinema with her cousin.
Wednesday: She is playing badminton in the evening.
Thursday: She is seeing off Maya at the station.
Friday: She is throwing a party for her friends.
Saturday: She is visiting the dentist in the evening.
Sunday: She is having a rest on Sunday.
Or, She is resting on Sunday.

Activity – 28
You plan to visit Koraput after your examination. Mention five things that you have arranged to do there.
(a) ……………………………………………………………………………………
(b) ……………………………………………………………………………………
(c) ……………………………………………………………………………………
(d) ……………………………………………………………………………………
(e) ……………………………………………………………………………………
Answer:
(a) I’m meeting one of my school friends there.
(b) I’m attending her birthday ceremony.
(c) I’m visiting the Damanjodi project there.
(d) I’m helping her with the party.
(e) I’m visiting new places there with my friend.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

SECTION – 2

The Present Simple for future time reference
Minister: Have you drawn up my tour program for the next week?
P. A.: Yes sir. You leave for Sambalpur at 7.00 a.m. on Monday morning.
Minister: When do I get there?
P. A. : You reach Sambalpur at 1.00 p.m. You halt at Angul for a few minutes, on the way Then, after lunch, you meet the Commissioner at 3.00 for a discussion.
Minister: Where do I stay in Sambalpur?
P.A.: The Guest House at the Hirakud Dam has been reserved for you, sir. Then, the next morning at 8.00, you proceed to Rourkela. The Commissioner accompanies you to Rourkela.
Minister: And when do I return to Bhubaneswar?
P. A. . On Thursday, sir.
Look at the use of the present simple in the dialogue. What is the time reference here: past time, present time, or future time?
The Present Simple Tense’ can be used for future time reference. We use this tense for future events, i.e. fixed by the calendar or an official or departmental timetable. It is used to talk about the activity which has already been planned and fixed.

Activity — 29
The following is the list of official engagements of the Chief Minister for next Monday. Write one sentence to describe each item. Use the Present Simple form of the verb given in brackets :
8.30 a.m. inaugural address, Conference on Preservation of Human Rights (deliver)
9.30 a.m. Speech on Syllabus Reform, Utkal University. (give)
1.00 p.m. Cabinet Committee meeting (preside over)
4.30 p.m. National Book Fair (inaugurate)
5.50 p.m. Parliamentary delegation from Turkey (welcome)
8.00 p.m. Dinner party in honor of the Prime Minister of Bangladesh (host)
____________________________________________
____________________________________________
____________________________________________
____________________________________________
____________________________________________
Answers
8.30 a.m. The Chief Minister delivers his inaugural address at the Conference on Preservation of Human Rights.
9.30 a.m. The Chief Minister gives his speech on Syllabus Reform, at Utkal University.
1.00 p.m. The Chíef Minister presides over the Cabinet Committee meeting.
4.30 p.m. The Chief Minister inaugurates the National Book Fair at Unit — III, Exhibition field, Bhubaneswar.
5.50 p.m. The Chief Minister welcomes the Parliamentary delegation from Turkey.
8.00 p.m. The Chief Minister hosts the Dinner party in honor of the Prime Minister of Bangladesh.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Activity — 30
A travel agency offers a number of packages for tourists. Here is an outline of such a travel package.
Imagine that you are a salesman in a travel agency and that you are describing the program to a group of tourists, who want to know the details. Use complete sentences, with the Present Simple, to describe the program.
Monday → Leave Bhubaneswar for Hyderabad by Konark Express
March 2 →2 days’ sight-seeing in Hyderabad
Thursday → Board Kaveri Express for Chennai
March 5 → 2 nights in Chennai, Visit to Mahabalipuram
Saturday → Board Vrindaban Express for Bangalore
March 7 → 2 nights in Bangalore
Monday → By Deluxe bus to Mysore
March 9 → 1 night in Mysore
Tuesday → Mysore to Goa by taxi
March 10 → 2 nights in Goa
Thursdaý → Board Flight IC 765 for Bhubaneswar
March 12
Answer:
Monday → The tourists leave Bhubaneswar for Hyderabad by Konark Express.
March 2 → They go for 2 days sightseeing in Hyderabad.
Thursday → They board the Kaveri Express for Chennai.
March 5 → They stay 2 nights in Chennai and visit Mahabalipuram.
Saturday → They board the Vrindaban Express for Bangalore.
March 7 → They halt 2 nights in Bangalore.
Monday → They go by Deluxe bus to Mysore.
March 9 → They halt for 1 night in Mysore.
Tuesday → They go from Mysöre to Goa by taxi.
March 10 → They put up 2 nights in Goa.
Thursday → They board flight IC 765 for Bhubaneswar.
March 12

SECTION-3

Future time reference with ‘be going to’
1. I’m sweating already. I think it’s going to be a very hot day.
2. Be careful of that dog; it’s going to bite.
3. Mohan is eating too much; he’s going to be sick.
In the above sentences ‘be going to’ structure is used. In ‘be’ verb family we have eight verbs such as: am, is, are, was, were, be, being, and been. But in this structure for futurity (future time reference) am, is, are only these three are used.
be going to = is / am / are going to.
We can use this ‘be going to ’ structure for ‘external evidence ’ at the moment of speaking. We can better mark in the above three sentences some evidence or reason at the moment of speaking which helps the speaker to predict/believe something that is likely to happen in the near future.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Activity – 31
Complete the sentences using ‘be going to’ and the verbs in brackets.
(a) Look at those dark clouds. It’s _____________(rain).
(b) The lady is gasping for breath. I think she’s _____________(faint).
(c) My neighbor has packed up all his belongings. I think he _____________ (leave) the house.
(d) Rakesh _____________(fail) the exam. I don’t see him studying at all.
(e) Bijoy Babu _____________(lose) in the election. The voters are very unhappy with him.
Answer:
(a) Look at those dark clouds. It’s going to rain.
(b) The lady is gasping for breath. I think she is going to faint.
(c) My neighbor has packed up all his belongings. I think he is going to leave the house.
(d) Rakesh is going to fail the exam. I don’t see him studying at all.
(e) Bijoy Babu is going to lose in the election. The voters are very unhappy with

Activity – 32
Study the situation and guess what is going to happen. (One example has been given)
(a) The old man has been ill for a long time. He stopped taking food 5 days ago.
Ans. He is going to die.
(b) My friend has been reading the “matrimonial” column in the newspaper and collecting photographs of girls.
_____________________________________________________.
(c) A man is getting into the house opposite through the window. The people who live there are away on holiday.
_____________________________________________________.
(d) Do you see that man is trying to walk on the ice? His feet are sleeping.
____________________________________________________.
(e) The policeman is running after the thief and pointing his gun at him.
_____________________________________________________.
(f) The boy has taken the book from the shelf and put it on the table. He is drawing up a chair now.
_____________________________________________________.
(g) India meets Pakistan in the final match today. Sachin Tendulkar is injured and will not be able to play.
_____________________________________________________.
(h) Water has got into the boat.
_____________________________________________________.
Answer:
(b) My friend is going to marry soon.
(c) The man is going to steal from the house.
(d) The man is going to fall.
(e) The policeman is going to fire.
(f) He is going to read the book.
(g) India is going to lose the match.
(h) The boat is going to sink.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

SECTION – 4

Here are some more sentences with ‘be going to’.
(a) A. Why have you bought so many books?
What are you going to do?
B. I‘m going to read all of them for my project.
(b) She has decided not to leave the house this year. She is going to stay on for another year.
(c) A. I’m going to buy a scooter
B. How‘re you going to pay for it?
A. I’m going to ask my brother to lend me some.
Look at these sentences with ‘be going to’. How are they different in meaning from the sentences in Section 3 (above)?
In this case, be going to is used to express an ‘intention’ to do something in the future. We can say: a decision or plan is based on a personal need or requirement.

Activity-33

There are a number of things that you haven’t done yet but intend to do. Answer
the questions below, using be going to as well as the words in brackets.
Friend: Have you had lunch?
You: No, but _____________. (after my friend arrives)
Friend: Have you written a letter to your father?
You: Not yet, _____________. (tomorrow)
Friend: Have you read the new novel by Vikram Seth?
You: No, _____________. (next week),
Friend: Have you watered the plants?
You: Not yet, _____________. (this afternoon)
Answer:
You: No, but I am going to have my lunch after my friend’s arrival.
Friend: Have you written a letter to your father?
You: Not yet, I am going to write a letter to my father tomorrow.
Friend: Have you read the new novel by Vikram Seth?
You: No, I am going to read the new novel by Vikram Seth next week.
Friend: Have you watered the plants?
You: Not yet, I am going to water the plants this afternoon.

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Activity – 34
The members of a Youth Club have taken a vow on Gandhi Jayanti. They have promised that each of them will do at least one good deed, in memory of Mahatma Gandhi.
Can you draw up a list of the good things that the boys intend to do? Here is an example.
I’m going to plant 100 trees inside the school compound.
(a) ____________________________________________
(b) ____________________________________________
(c) ____________________________________________
(d) ____________________________________________
(e) ____________________________________________
(f) ____________________________________________
(g) ____________________________________________
Answer:
(a) I’m going to clean the rubbish in our lane.
(b) I’m going to help the poor and sick.
(c) I’m going to be friends with people of other religions.
(d) I’m going to be truthful.
(e) I’m going to fight against injustice.
(f) I’m going to be punctual.
(g) I’m going to preach equality among people.

Multiple-Choice Questions (MCQs) with Answers

Question 1.
London ___________the capital of the United Kingdom.
(A) were
(B) are
(C) is
(D) is being
Answer:
(C) is

Question 2.
It ___________since yesterday evening.
(A) was snowing
(B) had been snowing
(C) snowed
(D) has been snowing
Answer:
(D) has been snowing

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Question 3.
Just as I was entering the room, the family was ___________for a party.
(A) leaving
(B) left
(C) had left
(D) going
Answer:
(A) leaving

Question 4.
The arm was so badly injured that he ___________it amputated.
(A) has to have
(B) had had
(C) had to have
(D) must have
Answer:
(C) had to have

Question 5.
I ___________ very busy lately.
(A) have been
(B) will be
(C) would be
(D) having being
Answer:
(A) have been

Question 6.
He was not thirsty because he ___________too much water.
(A) had drank
(B) had drunk
(C) had been drunk
(D) had drunken
Answer:
(B) had drunk

Question 7.
Where ___________since we last played together?
(A) were you playing
(B) had you been playing
(C) have you been playing
(D) do you play
Answer:
(C) have you been playing

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Question 8.
As soon as she noticed the workmen, she asked them what they ___________.
(A) have been doing
(B) are doing
(C) have done
(D) had been done
Answer:
(C) have done

Question 9.
The bus has been traveling for days and it times it ___________.
(A) stops
(B) will stop
(C) stopped
(D) would stop
Answer:
(C) stopped

Question 10.
You need not ___________when the barrister asked you where you were when the crime was committed.
(A) be lying
(B) to tell a lie
(C) tell a lie
(D) have tell a lie
Answer:
(C) tell a lie

Question 11.
The news about the disaster ___________six weeks ago.
(A) broadcasted
(B) was broadcasting
(C) was broadcasted
(D) was broadcast
Answer:
(D) was broadcast

Question 12.
___________daily keeps people healthy and vigorous.
(A) In eating
(B) Eating
(C) Having eaten
(D) To eat
Answer:
(D) To eat

Question 13.
I cannot imagine myself ___________ car repairs in the garage.
(A) to do
(B) doing
(C) to be doing
(D) in doing
Answer:
(B) doing

Question 14.
The pianist ___________his performance to be well accepted by the audience willingly practiced his art.
(A) expect
(B) expecting
(C) expected
(D) expects
Answer:
(B) expecting

Question 15.
After our football team lost the cup final, the manager told them ___________ and not winning is the most important.
(A) playing the game
(B) the game
(C) the play
(D) the gaming
Answer:
(B) the game

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Question 16.
I noticed the culprit ___________ away from the house.
(A) run
(B) would be running
(C) ran
(D) had running
Answer:
(B) would be running

Question 17.
I am convinced he ___________to school after his insolence.
(A) dare not return
(B) dare not returning
(C) dare not to return
(D) does not dare returning
Answer:
(A) dare not return

Question 18.
‘___________this week?’ ‘No, she’s on holiday.’
(A) Is Susan working
(B) Does Susan work
(C) Does work Susan
(D) none of these
Answer:
(A) Is Susan working

Question 19.
I don’t understand this sentence. What ___________?
(A) does mean this word
(B) does this word mean
(C) means this word
(D) none of these
Answer:
(B) does this word mean

Question 20.
John ___________tennis once or twice a week.
(A) is playing usually
(B) is usually playing
(C) usually plays
(D) none of these
Answer:
(C) usually plays

Question 21.
How ___________now ? Better than before?
(A) you are feeling
(B) do you feel
(C) are you feeling
(D) none of these
Answer:
(B) do you feel

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Question 22.
It was a boring weekend ___________anything.
(A) I didn’t
(B) I don’t do
(C) I didn’t do
(D) none of these
Answer:
(C) I didn’t do

Question 23.
Tom ___________his hand when he was cooking the dinner.
(A) burnt
(B) was burning
(C) has burnt
(D) none of these
Answer:
(A) burnt

Question 24.
Jim is away on holiday. He ___________to Spain.
(A) is gone
(B) has gone
(C) has been
(D) none of these
Answer:
(B) has gone

Question 25.
Everything is going well. We ___________any problems so far.
(A) didn’t have
(B) don’t have
(C) haven’t had
(D) none of these
Answer:
(C) haven’t had

Question 26.
Linda has lost her passport again. It’s the second time this ___________.
(A) has happened
(B) happens
(C) happened
(D) none of these
Answer:
(A) has happened

Question 27.
You’re out of breath ___________?
(A) Are you running
(B) Have you run
(C) Have you been running
(D) none of these
Answer:
C) Have you been running

Question 28.
Where’s the book I gave you? What ___________with it?
(A) have you, done
(B) have you been doing
(C) are you doing
(D) none of these
Answer:
(A) have you, done

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Question 29.
We’re good friends. We __________ each other for a long time.
(A) know
(B) have known
(C) have been knowing
(D) knew
Answer:
(B) have known

Question 30.
Sally has been working here __________.
(A) for six months
(B) since six months
(C) six months ago
(D)none of these
Answer:
(A) for six months

Question 31.
It’s two years __________ Joe.
(A) that I don’t see
(B) that I haven’t seen
(C) since I didn’t see
(D) since I saw
Answer:
(D) since I saw

Question 32.
They __________out after lunch and they’ve just come back.
(A) went
(B) have gone
(C) are gone
(D) none of these
Answer:
(A) went

Question 33.
The Chinese __________printing.
(A) invented
(B) have invented
(C) had invented
(D) none of these
Answer:
(A) invented

Question 34.
I am __________in Scotland for ten years. Now he lives in London.
(A) lived
(B) has lived
(C) has been living
(D) none of these
Answer:
(A) lived

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Question 35.
The man sitting next to me on the plane was nervous because he __________before.
(A) hasn’t flown
(B) didn’t fly
(C) hadn’t flown
(D) none of these
Answer:
(C) hadn’t flown

Question 36.
__________a car when they were living in London?
(A) Had they
(B) Did they have
(C) Were they having
(D) Have they had
Answer:
(B) Did they have

Question 37.
I __________television a lot but I don’t anymore.
(A) was watching
(B) was used to watch
(C) used to watch
(D) none of these
Answer:
(C) used to watch

Question 38.
__________ tomorrow, so we can go out somewhere.
(A) I’m not working
(B) I don’t work
(C) I won’t work
(D) none of these
Answer:
(A) I’m not working

Question 39.
That hag looks heavy, __________ you with it.
(A) I’m helping
(B) I help
(C) I’ll help
(D) none of these
Answer:
(C) I’ll help

Question 40.
I think the weather __________be nice later.
(A) will
(B) shall
(C) is going to
(D) none of these
Answer:
(A) will

Question 41.
‘Ann is in hospital.’ ‘Yes, I know. __________her tomorrow.’
(A) I visit
(B) I’m going to visit
(C) I’ll visit
(D) none of these
Answer:
(B) I’m going to visit

Question 42.
We’re late. The film __________by the time we get to the cinema.
(A) will already start
(B) will be already started
(C) will already have started
(D) none of these
Answer:
(C) will already have started

CHSE Odisha Class 12 English Grammar Tense Patterns Unit 7 Future Time Reference

Question 43.
Don’t worry __________late tonight.
(A) if I am
(B) when I am
(C) when I’ll be
(D) if I’ll be
Answer:
(A) if I am

Question 44.
The film __________by the time we get to the cinema.
(A) will start
(B) will have started
(C) will be starting
(D) will have been starting
Answer:
(B) will have started

Question 45.
Next year they __________for 25 years.
(A) will have been marrying
(B) will have been married
(C) will be marrying
(D) none of these
Answer:
(B) will have been married

CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three-Dimensional Geometry Ex 13

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 13 Introduction To Three-Dimensional Geometry Ex 13 Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three-Dimensional Geometry Exercise 13

Question 1.

Fill in the blanks in each of the following questions by choosing the appropriate answer from the given ones.
(a) The distance of the point P(x0, y0, z0) from z – axis is [\(\sqrt{x_0^2+y_0^2}, \sqrt{y_0^2+z_0^2}, \sqrt{x_0^2+z_0^2},\)\(\sqrt{\left(x-x_0\right)^2+\left(y-y_0\right)^2}\)]
Solution:
\(\sqrt{x^2+y^2}\)

(b) The length of the projection of the line segment joining (1, 3, -1) and (3, 2, 4) on z – axis is ___________. [1, 3, 4, 5]
Solution:
5

(c) the image of the point (6, 3, -4) with respect to yz – plane is _____________. [(6, 0, -4), (6, -3, 4), (-6, -3, -4), (-6, 3, -4)]
Solution:
(-6, 3, -4)

(d) If the distance between the points (-1, -1, z) and (1, -1, 1) is 2 then z = _______________. [1, √2, 2, 0]
Solution:
1

Question 2.
(a) identify the axis on which the given points lie : (1, 0, 0), (0, 1, 0), (0, 0, 1)
Solution:
x-axis, y-axis, z-axis

(b) Identify the planes containing the points! (7, 0, 4), (2, -5, 0), (0, √2, -3)
Solution:
xz-plane, xy-plane, yz-plane.

CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13

Question 3.
(a) Determine, which of the following points have the same projection on x-axis. (2, -5, 7), (2, √2, -3), (-2, 1, 1), (2, -1, 3)
Solution:
(2, -5, 7), (2, √2, -3) and (2, -1, 3) have the same projection on x-axis.

(b) Find the projection of the point (7, -5, 3) on:
(i) xy-plane
Solution:
(7, -5, 0)

(ii) yz-plane,
Solution:
(0, -5, 3)

(iii) zx-plane
Solution:
(7, 0, 3)

(iv) x-axis
Solution:
(7, 0, 0)

(v) y-axis,
Solution:
(0, -5, 0)

(vi) z-axis.
Solution:
(0, 0, 3)

Question 4.
When do you say two lines in space are skewed? Do they intersect?
Solution:
A pair of non-co-planar lines are called skew lines. Skew lines do not intersect.

Question 5.
From the three pairs of lines given below, identify those which uniquely determine a plane:
(i) intersecting pair,
(ii) parallel pair,
(iii) a pair of skew lines.
Solution:
Out of given three pairs
(i) Intersecting pair and
(ii) Parallel pair of lines determine a plane.

Question 6.
Determine the unknown coordinates of the following points if :
(i) P(a, 2, -1)∈ yz – plane
Solution:
a = 0

(ii) Q(-1, y, 3) ∈ zx-plane
Solution:
y = 0

(iii) R(√2, -3, c) ∈ xy-plane
Solution:
c = 0

(iv) S(7, y, z) ∈ x-axis
Solution:
y = 0, z = 0

(v) T(x, 0, z) ∈ y-axis
Solution:
x = 0 , z = 0

(vi) V(a, b, -3) ∈ z-axis
Solution:
a = b = 0

CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13

Question 7.
Which axis is determined by the intersection of:
(i) xy-plane and yz-plane
Solution:
y-axis

(ii) yz-plane and zx-plane
Solution:
z-axis

(iii) zx-plane and xy-plane
Solution:
x-axis

Question 8.
Which axis is represented by a line passing through origin and normal to:
(i) xy-plane
Solution:
z-axis

(ii) yz-plane
Solution:
x-axis

(iii) zx-plane.
Solution:
y-axis

Question 9.
What are the coordinates of a point which is common to all the coordinate planes?
Solution:
Origin 0(0, 0, 0) is common to all coordinate planes.

Question 10.
If A, B, and C are projections of P(3, 4, 5) on the coordinate planes, find PA, PB, and PC.
Solution:
PA = 5, PB = 3, PC = 4.

Question 11.
(a) Find the perimeter of the triangle whose vertices are (0, 1, 2) (2, 0, 4) and (-4, -2, 7).
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13

(b) Show that the points (a, b, c), (b, c, a), and (c, a, b) form an equilateral triangle.
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13 1

(c) Show that the points (3, -2, 4) (1, 1, 1) and (-1, 4, -1) are collinear.
Solution:
Let A = (3, -2, 4), B = (1, 1, 1) and C = (-1, 4, -2)
D. rs of AB are < -2, 3, -3 >
D. rs of BC are < -2, 3, -3 >
As D. rs of AB is the same as d.rs of
BC it follows that A, B, and C lie on the same straight line.
So the points are collinear. (Proved)

(d) Show that points (0, 1, 2), (2, 5, 8), (5, 6, 6), and (3, 2, 0) form a parallelogram.
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13 2

(e) Show that the line segment joining (7, -6, 1) (17, -18, -3) intersect the line segment joining (1, 4, -5), (3, -4, 11) at (2, 0, 3).
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13 3
D.rs of AP are < -5, 6, 2 >
D.rs of PB are < -15, 18, 6>
i.e., < -5, 6, 2 >
Thus d.r.s. of AP are the same as the d.r.s. of PB.
So A.P.B. are collinear.
Again d.rs. of CP are < 1, -4, 8 >
D. rs. of PD are < 1, -4, 8 >
Thus d.rs. of CP and d.rs. of PD are equal.
So the points C.P.D. are collinear.
Hence line AB intersects the line CD at P.        (Proved)

(f) Find the locus of points that are equidistant from points (1, 2, 3) and (3, 2, -1).
Solution:
Let A = (1, 2, 3), B = (3, 2, -1)
Let P (x, y, z) be equidistant from A and B.
Then PA = DB
(x – 1 )2 + (y – 2)2 + (z – 3)2
= (x – 3)2 + (y – 2)2 + (z + 1)2
⇒ (x – 1)2 – (x – 3)2 + (y – 2)2 – (y – 2)2 + (z – 3)2 – (z + 1)2 = 0
⇒ (x – 1 + x – 3) (x – 1 – x + 3) + (z – 3 + z + 1)(z – 3 – z – 1) = 0
⇒ (2x – 4) . 2 + (2z – 2) . (- 4) = 0
⇒ x – 2 – 2z + 2 = 0
⇒ x – 2z = 0 This is the required locus.

Question 12.
(a) Find the ratio in which the line segment through (1, 3, -1) and (2, 6, -2) is divided by zx-plane.
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13 4

(b) Find the ratio in which the lines segment through (2, 4, 5), (3, 5, -4) is divided by xy-plane.
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13 5

(c) Find the coordinates of the centroid of the triangle with its vertices at (a1, b1, c1), (a2, b2, c2), and (a3, b3, c3)
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13 6

(d) If A (1, 0, -1), B (-2, 4, -2), and C (1, 5, 10) be the vertices of a triangle and the bisector of the angle BAC, meets BC at D, then find the coordinates of the point D.
Solution:
CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three Dimensional Geometry Ex 13 7

(e) Prove that the points P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which point Q divides the line segment PR.
Solution:
Given that P = (3, 2, -4)
Q = (5, 4, -6), R = (9, 8, -10)
D. rs. of PQ are < 2, 2, -2 >
D. rs. of QR are < 4, 4, -4 >
i.e., < 2, 2, -2 >
Thus D.rs. of PQ and QR are the same.
So P, Q, R lie on the same straight line.
Hence P, Q, and R are collinear.     (Proved)
Let Q divides the join of PR in ratio k: 1
∴ \(\frac{9 k+3}{k+1}\) = 5, \(\frac{8 k+2}{k+1}\) = 4, \(\frac{-10 k-4}{k+1}\) = -6
⇒ k = \(\frac{1}{2}\)
Thus the ratio is 1: 2

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Odisha State Board BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) Textbook Exercise Questions and Answers.

BSE Odisha Class 10 Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 1.
ନିମ୍ନଲିଖ ଉକ୍ତିଗୁଡ଼ିକରେ ଥ‌ିବା ତ୍ରୁଟିକୁ ସଂଶୋଧନ କରି ଲେଖ ।
(i) x² – 4x + 4 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ବାସ୍ତବ ଓ ଭିନ୍ନ ।
(ii) x² – 5x + 6 = 0 ସମୀକରଣର ପ୍ରଭେଦକ 2 ଅଟେ ।
(iii) ax? + bx – c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ସମଷ୍ଟି \(\frac{c}{a}\)।
(iv) ax’ + bx + c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ \(\frac{b}{a}\)।
(v) 1 ଓ -1 ମୂଳ ବିଶିଷ୍ଟ ଦ୍ୱିଘାତ ସମୀକରଣଟି x² + 1 = 0 ।
(vi) x² = 0 ଦ୍ୱିଘାତ ସମୀକରଣର ମୂଳ ସମାନ ନୁହଁନ୍ତି ।
(vii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳ ଦ୍ଵୟର ସମଷ୍ଟି \(– \frac{3}{2}\)।
(viii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ \(\frac{1}{3}\)।
ଉ-
(i) x² – 4x + 4 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ ବାସ୍ତବ ପରିମେୟ ଓ ସମାନ ।
(ii) x² – 5x + 6 = 0 ସମୀକରଣର ପ୍ରଭେଦକ 1 ଅଟେ ।
(iii) ax² + bx – c = 0 ମୂଳଦ୍ଵୟର ସମଷ୍ଟି \(\frac{-b}{a}\)।
(iv) ax² + bx + c = 0 ସମୀକରଣର ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{c}{a}\)।
(v) 1 ଓ – 1 ମୂଳବିଶିଷ୍ଟ ଦ୍ୱିଘାତ ସମୀକରଣଟି x² – 1 = 0।
(vi) x² = 0 ଦ୍ବିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ ସମାନ ଅଟନ୍ତି ।
(vii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟର ସମଷ୍ଟି \(\frac{2}{3}\)
(viii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{-1}{3}\)।

(i) ଏଠାରେ a = 1, b = -4, c = 4
ପ୍ରଭେଦକ (D) = b² – 4ac = (-4)² – 4 × 1 × 4 = 16 – 16 = 0
∴ ମୂଳଦ୍ବୟ ବାସ୍ତବ ଓ ସମାନ ।

(ii) ଏଠାରେ a = 1, b=-5, c = 6
ପ୍ରଭେଦକ (D) = b² – 4ac = (- 5)² – 4 (1) (6) = 25 – 24 = 1

(iii) ax² + bx – c = 0 ମୂଳଦ୍ଵୟର ସମଷ୍ଟି \(\frac{-b}{a}\)।
(iv) ax² + bx + c = 0 ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{c}{a}\)।
(v) ମୂଳବିଶିଷ୍ଟ ଦ୍ୱିଘାତ ସମୀକରଣ, x² – (α + ß) x + αß = 0
⇒ x² – { 1 + (- 1)} x + 1 (-1) = 0 ⇒ x² – 1 = 0
(vi) x = 0 ଦ୍ୱିଘାତ ସମୀକରଣ ମୂଳଦ୍ଵୟ ସମାନ ଅଟନ୍ତି । (କାରଣ ପ୍ରଭେଦକ (D) = 0)
(vii) ଏଠାରେ a = 3, b = -2, c = -1 ମୂଳଦ୍ଵୟ ସମାନ = \(\frac{-b}{a}\) = \(\frac{-(-2)}{a}\) = \(\frac{2}{3}\)
(viii) 3x² – 2x-1=0 ଏଠାରେ a = 3, b = -2, c = 1 ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{c}{a}\) = \(\frac{-1}{3}\)

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 2.
ନିମ୍ନଲିଖୂ ପ୍ରଶ୍ନମାନଙ୍କର ସଂକ୍ଷିପ୍ତ ଉତ୍ତର ଦିଅ ।
(i) ଗୋଟିଏ ଦ୍ବିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ 3 ଓ -5 ହେଲେ, ସମୀକରଣଟି ନିରୂପଣ କର ।
(ii) mx² – 2x + (2m – 1) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ 3 ହେଲେ, m ର ମାନ ନିରୂପଣ କର ।
(iii) x² – px + 2 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 2 ହେଲେ, p ର ମାନ ନିରୂପଣ କର ।
(iv) 4x² – 2x + c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ଏକ ଓ ଅଭିନ୍ନ ହେଲେ, c ର ମାନ ନିରୂପଣ କର ।
(v) 5x² + 2x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ – 2 ହେଲେ, k ର ମାନ ନିରୂପଣ କର ।
(vi) x² – kx + 6 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 3 ହେଲେ, k ର ମାନ ନିରୂପଣ କର ।
(vii) 2x² + kx + 3 = 0 ସମୀକରଣର ଦୁଇଟି ମୂଳ ବାସ୍ତବ ଓ ସମାନ ହେଲେ, k ର ମାନ ନିରୂପଣ କର ।
ସମାଧାନ :
(i) ଗୋଟିଏ ଦ୍ଵିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ 3 ଓ – 5 । ଅର୍ଥାତ୍ α = 3 ଓ ß = – 5
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -1 x² – (α + ß) x + αß = 0
⇒ x² – (3 – 5) x + (3)(-5) = 0 ⇒ x² + 2x – 15 = 0
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -2

(ii) mx² – 2x + (2m – 1) = 0 ମୂଳଦ୍ଵୟର ଗୁଣଫଳ = 3
ଏଠାରେ a = m, b = – 2, c = 2m – 1
ମୂଳଦ୍ବୟର ଗୁଣଫଳ = \(\frac{c}{a}\) ⇒ 3 \(\frac{2m-1}{m}\)
⇒ 3m = 2m – 1 ⇒ 3m – 2m = 1 ⇒ m = -1
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ 3 ହେଲେ m = -1 ହେବ ।

(iii) x² – px + 2 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 2।
⇒ 2² – p(2) + 2 =0 ⇒ 4 – 2p + 2 = 0 ⇒ 6 = 2p ⇒ p = \(\frac{6}{2}\) = 3
∴ pର ମାନ = 3

(iv) 4x² – 2x + c = ଫିର ମୂଳଦ୍ବୟ ଏକ ଓ ଅଭିନ୍ନ । ଏଠାରେ a = 4, b = – 2, c = c
ପ୍ରଭେଦକ (D) = 0 ⇒ b² – 4ac = 0 ⇒ (-2)² – 4 (4) c = 0 ⇒ 4 – 16c = 0
⇒ -16c = -4 = c = – \(\frac{-4}{16}=\frac{1}{4}\)
∴ c = \(\frac{1}{4}\)
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟ ଏକ ଏବଂ ଅଭିନ୍ନ ହେଲେ c ର ମାନ \(\frac{1}{4}\) ହେବ।

(v) 5x² + 2x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ – 2 ।
⇒ 5(- 2)² + 2(- 2) + k = 0 ⇒ 20 – 4 + k = 0 ⇒ 16 + k = 0 ⇒ k = -16
∴ ‘k’ ର ମାନ -16 ପାଇଁ ଦତ୍ତ ସମୀକରଣର ଗୋଟିଏ ମୂଳ -2 ହେବ ।

(vi) x² – kx + 6 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 3।
⇒ 3² – 3k + 6 = 0 ⇒ 9 – 3k + 6 = 0 ⇒ -3k = -15 ⇒ \(\frac{-15}{-3}=5\)
∴ ଦତ୍ତ ସମୀକରଣର ଗୋଟିଏ ମୂଳ 3 ହେଲେ k ର ମାନ 5 ହେବ ।

(vii) 2x² + kx + 3 = 0, ଏଠାରେ a = 2, b = k, c = 3
ସମୀକରଣର ମୂଳଦ୍ୱୟ ବାସ୍ତବ ଓ ସମାନ ହେଲେ b² – 4ac = 0
⇒ k² – 4 (2) (3) = 0 ⇒ k² – 24 = 0 ⇒ k² = 24 ⇒ k = ±√24 ⇒ k = ± 2√6
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟ ବାସ୍ତବ ଓ ସମାନ ହେଲେ k ର ମାନ ±2√6 ହେବ ।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 3.
ପ୍ରତ୍ୟେକ ପ୍ରଶ୍ନପାଇଁ ଥ‌ିବା ସମ୍ଭାବ୍ୟ ଉତ୍ତରଗୁଡ଼ିକ ମଧ୍ୟରୁ ଠିକ୍ ଉତ୍ତରଟି ବାଛି ଲେଖ ।
(i) ନିମ୍ନଲିଖ୍ ସମୀକରଣମାନଙ୍କ ମଧ୍ୟରୁ କେଉଁଟି x ରେ ଏକ ଦ୍ଵିଘାତ ସମୀକରଣ ?
(a) x² – x – 12 = 0
(b) x² + 12 = 3
(c) x + = x²
(d)x (x – 1 ) (x + 5) = 0

(ii) 7x² – 9x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ସ୍ବରୂପ କ’ଣ ?
(a) ବାସ୍ତବ ସଂଖ୍ୟା ଓ ପରସ୍ପରଠାରୁ ପୃଥକ୍
(b) ବାସ୍ତବ ସଂଖ୍ୟା ଏବଂ ଏକ ଓ ଅଭିନ୍ନ
(c) ବାସ୍ତବ ହେବେ ନାହିଁ
(d) ଏଥୁରୁ କେଉଁଟି ନୁହେଁ

(iii) ନିମ୍ନଲିଖ ମଧ୍ୟରୁ କେଉଁଟି – 6 ଓ 8 ମୂଳ ବିଶିଷ୍ଟ ଦ୍ବିଘାତ ସମୀକରଣ ?
(a) (x + 6) (x+8)= 0
(b) (x + 6) (x – 8) = 0
(c) (x – 6) (x + 8) = 0
(d) (x – 6) (x – 8) = 0

(iv) 3x² + 2√5 x – 5 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ଓ ହେଲେ αß ର ମୂଲ୍ୟ କେତେ ?
(a) 3
(b) 2√5
(c) \(\frac{2√5}{3}\)
(d) \(\frac{-5}{3}\)

(v) 4x – 2x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ α ଓ ß ହେଲେ α + ß ର ମୂଲ୍ୟ କେତେ ?
(a) \(\frac{1}{16}\)
(b) 4
(c) \(\frac{1}{2}\)
(d) -8

(vi) 4x + 3x + 7 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହେଲେ \(\frac{1}{α}+\frac{1}{ß}\) ର ହେଲେ କେତେ ?
(a) \(\frac{3}{7}\)
(b) \(– \frac{3}{7}\)
(c) \(\frac{7}{3}\)
(d) \(– \frac{7}{3}\)

(vii) ଗୋଟିଏ ଦ୍ବିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ସମଷ୍ଟି ଓ ଗୁଣଫଳ ଯଥାକ୍ରମେ 4 ଓ \(\frac{5}{2}\) ହେଲେ ନିମ୍ନଲିଖ ମଧ୍ୟରୁ କେଉଁଟି ?
(a) 2x² + 8x + 5 = 0
(b) 2x² – 8x + 5 = 0
(c) 2x² + 8x – 5=0
(d) 2x² – 8x – 5 = 0
ଉ-
(i) x² – x – 12 = 0
(ii) ବାସ୍ତବ ସଂଖ୍ୟା ଓ ପରସ୍ପରଠାରୁ ପୃଥକ୍
(iii) (x +6) (x – 8) = 0
(iv) \(\frac{-5}{3}\)
(v) \(\frac{1}{2}\)
(vi) \(– \frac{3}{7}\)
(vii) 2x² – 8x + 5 = 0

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 4.
ନିମ୍ନଲିଖୂତ ଦ୍ବିଘାତ ସମୀକରଣମାନଙ୍କୁ ପୂର୍ବ ବର୍ଗରେ ପରିଣତ କରି ସମାଧାନ କର ।
(i) x² + x – 6 = 0
(ii) 2x² – 9x + 4 = 0
(iii) 14x² + x – 3 = 0
(iv) 3x² – 32x + 12=0
(v) x² + 2px – 3qx – 6pq = 0
(vi) √3x² + 10x + 8√3 = 0
(vii) 25x² + 30x + 7 = 0
(viii) 3a²x² + 8abx + 4b² = 0 (a ≠ 0)
(ix) x² + ax + b = 0
(x) x² + bx = a² – ab
ସମାଧାନ :
(i)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -3
(ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -4
(iii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -5
(iv)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -6
(v) x² + 2px – 3qx – 6pq = 0
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -7

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

(vi) √3x² + 10x + 8√3 = 0
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -8
(vii) 25x² + 30x + 7 = 0
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -9
(viii) 3a²x² + 8abx + 4b² = 0 (a ≠ 0)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -10
(ix) x² + ax + b = 0
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -11
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -11.2
(x) x² + bx = a² – ab
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -12

Question 5.
ଦ୍ଵିଘାତ ସୂତ୍ର ପ୍ରୟୋଗ କରି ନିମ୍ନଲିଖ ସମୀକରଣମାନଙ୍କର ବୀଜ ବା ମୂଳ ନିରୂପଣ କରି ।
(i) 4x² – 11x + 6 = 0
(ii) (2x – 1)(x – 2) = 0
(iii) x² – (1+√2)x+ 2 = 0
(iv) a(x² + 1) = x(a2 + 1), a ≠ 0
(v) 6x² + 11x + 3 = 0
(vi) 2x² + 41x – 115 = 0
(vii) 12x² +x – 6 = 0
(viii) (6x + 5)(x – 2) = 0
(ix) 15x² – x – 8 = 0
(x) (x + 5)(x – 5) = 39
ସମାଧାନ :
(i) 4x² – 11x + 6 = 0
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -13
(ii) (2x – 1)(x – 2) = 0
⇒ 2x² – 4x -x + 2 = 0 ⇒ 2x² – 5x + 2 = 0
ଏଠାରେ a = 2, b = -5, c = 2
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -14
(iii) x² – (1+√2)x+ 2 = 0
ଏଠାରେ a = 1, b = – (1+√2), c = √2
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -15
(iv) a(x² + 1) = x(a² + 1) ⇒ a(x² + 1) – x(a² + 1) = 0
⇒ ax² + a – x(a² + 1) = 0 ⇒ ax² – x(a² + 1) + a = 0
ଏଠାରେ a = a, b = -(a² + 1), c = a
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -16
(v) 6x² + 11x + 3 = 0
ଏଠାରେ a = 6, b = 11, c = 3
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -17
(vi) 2x² + 41x – 115 = 0
ଏଠାରେ a = 2, b = 41, c = -115
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -18
(vii) 12x² +x – 6 = 0
ଏଠାରେ a = 12, b = 1, c = -6
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -19
(viii) (6x + 5)(x – 2) = 0 ⇒ 6x² -12x + 5x – 10 = 0 ⇒ 6x² -7x – 10 = 0
ଏଠାରେ a = 6, b = -7, c = -10
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -20
(ix) 15x² – x – 8 = 0
ଏଠାରେ a = 15, b = -1, c = -8
BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) -21
(x) (x + 5)(x – 5) = 39 ⇒ x² – 25 = 39 ⇒ x² – 25 – 39 = 0 ⇒ x² – 64 = 0
ଏଠାରେ a = 1, b = 0, c = -64
x = \(\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}=\frac{0 \pm \sqrt{0^2-4(1) 64}}{2(1)}=\frac{0 \pm \sqrt{256}}{2}=\frac{\pm 16}{2}=\pm 8\)
⇒ x = 8 ବ। x = -8
∴ ସମୀକରଣର ମୂଳଦ୍ଵୟ 8 ଓ -8 ।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 6.
ଯଦି 4x² – 13x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 12 ଗୁଣ ହେଲେ kରେ ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର 4x² – 13x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ । ଏବଂ ଅନ୍ୟଟି 12α ।
ଏଠାରେ a = 4, b = 13 6 c = k
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = \(\frac{-b}{a}\) ⇒ α + 12α = \(\frac{-(-13)}{4}\) ⇒ 13α = \(\frac{13}{4}\) ⇒ α = \(\frac{13}{4}\) × \(\frac{1}{13}\) = \(\frac{1}{4}\)
ମୂଳଦ୍ବୟର ଗୁଣଫଲ = \(\frac{-c}{a}\) ⇒ α.12α = \(\frac{k}{4}\) ⇒ 12α² = \(\frac{k}{4}\) ⇒ 12 × (\(\frac{1}{4}\))² = \(\frac{k}{4}\) ⇒ \(\frac{12}{16}\) = \(\frac{k}{4}\) ⇒ 16k = 48 ⇒ k = 3
∴ kର ମାନ 3 ହେଲେ ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 12 ଗୁଣ ହେବ ।

Question 7.
x² – 5x + p = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟି ଅପେକ୍ଷା 3 ଅଧିକ ହେଲେ pର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର x² – 5x + p = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ α ଓ ଅନ୍ୟଟି α + 3
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + α + 3 = \(\frac{-(-5)}{1}\)
⇒ 2α + 3 = 5 ⇒ 2α = 5 – 3 = 2 ⇒ α = \(\frac{2}{2}\) = 1
α ର ମାନ ସମୀକରଣରେ ବସାଇଲେ 1² – 5 (1) + p = 0
⇒ 1 – 5 + p = 0 ⇒ p – 4= 0 ⇒ p = 4
∴ p ର ମାନ 4 ହେଲେ ଗୋଟିଏ ମୂଳ ଅପରୂଟି ଅପେକ୍ଷା 3 ଅଧିକ ହେବ ।

Question 8.
ଯଦି 2x² – 5x + 3 = 0 ସମୀକରଣର ମୂଳଦ୍ୱୟ α ଓ ß ହୁଏ ତେବେ α²ß + αß²ର ମୂଲ୍ୟ ନିରୂପଣ ‘କର ।
ସମାଧାନ :
2x² – 5x + 3= 0 ସମୀକରଣର ମୂଳଦ୍ୱୟ α ଓ ß।
ମୂଳଦ୍ଵୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-5)}{2}\) ⇒ α + ß = \(\frac{5}{2}\)
ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{3}{2}\)
∴ α²ß + αß² = αß (α + ß)\(\frac{3}{2}\)(\(\frac{5}{2}\)) = \(\frac{15}{4}\)

Question 9.
ଯଦି 2x² – 6x + 3 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ, ତେବେ (α + 1) (ß + 1) ର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
2x² – 6x + 3= 0 ସମୀକରଣର ମୂଳଦ୍ୱୟ α ଓ ß।
ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-6)}{2}\) = \(\frac{6}{2}\) = 3
ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{3}{2}\)
∴ (α + 1) (ß + 1) = αß + α + ß + 1 = \(\frac{3}{2}\) + 3 + 1 = \(\frac{3+6+2}{2}\) = \(\frac{11}{2}\)
∴ (α + 1) (ß + 1) = \(\frac{11}{2}\)

Question 10.
ଯଦି 2x² – (p + 1) x + p – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଅନ୍ତର ଓ ଗୁଣଫଳ ସମାନ ହେଲେ pର ମାନ ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର 2x² – (p + 1) x + (p – 1) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß।
ବୀଜଦ୍ଵୟର ସମଷ୍ଟି α + ß = \(\frac{-{-(p+1)}}{2}\) = \(\frac{p+1}{2}\) ଏବଂ αß = \(\frac{p-1}{2}\)
ପ୍ରଶାନୁସାରେ ବୀଜଦ୍ଵୟର ଅନ୍ତର, ବୀଜଦ୍ୱୟର ଗୁଣଫଳ ସହ ସମାନ ।
∴ α – ß = aß ⇒ (α – ß)² = (aß)² ⇒ (α + B)² – 4aß = (αß)²
⇒ (\(\frac{p+1}{2}\))² – 4(\(\frac{p-1}{2}\)) ⇒ (\(\frac{p-1}{2}\))² = (\(\frac{p+1}{2}\))² – (\(\frac{p-1}{2}\))² = 4 (\(\frac{p-1}{2}\))
⇒ p . 1 = 2p – 2 ⇒ p = 2
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ଅନ୍ତର ଓ ଗୁଣଫଳ ସମାନ ହେଲେ p ର ମାନ 2 ହେବ ।

Question 11.
ଯଦି 5x² – 3x – 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ α³ + ß³ = \(\frac{117}{125}\)
ସମାଧାନ :
5x²-3x-2=0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß।
ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-3)}{5}\) = \(\frac{3}{5}\), ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{-2}{5}\)
∴ α³ + ß³ = (α + ẞ)³ – 3αß (α + B)
= (\(\frac{3}{5}\))³ – 3(\(\frac{3}{5}\))(\(\frac{-2}{5}\)) = \(\frac{27}{125}+\frac{18}{25}\) = \(\frac{27+90}{125}\) = \(\frac{117}{125}\)
∴ α³ + ß³ = \(\frac{117}{125}\) (ପ୍ରମାଣିତ)

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 12.
ଯଦି 5x² + 17x + 6 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ ତେବେ \(\frac{1}{α²}+\frac{1}{ß²}\) ର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
5x² + 17x + 6 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß।
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-17}{5}\), ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{6}{5}\)
\(\frac{1}{α²}+\frac{1}{ß²}\) = \(\frac{ß²+α²}{α²ß²}\) = \(\frac{(α+ß)²-2αẞ}{(αß)²}\)
=\(\frac{\left(\frac{-17}{5}\right)^2-2\left(\frac{6}{5}\right)}{\left(\frac{6}{5}\right)^2}=\frac{\frac{289}{25}-\frac{12}{5}}{\frac{36}{25}}\) = \(\frac{289-60}{25}\) × \(\frac{25}{36}\) = \(\frac{229}{36}\)
∴ \(\frac{1}{α²}+\frac{1}{ß²}\) ର ମୂଲ୍ୟ \(\frac{229}{36}\) ।

Question 13.
x² – 8x + 16p = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହେଲେ \(\frac{αß}{α + ß}\) ପରିପ୍ରକାଶକୁ p ମାଧ୍ୟମରେ ପ୍ରକାଶ କର ।
ସମାଧାନ :
x² – 8x + 16p = 0 ମୂଳ ଦ୍ଵୟ α ଓ ß।
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-8)}{1}=8\), ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{16p}{1}=16p\)
∴ \(\frac{αß}{α + ß}\) = \(\frac{16p}{8}\) = 2p

Question 14.
ଯଦି x² – 2 (5 + 2m) x + 3 (7 + 10m) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ଏକ ଓ ଅଭିନ୍ନ ହୁଏ, m ର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
x² – 2 (5 + 2m) x + 3 (7 + 10m) = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ ଏକ ଓ ଅଭିନ୍ନ ।
ପ୍ରଭେଦକ (D) = 0
ଏଠାରେ a = 1, b = – 2 (5+ 2m), c = 3 (7 + 10m)
D = b² – 4ac = 0
⇒ {-2(5+ 2m)}² – 4 × 1 × 3 (7 + 10m) = 0
⇒ 4 (25 + 20m + 4m²) – 4 × 3 (7 + 10m) = 0
⇒ 100+ 80m + 16m² – 12 (7 + 10m) = 0
⇒ 16m² + 80m + 100 – 84 – 120m = 0 16m² – 40m + 16 = 0 ⇒ 2m² – 5m+2=0 2m² – 4m – m + 2=0
⇒ 2m (m – 2) – 1 (m – 2) = 0 ⇒ (m – 2) (2m – 1) = 0
m – 2 = 0 | 2m – 10 ⇒ m = 2 | m =
∴ m ର ମାନ 2 କିମ୍ବା \(\frac{1}{2}\) ହେଲେ x² – 2 (5 + 2m) x + 3 (7 + 10m) = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ ଏକ ଓ ଅଭିନ୍ନ ହେବେ ।

Question 15.
(i) ଯଦି a = b = c ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ, ସମୀକରଣ
(x – a)(x – b) + (x – b)(x – c) + (x – c)(x – a) = 0 ର ମୂଳଦ୍ୱୟ ବାସ୍ତବ ଏବଂ ଏକ ଓ ଅଭିନ୍ନ ।
(ii) ଯଦି a + b + c = 0 ଏବଂ a, b, c ∈ Q ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ
(b + c – a) x² + (c + a – b) x + (a + b – c) = 0 ସମୀକରଣର ପରିମେୟ ହେବେ ।
ସମାଧାନ :
(i) a = b = c ହେଲେ, (x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0
⇒ (x – a)² + (x – a)² + (x – a)² = 0
⇒ 3 (x – a)² = 0 ⇒ (x – a)² = 0 ⇒ x² – 2ax + a² = 0
ଏଠାରେ ପ୍ରଭେଦକ (D) = b² – 4ac = (-2a)² – 4(1) a² = 4a² – 4a² = 0
∴ D = 0 ହେଲେ, ମୂଳଦ୍ୱୟ ବାସ୍ତବ ଏବଂ ଏକ ଓ ଅଭିନ୍ନ ।

(ii) ଯଦି a+b+c=0, a, b, c ∈ Q
(b + c – a) x² + (c + a – b) x + (a + b – c) = 0
a + b + c = 0
⇒ b + c = a, c + a = – b, a + b = -c
(b + c – a) x² + (c + a – b) x + (a + b – c) = 0
⇒ -2ax² + (-2b) x + (- 2c) = 0 ⇒ 2 (ax² + bx + c) = 0
⇒ ax² + bx + c = 0
ପ୍ରଭେଦକ (D) = b² – 4ac = (-b)² – 4ac = (a + c)² – 4ac = (a – c)²

Question 16.
ଗୋଟିଏ ଦ୍ଵିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ସମଷ୍ଟି 3 ଓ ମୂଳଦ୍ବୟର ବର୍ଗର ସମଷ୍ଟି 29 ହେଲେ, ସମୀକରଣଟି ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର ସ୍ଵିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ।
ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = 3
ମୂଳଦ୍ଵୟର ବର୍ଗର ସମଷ୍ଟି = α² + ß² = 29
⇒ (α + ß)² – 2 aẞ = 29 ⇒ 3² – 2αß = 29
⇒9 – 2αẞ = 29 ⇒ – 2αß = 29 – 9 = 20
αß = \(\frac{-20}{2}\) = -10
ସମୀକରଣଟି x² – (a + ẞ) x + αß = 0
⇒ x² – 3x + (-10) = 0 ⇒ x² – 3x – 10 = 0

Question 17.
ଯଦି 2x² – 4x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ \(\frac{α}{ß}+\frac{ß}{α}\) + 4(\(\frac{1}{α}+\frac{1}{ß}\)) + 2αß = 12
ସମାଧାନ :
2x² – 4x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ।
∴ ମୂଳଦ୍ଵୟର ସମଷ୍ଟି α + ß = \(\frac{-(-4)}{2}\) = -2 ଏବଂ ମୂଳଦ୍ଵୟର ଗୁଣଫଲ αβ = \(\frac{2}{2}\) = 1
L.H.S. = \(\frac{α}{ß}+\frac{ß}{α}\) + 63(\(\frac{1}{α}+\frac{1}{ß}\)) – 2αß
= \(\frac{ß²+α²}{αß}\) + 63\(\frac{(α+ß)}{(αß)}\) – 2αß
= \(\frac{(α+ß)²-2αß}{(αß)}\) + 4\(\frac{(α+ß)}{(αß)}\) + 2αß
= \(\frac{(2)²-2×1}{1}\) + \(\frac{4(2)}{1}\) + 2 × 1
= 2 + 8 + 2 = 12 = R.H.S.

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 18.
(i) ଯଦି ax² + bx + c = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 4 ଗୁଣ ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ 4b² = 25ac।
(ii) ଯଦି x² – px + q = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 2 ଗୁଣ ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ 2p² = 9q ।
ସମାଧାନ :
(i) ମନେକର ax² + bx + c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଏବଂ 4α।
∴ ମୂଳଦ୍ଵୟର ସମଷ୍ଟି α + 4α = \(\frac{-b}{a}\) ⇒ 5α = \(\frac{-b}{a}\) ⇒ α= \(\frac{-b}{5a}\) .. (i)
ମୂଳଦ୍ଵୟର ଗୁଣଫଲ α.4α = \(\frac{c}{2}\)
⇒ \(4 α^2=\frac{c}{a} \Rightarrow 4 \times (\frac{-b}{5a})^2=\frac{c}{a}\) [(i)]
⇒ \(\frac{4b²}{25a²}=\frac{c}{a} \Rightarrow 4ab²=25a²c \Rightarrow 4b²=25 ac\) (ପ୍ରମାଣିତ)

(ii) ମନେକର x² – px + q = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଏବଂ 2α।
∴ ମୂଳଦ୍ଵୟର ସମଷ୍ଟି α + 2α = \(\frac{-(-p)}{1}\) ⇒ 3α = p ⇒ α= \(\frac{p}{3}\) .. (i)
ମୂଳଦ୍ଵୟର ଗୁଣଫଲ α.2α = \(\frac{q}{1}\) = 2α² = q
⇒ 2 × (\(\frac{p}{3}\))³ = q ⇒ \(\frac{2p²}{3}\) = q ⇒ 2p² = 9q (ପ୍ରମାଣିତ)

Question 19.
(i) ଯଦି 41x² – 2 (5a + 4b) x + (a² + b²) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ସମାନ ହୁଅନ୍ତି, ତେବେ ପ୍ରମାଣ କର ଯେ, \(\frac{a}{b}=\frac{5}{4}\)।
(ii) ଯଦି x² + px + q = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟର ସମଷ୍ଟି ସେମାନଙ୍କର ବର୍ଗର ସମଷ୍ଟି ସହ ସମାନ ଯେ, 2q = p (p + 1)।
(ii) ଯଦି x² + px + q = 0 ସମୀକରଣର ଗୋଟିଏ ବୀଜ ଅନ୍ୟଟିର ବର୍ଗ ହୁଏ, ତେବେ ଦର୍ଶାଅ ଯେ p³ + q² + q = 3pq।
ସମାଧାନ :
(i) 41x² – 2 (5a + 4b) x + (a² + b²) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ସମାନ।
ଏଠାରେ a = 41, b = -2(5a + 4b), c = (a² + b²)
ପ୍ରଭେଦକ (D) = b² – 4ac = 0
⇒ {-2 (5a + 4b)}² – 4 (41) (a² + b²) = 0
⇒ 4 (25a² + 40ab + 16b²) – 4 (41a² + 41b²) = 0
⇒(25a² + 40ab + 16b² – 41a² – 41b²) = 0
⇒(-16a² + 40ab – 25b²) = 0
⇒(16a² – 40ab + 25b²) = 0
⇒(4a)² – 2.4a.5b + (5b)² = 0
⇒ (4a – 5b)² = 0
⇒4a – 5b = 0 [∴ a² – 2ab + b² = (a – b)²]
⇒ 4a = 5b ⇒ \(\frac{a}{b}=\frac{5}{4}\)।

(ii) x² + px + q = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟର ସମଷ୍ଟି ସେମାନଙ୍କର ବର୍ଗର ସମଷ୍ଟି ସହ ସମାନ ।
ମନେକର ସମୀକରଣର ବୀଜଦ୍ଵୟ α ଓ ß।
ବୀଜଦ୍ୱୟର ସମଷ୍ଟି α + ß = – p ଏବଂ ବୀଜଦ୍ବୟର ଗୁଣଫଳ αß = q
କିନ୍ତୁ ଦତ୍ତ ଅଛି α + ß = α² + ß²
⇒ α + ß = α² + ß² – 2αß ⇒ – p = (- p)² – 2q
⇒ 2q = p² + p ⇒ 2q = p (p + 1) (ପ୍ରମାଣିତ)

(iii) x + px + g = 0 ସମୀକରଣର ଗୋଟିଏ ବୀଜ ଅପରଟିର ବର୍ଗ ।
ମନେକର ସମୀକରଣର ବୀଜଦ୍ଵୟ α ଓ α²।
ବୀଜଦ୍ୱୟର ସମଷ୍ଟି α + α² = – p
ବୀଜଦ୍ବୟର ଗୁଣଫଳ α.α² = q ⇒ α³ = q
α + α² = – p = (α + α²)³ = -p³
⇒ a³ + α6 + 3α · a² (α + α²) = – p³ ⇒ q + q² + 3q (- p) = – p³
⇒ q² + q – 3pq = -p³ ⇒ p³ + q² + q = 3pq (ପ୍ରମାଣିତ)

BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 20.
ଯଦି a(b – c) x² + b(c – a) x + c (a – b) = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟ ସମାନ ହୁଏ, ତେବେ ଦର୍ଶାଅ ଯେ, \(\frac{2}{b}=\frac{1}{a}+\frac{1}{c}\)
ସମାଧାନ :
a(b – c) x² + b(c – a) x + c (a – b) = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟ ସମାନ ।
ସମୀକରଣର ପ୍ରଭଦେକ (D) = 0
⇒ {b (c – a)}² – 4a (bc) c (a – b) = 0
⇒ b² (ca)² – 4a (b -c) c (a – b) = 0
⇒(bc – ab)² – 4 a(b – c) · c (a – b) = 0
⇒ (ab – ca + ca – bc)² – 4a (b- c) · c (a – b) = 0
⇒ {a (b-c) + c (a – b)}² – 4a (b – c) c (a – b) = 0
⇒ {a (bc) -c (a – b)}² = 0 ⇒ (ab – ac- ca + bc) = 0
⇒ ab + bc = 2 ca ⇒ \(\frac{ab}{abc}+\frac{bc}{abc}=\frac{2ca}{abc}\) (abc ଦ୍ବାରା ଉଭୟ ପାର୍ଶ୍ଵକୁ ଭାଗ କଲେ)
⇒ \(\frac{1}{c}+\frac{1}{a}=\frac{2}{b}\) (ପ୍ରମାଣିତ)

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

Odisha State Board BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) Textbook Exercise Questions and Answers.

BSE Odisha Class 10 Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

Question 1.
ପ୍ରତିକଳ୍ପନ ପ୍ରଣାଳୀରେ ନିମ୍ନଲିଖ୍ ସହସମୀକରଣ ଦ୍ଵୟର ସମାଧାନ କର ।
(i) x + y – 8 = 0, 2x – 3y – 1 = 0
(ii) 3x + 2y – 5 = 0, x – 3y – 9 = 0
(iii) 2x – 5y + 8 = 0, x – 4y + 7 = 0
(iv) 11x + 15y + 23 = 0, 7x – 2y – 20 = 0
(v) ax + by – a + b = 0, bx – ay – a – b = 0
(vi) x + y – a = 0, ax + by – b² = 0
ସମାଧାନ ପ୍ରଣାଳୀ :
(i) ସହସମୀକରଣଦ୍ଵୟ ମଧ୍ୟରୁ ଗୋଟିକରୁ ‘x’ କିମ୍ବା ‘y’ର ମାନ ନେଇ ଯଥାକ୍ରମେ y କିମ୍ବା x ମାଧ୍ୟମରେ ପ୍ରକାଶ କରାଯାଏ ।
(ii) x କିମ୍ବା yର ମାନକୁ ଅନ୍ୟ ସମୀକରଣରେ ପ୍ରୟୋଗ କରି ଯଥାକ୍ରମେ y କିମ୍ବା x ର ମାନ ନିର୍ଣ୍ଣୟ କରାଯାଉ ।
(iii) ଉକ୍ତ ନିର୍ଣ୍ଣୟ ମାନକୁ (y କିମ୍ବା x) ନେଇ ଯେକୌଣସି ଗୋଟିଏ ସମୀକରଣରେ ପ୍ରୟୋଗ କରି ଅନ୍ୟଟିର ମାନ ନିର୍ଣ୍ଣୟ କରାଯାଏ ।
ସମାଧାନ :
(i) x + y – 8 = 0 …….(i) ଏବଂ
2x – 3y – 1 = 0 …….(ii)
ସମୀକରଣ (i)କୁ ବିଚାର କରି yକୁ x ମାଧ୍ୟମରେ ପ୍ରକାଶ କରାଯାଉ ।
x + y – 8 = 0 ⇒ y = 8 – x ……..(iii)
y ର ମାନକୁ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗ କଲେ ପାଇବା 2x – 3(8 – x) – 1 = 0
⇒ 2x – 24 + 3x – 1 = 0 ⇒ 5x = 25 ⇒ x = \(\frac{25}{5}\) = 5
x ର ମାନ ସମୀକରଣ (iii)ରେ ପ୍ରୟୋଗ କଲେ, y = 8 – x = 8 – 5 = 3
∴ ନିର୍ଦେୟ ସମୀକରଣଦ୍ଵୟର ସମାଧାନ (x, y) = (5, 3) ଅଟେ ।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

(ii) 3x + 2y – 5 = 0 …….(i) ଏବଂ
x – 3y – 9 = 0 …….(ii)
ସମୀକରଣ (i) ରୁ 3x = 5 – 2y ⇒ x = \(\frac{5-2y}{3}\) …….(iii)
‘x’ ର ମାନ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗ କଲେ, \(\frac{5-2y}{3}\) – 3y – 9 = 0
⇒ \(\frac{5-2y-9y-27}{3}\) ⇒ 0 = -22 – 11y = 0
⇒ 11y = -22 = y = \(\frac{-22}{11}\) = -2
yର ମାନ ସମୀକରଣ (iii)ରେ ପ୍ରୟୋଗ କଲେ,
x = \(\frac{5-2y}{3}\) = \(\frac{5-2(-2)}{3}\) = \(\frac{5+4}{3}\) = \(\frac{9}{3}=3\)
∴ ନିର୍ଦେୟ ସମୀକରଣଦ୍ଵୟର ସମାଧାନ (x, y) = (3, -2) ଅଟେ ।

(iii) 2x – 5y + 8 = 0 …….(i) ଏବଂ
x – 4y + 7 = 0 …….(ii)
ସମୀକରଣ (i) ରୁ ବିଚ।ର କରି x କୁ y ମାଧ୍ୟମରେ ପ୍ରକାଶ କରାଯାଉ ।
2x – 5y + 8 = 0 ⇒ 2x = 5y – 8 ⇒ x = \(\frac{1}{2}\)(5y – 8) …….(iii)
‘x’ ର ମାନ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗ କଲେ, \(\frac{1}{2}\)(5y – 8) – 4y + 7 = 0
⇒ \(\frac{5y-8-8y+14}{2}\) = 0
⇒ -3y + 6 = 0 ⇒ y = \(\frac{-6}{-3}\) = 2
yର ମାନ ସମୀକରଣ (iii)ରେ ପ୍ରୟୋଗ କଲେ, x = \(\frac{1}{2}\)(5 × 2 – 8) = \(\frac{1}{2}\) × 2 = 1
∴ ନିର୍ଦେୟ ସମୀକରଣଦ୍ଵୟର ସମାଧାନ (x, y) = (1, 2) ଅଟେ ।

(iv) 11x + 15y + 23 = 0 …….(i) ଏବଂ
7x – 2y – 20 = 0 …….(ii)
ସମୀକରଣ (i) ରୁ ବିଚ।ର କରି y କୁ x ମାଧ୍ୟମରେ ପ୍ରକାଶ କରାଯାଉ ।
11x + 15y + 23 = 0 ⇒ 15y = -11x – 23
⇒ y = \(\frac{1}{15}\)(-11x – 23) …….(iii)
‘y’ ର ମାନ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗ କଲେ, 7x – \(\frac{2}{15}\)(-11x – 23) = 20
⇒ \(\frac{105x+22x+46}{15}\) = 20
⇒ 127x = 300 – 46 ⇒ x = \(\frac{254}{127}\) = 2
x ର ମାନକୁ ସମୀକରଣ (iii) ରେ ପ୍ରୟୋଗ କଲେ, y = latex]\frac{1}{15}[/latex](-22 – 23) = \(\frac{1}{15}\) × -45 = -3
∴ ନିର୍ଦେୟ ସମାଧାନ (x, y) = (2, -3) ।

(v) ax + by – a + b = 0 …….(i) ଏବଂ
bx – ay – a – b = 0 …….(ii)
ସମୀକରଣ (i) ରୁ ବିଚ।ର କରି y କୁ x ମାଧ୍ୟମରେ ପ୍ରକାଶ କରାଯାଉ ।
ax + by – a + b = 0 ⇒ by = -ax + a – b
⇒ y = \(\frac{1}{b}\)(-ax + a – b) …….(iii)
y ର ମାନ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗ କଲେ, bx – \(\frac{a}{b}\)(-ax + a – b) = 0
⇒ \(\frac{b^2x+a^2x-a^2 +ab-ab-b^2}{b}\) = 0
⇒ x(a² + b²) = a² + b² ⇒ x = \(\frac{a^2+b^2}{a^2+b^2}\) = 1
x ର ମାନକୁ ସମୀକରଣ (iii) ରେ ପ୍ରୟୋଗ କଲେ, y = latex]\frac{1}{b}[/latex](-a + a – b) ⇒ y = \(\frac{-b}{b}\) = -1
∴ ନିର୍ଦେୟ ସମାଧାନ (x, y) = (1, -1) ଅଟେ।

(vi) x + y – a = 0 …….(i) ଏବଂ
ax + by – b² = 0 …….(ii)
ସମୀକରଣ (i) ରୁ ବିଚ।ର କରି y କୁ x ମାଧ୍ୟମରେ ପ୍ରକାଶ କରାଯାଉ ।
x + y – a = 0 ⇒ y = a – x …….(iii)
y ର ମାନ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗ କଲେ, ax + b(a – x) – b² = 0
⇒ ax + by – bx – b² = 0 ⇒ ax – bx = b² – ab
⇒ x(a – b) = -b(a – b) [a = b ତେଣୁ a – b ≠ 0]
ତେଣୁ x = -b
‘x’ ର ମାନକୁ ସମୀକରଣ (iii) ରେ ପ୍ରୟୋଗ କଲେ, y = a + b
∴ ନିର୍ଦେୟ ସମାଧାନ (x, y) = (-b, a+b)।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

Question 2.
ଅପସାରଣ ପ୍ରଣାଳୀରେ ନିମ୍ନଲିଖ ସହ ସମୀକରଣମାନଙ୍କର ସମାଧାନ କର ।
(i) x – y – 3 = 0, 3x – 2y – 1 = 0
(ii) 3x + 4y = 10, 2x – 2y = 2
(iii) 3x – 5y – 4 = 0, 9x = 2y – 1
(iv) 0.4x – 1.5y = 6.5, 0.3x + 0.2y = 0.9
(v) √2x + √3y = 0, √5x + √2y = 0
(vi) ax + by = 0, x + y – c = 0 (a+b ≠ 0)
ସମାଧାନ ପ୍ରଣାଳୀ :
(i) ସମୀକରଣଦ୍ବୟରୁ ‘x’ ଅପସାରଣ କରାଯାଇ y ର ମାନ ନିର୍ଣ୍ଣୟ କରାଯାଏ ।
(ii) y ର ମାନକୁ ଯେକୌଣସି ସମୀକରଣରେ ପ୍ରୟୋଗ କରି x ର ମାନ ନିର୍ଣ୍ଣୟ କରାଯାଏ ।
(iii) ସେହିପରି ସମୀକରଣଦ୍ଵୟରୁ yକୁ ଅପସାରଣ କରାଯାଇ ‘x’ର ମାନ ନିର୍ଣ୍ଣୟ କରି ଏହାକୁ ଯେକୌଣସି ସମୀକରଣରେ ପ୍ରୟୋଗ କରି ‘y’ର ମାନ ନିର୍ଣ୍ଣୟ କରାଯାଇ ପାରିବ ।
ସମାଧାନ :
(i) x – y – 3 = 0 ……… (i) ଏବଂ
3x – 2y – 1 = 0 ………. (ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -1
x ର ମାନକୁ ସମୀକରଣ (iii) ରେ ପ୍ରୟୋଗ କଲେ,
x – y – 3 = 0 ⇒ 4 – y – 3 = 0 ⇒ -y + 1 = 0 ⇒ y = 1
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (4, 1) ଅଟେ।

(ii) 3x + 4y = 10 ……… (i) ଏବଂ
2x – 2y = 2 ………. (ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -2
x ର ମାନକୁ ସମୀକରଣ (i) ରେ ପ୍ରୟୋଗ କଲେ,
3x + 4y = 10 ⇒ 2 + 4y = 10 ⇒ 4y = 10 – 6 ⇒ y = \(\frac{4}{4}\) = 1
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (2, 1) ଅଟେ।

(iii) 3x – 5y – 4 = 0 ……… (i) ଓ
9x = 2y – 1 ⇒ 9x – 2y + 1 = 0 ………. (ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -3
x ର ମାନକୁ ସମୀକରଣ (i) ରେ ପ୍ରୟୋଗ କଲେ,
3x – 5y – 4 = 0
⇒ 3 × (\(– \frac{1}{3}\)) – 5y – 4 = 0
⇒ -5y – 5 = 0 ⇒ y = \(\frac{5}{-5}\) = -1
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (\(– \frac{1}{3}\), -1) ଅଟେ।

(iv) 0.4x – 1.5y = 6.5 ……… (i) ଓ
0.3x + 0.2y = 0.9 ………. (ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -4
y ର ମାନକୁ ସମୀକରଣ (i) ରେ ପ୍ରୟୋଗ କଲେ,
0.4x – 1.5y = 6.5 ⇒ 0.4x + 4.5 = 6.5
⇒ 0.4x = 6.5 – 4.5 ⇒ 1.4x = 2 ⇒ x = \(\frac{2}{0.4}\) = 5
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (5, -3) ଅଟେ।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

(v) √2x + √3y = 0 ……… (i) ଓ
√5x + √2y = 0 ………. (ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -5
c1 = c2 = 0 ଓ a1b2 – a2b1 = 0 ହେଲେ ସମୀକରଣଦ୍ଵୟର ସମାଧାନଟି (0, 0) ଅଟେ ।
ଏଠାରେ c1 = c2 = 0 ଏବଂ \(\frac{\sqrt{2}}{\sqrt{5}} \neq \frac{\sqrt{3}}{\sqrt{2}}\)
ତେଣୁ ସହସମୀକରଣ ଦ୍ଵୟର ସମାଧାନ (0, 0) ଅଟେ ।
ବିକଳ୍ପ ପ୍ରଣାଳୀ :
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -6
‘y’ ର ମାନକୁ ସମୀକରଣ (i)ରେ ପ୍ରୟୋଗ କଲେ,
√2x + √3 × 0 = 0 ⇒ √2x = 0 ⇒ x = 0
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (0, 0) ଅଟେ।

(v) ax + by = 0 ……… (i) ଏବଂ
x + y – c = 0 ………. (ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -7
‘x’ ର ମାନକୁ ସମୀକରଣ (ii)ରେ ପ୍ରୟୋଗ କଲେ, y = c – x = c – \(\frac{bc}{b-a}\) =
= \(\frac{bc-ca-bc}{b-a}\) = \(\frac{-ca}{b-a}\) = \(\frac{ca}{a-b}\)
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (\(\frac{bc}{b-a}\), \(\frac{ca}{a-b}\)) ଅଟେ।

Question 3.
ବଜ୍ରଗୁଣନ ପ୍ରଣାଳୀରେ ନିମ୍ନଲିଖୂତ ସହ ସମୀକରଣମାନଙ୍କର ସମାଧାନ କର ।
(1) x + 2y + 1 = 0, 2x – 3y – 12 = 0
(ii) 2x + 5y = 1, 2x + 3y = 3
(iii) x + 6y + 1 = 0, 2x + 3y + 8 = 0
(iv) \(\frac{x}{a}+\frac{y}{b}\) = a+b, \(\frac{x}{a^2}+\frac{y}{b^2}\) = 2
(v) x + 6y + 1 = 0, 2x + 3y + 8 = 0
(vi) 4x – 9y = 0, 3x + 2y – 35 = 0
ବଜ୍ରଗୁଣନ ପୃତ୍ର : \(\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{x}{a_1b_2-a_2b_1}\)
ଯେଉଁଠାରେ a1b2 = a2b1 ≠ 0
ସମାଧାନ :
(i) x + 2y + 1 = 0 ……… (i) ଏବଂ
2x – 3y – 12 = 0 ………. (ii)
ସମୀକରଣମାନଙ୍କର a1b2 – a2b1 = (1)(-3) – (2)(2) = -7 ≠ 0
ତେଣୁ ସମାଧାନ ସମ୍ଭବ।
ବଜ୍ରଗୁଣନ ପ୍ରଣାଳୀ ଅବଲମୂନରେ।
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -8
⇒ \(\frac{x}{-21}=\frac{y}{14}=\frac{1}{-7}\)
⇒ x = \(\frac{-21}{-7}\) ଓ y = \(\frac{14}{-7}\)
⇒ x = 3 ଓ y = -2
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (3, -2) ଅଟେ।

(ii) 2x + 5y = 1 ……… (i) ଏବଂ
2x + 3y = 3 ………. (ii)
ସମୀକରଣ (i) ଓ (ii) ଦ୍ବୟରୁ 2x + 5y = 1, 2x + 3y = 3
ସମୀକରଣମାନଙ୍କର a1b2 – a2b1 = (2)(3) – (2)(5) = -4 ≠ 0
ତେଣୁ ସହସମୀକରଣ ଦ୍ଵୟର ସମାଧାନ ସମ୍ଭବ ।
ବଜ୍ରଗୁଣନ ପ୍ରଣାଳୀ ଅବଲମୂନରେ।
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -9
⇒ \(\frac{x}{15-(-3)}=\frac{y}{-2-(-6)}=\frac{1}{6-10}\)
⇒ \(\frac{x}{15+3}=\frac{y}{-2+6}=\frac{1}{6-10}\)
⇒ \(\frac{x}{-12}=\frac{y}{4}=\frac{1}{-4}\)
⇒ x = \(\frac{-12}{-4}=3\) ଓ y = \(\frac{4}{-4}=-1\)
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (3, -2) ଅଟେ।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

(iii) x + 6y + 1 = 0 ……… (i) ଏବଂ
2x + 3y + 8 = 0 ………. (ii)
ଏଠାରେ a1b2 – a2b1 = (1)(3) – (2)(6) = 3- 12 = -9 ≠ 0
ତେଣୁ ଦତ୍ତ ସହସମୀକରଣ ଦ୍ଵୟର ସମାଧାନ ସମ୍ଭବ ।
ବଜ୍ରଗୁଣନ ପ୍ରଣାଳୀ ଅବଲମୂନରେ
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -10
⇒ \(\frac{x}{48-3}=\frac{y}{2-86}=\frac{1}{3-12}\)
⇒ \(\frac{x}{45}=\frac{y}{-6}=\frac{1}{-9}\)
⇒ x = \(\frac{-45}{-9}=-5\) ଓ y = \(\frac{-6}{-9}=\frac{2}{3}\)
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (-5, \(\frac{2}{3}\)) ଅଟେ।

(iv) \(\frac{x}{a}+\frac{y}{b}\) = a+b ……… (i)
\(\frac{x}{a^2}+\frac{y}{b^2}=2\) ………. (ii)
ସମୀକରଣ (i) ଓ (ii) ରୁ \(\frac{x}{a}+\frac{y}{b}-(a+b)=0\), \(\frac{x}{a^2}+\frac{y}{b^2}-2=0\)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -11
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (a², b²) ଅଟେ।

(v) x + 6y + 1 = 0 ……… (i)
2x + 3y + 8 = 0 ………. (ii)
ଏଠାରେ a1 = 1
b1 = 6
c1 = 1
a2 = 5
b2 = 3
c2 = 8
ପୁନଶ୍ଚ \({a_1}{a_2}=\frac{1}{2}\), \({b_1}{b_2}=\frac{6}{3}=2\)
\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\), ତେଣୁ ସହ-ସମୀକରଣଦ୍ୱୟର ଅନନ୍ୟ ସମାଧାନ ରହିବ ।
b1c2 – b2c1 = 6 × 8 – 3 × 1 = 48 – 3 = 45
c1a2 – c2a1 = 1 × 2 – 8 × 1 = 2 – 8 = -6
a1b2 – a2b1 = 1 × 3 – 2 × 6 = 3 – 12 = -9
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -12
⇒ \(\frac{x}{45}=\frac{y}{-6}=\frac{1}{-9}\)
⇒ x = \(\frac{-45}{-9}=-5\) ଓ y = \(\frac{-6}{-9}=\frac{2}{3}\)
∴ ସମାଧାନ (x, y) = (-5, \(\frac{2}{3}\) ) ।

(vi) 4x – 9y = 0 ……… (i)
3x + 2y – 35 = 0 ………. (ii)
ଏଠାରେ a1 = 4
b1 = -9
c1 = 0
a2 = 3
b2 = 2
c2 = -35
ତେଣୁ ସହ-ସମୀକରଣଦ୍ୱୟର ଅନନ୍ୟ ସମାଧାନ ରହିବ ; \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\) (\(\frac{4}{3} \neq \frac{-9}{2}\))
b1c2 – b2c1 = (-9)(-35) – 2 × 0 = 315
c1a2 – c2a1 = 0 × 3 – (-35) × 4 = 140
a1b2 – a2b1 = 4 × 2 – 3 × (-9) = 35 ≠ 0
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -12.1
⇒ \(\frac{x}{315}=\frac{y}{140}=\frac{1}{35}\)
⇒ \(\frac{x}{9}=\frac{y}{4}=1\) ⇒ x = 9 ଓ y = 4
∴ ସମାଧାନ (x, y) = (9, 4) ।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

Question 4.
ନିମ୍ନଲିଖ୍ ସହସମୀକରଣମାନଙ୍କ ସମାଧାନ କର ।
(i) \(\frac{2}{x}+\frac{3}{y}=17, \frac{1}{x}+\frac{1}{y}=7(x \neq 0, y \neq 0)\)
(ii) \(\frac{5}{x}+6 y=13, \frac{3}{x}+20 y=35(x \neq 0)\)
(iii) \(2 x-\frac{3}{y}=9,3 x+\frac{7}{y}=2(y \neq 0)\)
(iv) 4x + 6y = 3xy, 8x + 9y = 5xy (x ≠ 0, y ≠ 0)
(v) (a – b)x + (a + b)y = a² – 2ab – b², (a + b)x+(a + b)y = a² + b²
(vi) \(\frac{2}{x}+\frac{3}{y}=2\), ax – by = a² – b²
(vii) \(\frac{5}{x+y}-\frac{2}{x-y}+1=0, \frac{15}{x+y}+\frac{7}{x-y}-10=0\)
(viii) \(\frac{xy}{x+y}=\frac{6}{5}, \frac{xy}{x+y}=6(x+y \neq 0, x-y \neq 0)\)
(ix) 6x + 5y = 7, x + 3y + 1 = 2 (x + 6y – 1)
(x) \(\frac{x+y-8}{2}=\frac{x+2 y-14}{3}=\frac{3 x+y-12}{11}\)
(xi) \(\frac{x+y}{2}-\frac{x-y}{3}=8, \frac{x+y}{3}+\frac{x-y}{4}=11\)
(xii) \(\frac{x}{a}=\frac{y}{b}, ax + by=a^2+b^2 \)
ସମାଧାନ :
(i) \(\frac{2}{x}+\frac{3}{y}=17\) ⇒ \(\frac{2}{x}+\frac{3}{y}-17=0\) …….(1)
\(\frac{1}{x}+\frac{1}{y}=7\) ⇒ \(\frac{1}{x}+\frac{1}{y}-7=0\) …….(2)
ଏଠାରେ \(\frac{1}{x}=u\) ଏବଂ \(\frac{1}{x}=v\) ନେଲେ ଦତ୍ତ ସମୀକରଣଦ୍ବୟ
2u + 3v – 17 = 0, ଏବଂ u + v – 7 = 0 ହେବ ।
ଏଠାରେ a1 = 2
b1 = 3
c1 = -17
a2 = 1
b2 = 1
c2 = -7
\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\) ହୋଇଥିବାରୁ ସମୀକରଣ ଦ୍ଵୟର ଅନନ୍ୟ ସମାଧାନ ରହିବ ।
b1c2 – b2c1 = (3)(-7) – 1(-17) = -21 – 17 = -4
c1a2 – c2a1 = (-17) × 1 – (-7) × 2 = -17 + 14 = -3
a1b2 – a2b1 = 2 × 1 – 1 × 3 = 2 – 3 = -1 (≠ 0)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -13
⇒ \(\frac{u}{-4}=\frac{v}{-3}=\frac{1}{-1}\) ⇒ u = 4 ଏବଂ v = 3
⇒ \(\frac{1}{x}=4\) ଏବଂ \(\frac{1}{y}=3\) ⇒ x = \(\frac{1}{4}\) ଏବଂ y = \(\frac{1}{3}\)
∴ ସମାଧାନ (x, y) = (\(\frac{1}{4}\), \(\frac{1}{3}\)) ।
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -14
‘x’ ର ମାନ ସମୀକରଣରେ (ii) ପ୍ରୟୋଗ କଲେ y = \(\frac{1}{3}\) ହେବ ।

(ii) \(\frac{5}{x}+6 y=13\) ⇒ \(\frac{5}{x}+6 y-13=0\) ……..(1)
\(\frac{3}{x}+20 y=35\) ⇒ \(\frac{3}{x}+20 y-35=0\) ……….(2)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -15
ସମୀକରଣ (1) ରେ x = \(\frac{41}{25}\)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -17
⇒ \(\frac{125}{41}+6 y-13=0 \Rightarrow 6 y=13-\frac{125}{41}=\frac{533-125}{41}\)
⇒ \(6 y=\frac{408}{41} \Rightarrow y=\frac{408}{41} \times \frac{1}{6}=\frac{68}{41}\)
∴ ସମାଧାନ (x, y) = (\(\frac{41}{25}\), \(\frac{68}{41}\)) ।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

(iii) \(2 x-\frac{3}{y}=9,\) …….(i)
\(3 x+\frac{7}{y}=2\) …….(ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -18
‘x’ ର ମାନ ସମୀକରଣରେ (ii) ପ୍ରୟୋଗ କଲେ 2 × 3 – \(\frac{3}{y}\) = 9 ⇒ – \(\frac{3}{y}\) = 9 – 6
⇒ 3y = -3 ⇒ y = -1
∴ ସମାଧାନ (x, y) = (3, -1)।

(iv) 4x + 6y = 3xy ………..(i)
8x + 9y = 5xy ………. (ii)
ସମୀକରଣ (i) ଓ (ii) ର ଉଭୟ ପାର୍ଶ୍ଵକୁ xy ଦ୍ବାରା ଭାଗକଲେ,
\(\frac{4}{y}+\frac{6}{x}=3\) …..(iii)
\(\frac{8}{y}+\frac{9}{x}=5\)
ମନେକର \(\frac{1}{x}=u\) ଓ \(\frac{1}{y}=v\)। ତେଣୁ ସମୀକରଣ (iii) ଓ (iv) ରୁ
6u + 4v = 3 ……(v), 9u + 8v = 5 ……..(vi)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -19
ସମୀକରଣ (v) ରେ u = \(\frac{1}{3}\) ବସୀକଲେ, 6 × \(\frac{1}{3}\) + 4v = 3 ⇒ 4v = 1 ⇒ v = \(\frac{1}{4}\)
u = \(\frac{1}{3}\) ⇒ \(\frac{1}{x}\) = \(\frac{1}{3}\) ⇒ x = 3, v = \(\frac{1}{4}\) ⇒ \(\frac{1}{y}\) = \(\frac{1}{4}\) ⇒ y = 4
∴ ସମାଧାନ (x, y) = (3, 4)।

(v) (a – b)x + (a + b)y = a² – 2ab – b² ……..(i)
(a + b)x+(a + b)y = a² + b² ……….(ii)
ସମୀକରଣ (ii) କୁ ସମୀକରଣ (i) ରୁ ବିପ୍ରୟୋଗ କଲେ,
x(a + b) – x(a + b) = -2ab – 2b²
⇒ x(a + b – a – b) = -2ab – 2b²
⇒ -2bx = -2b(a + b) ⇒ x = a + b
‘x’ ର ମାନ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗ କଲେ, (a+b)(a+b) + (a+b) y = a² + b²
⇒ a² + b² + 2ab + (a + b) y = a² + b²
⇒ (a + b) y = -2ab ⇒ y = \(\frac{-2ab}{a+b}\)
∴ ସମାଧାନ (x, y) = (a+b, \(\frac{-2ab}{a+b}\))।

(vi) \(\frac{2}{x}+\frac{3}{y}=2\) ⇒ \(\frac{bx+ay}{ab}=2\)
⇒ bx + ay = 2ab ……(1), ax – by = a² – b² ………(2)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -20
⇒ x(a² + b²) = a³ + ab² ⇒ x(a² + b²) = a(a² + b²) ⇒ x = a
ସମୀକରଣ (1) ରେ x = a ସ୍ଥାପନ କଲେ, b.a + ay = 2ab ⇒ ay = ab
⇒ y = b
∴ ସମାଧାନ (x, y) = (a, b)।

(vii) \(\frac{5}{x+y}-\frac{2}{x-y}+1=0\) ……..(i) ଏବଂ
\(\frac{15}{x+y}+\frac{7}{x-y}-10=0\) ……..(ii)
\(\frac{1}{x+y}=a\) ଏବଂ \(\frac{1}{x-y}=b\) ହେଲେ
ସମୀକରଣଦ୍ଵୟ 5a – 2b + 1 = 0 ………(iii) ଏବଂ 15a + 7b – 10 = 0 ……….(iv)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -21
⇒ x – y = 1 …….. (v)
b ର ମାନ ସମୀକରଣ (ii) ରେ ପ୍ରୟୋଗକଲେ,
5a – 2 × 1 + 1 = 0
⇒ 5a – 1 = 0 ⇒ 5a = 1 ⇒ a = \(\frac{1}{5}\)
⇒ \(\frac{1}{x+y}=\frac{1}{5}\) ⇒ x + y = 5 ……..(iv)
ସମୀକରଣ (v) ଓ (vi) ରୁ ୟୋଗକଲେ x + y + x – y = 5 + 1
⇒ 2x = 6 ⇒ x = 3
∴ ନିଶ୍ଚେୟ ସମାଧାନ (x, y) = (3, 2)।

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

(viii) \(\frac{xy}{x+y}=\frac{6}{5}\) …….(i)
\(\frac{xy}{x+y}=6\) ……..(ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -22
⇒ \(\frac{1}{y}=\frac{2}{6}\) ⇒ \(\frac{1}{y}=\frac{1}{3}\) ⇒ y = 3
∴ ସମାଧାନ (x, y) = (2, 3)।

(ix) 6x + 5y = 7x + 3y + 1 = 2 (x + 6y – 1)
⇒ 6x + 5y = 7x + 3y + 1 ⇒ x – 2y + 1 = 0 ……(i)
ପୁନଶୃ 7x + 3y + 1 = 2 (x + 6y – 1)
⇒ 7x + 3y + 1 = 2x + 12y – 2 ⇒ 5x – 9y + 3 = 0 …..(ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -23
ସମୀକରଣ (i) ରେ x = 3 ସ୍ଥାପନ କଲେ, 3 – 2y + 1 = 0
⇒ 2y = 4 ⇒ y = 2
∴ ସମାଧାନ ପେଟ୍ (x, y) = (3, 2)।

(x) \(\frac{x+y-8}{2}=\frac{x+2 y-14}{3}=\frac{3 x+y-12}{11}\)
⇒ \(\frac{x+y-8}{2}=\frac{x+2 y-14}{3}\) ⇒ 3(x + y – 8) = 2(x + 2y – 14)
⇒ 3x + 3y – 24 = 2x + 4y – 28 ⇒ x – y = -4 ……..(i)
ପୁନଶୃ \(\frac{x+2 y-14}{3}=\frac{3 x+y-12}{11}\) ⇒ 11(x + 2y – 14) = 3(3x + y – 12)
⇒ 11x + 22y – 154 = 9x + 3y – 36 ⇒ 2x + 19y = 118 ……….(ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -24
ସମୀକରଣ (i) ରେ x = 2 ସ୍ଥାପନ କଲେ, 2 – y = -4 ⇒ y = 6
∴ ସମାଧାନ (x, y) = (2, 6)।

(xi) \(\frac{x+y}{2}-\frac{x-y}{3}=8\) ⇒ \(\frac{3(x+y)-2(x-y)}{6}=8\)
⇒ 3x + 3y – 2x + 2y = 48 ⇒ x + 5y = 48 ……..(i)
ପୁନଶୃ \(\frac{x+y}{3}+\frac{x-y}{4}=11\) ⇒ \(\frac{4(x+y)+3(x-y)}{12}=11\)
⇒ 4x + 4y + 3x – 3y = 132 ⇒ 7x + y = 132 ……..(ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -25
ସମୀକରଣ (i) ରେ y = 6 ସ୍ଥାପନ କଲେ, x + 5 × 6 = 48 ⇒ x = 18
∴ ସମାଧାନ (x, y) = (18, 6)।

(xii) \(\frac{x}{a}=\frac{y}{b}\) ⇒ bx = ay ⇒ bx – ay = 0 ……..(i)
ଏବଂ \(ax + by=a^2+b^2 \) ………(ii)
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -26
x ର ମାନ ସମୀକରଣ (i) ରେ କଲେ, ba – ay = 0 ⇒ ay = ab ⇒ y = b
BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b) -27
ବିକଳ୍ପ ସମାଧାନ :
\(\frac{x}{a}=\frac{y}{b}=k\) (ମନେକର) x = ak, y = bk
ax + by = a² + b² = a.ak + b.bk = a² + b²
k (a² + b²) = a² + b² ⇒ k = 1
∴ x = ak = a . 1 = a; y = bk = b . 1 = b

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

Question 5.
ନିମ୍ନଲିଖତ ଡିଟରମିନାଣ୍ଟର ମୂଲ୍ୟ ନିର୍ଣ୍ଣୟ କର ।
(i) \(\left|\begin{array}{ll}
2 & 5 \\
6 & 0
\end{array}\right|\)
(ii) \(\left|\begin{array}{ll}
2 & -1 \\
3 & 2
\end{array}\right|\)
(iii) \(\left|\begin{array}{ll}
0 & 4 \\
5 & -1
\end{array}\right|\)
(iv) \(\left|\begin{array}{ll}
\frac{1}{2} & 1 \\
\frac{3}{4} & \frac{1}{5}
\end{array}\right|\)
ସମାଧାନ :
(i) \(\left|\begin{array}{ll}
2 & 5 \\
6 & 0
\end{array}\right|\) = 2(0) – 6(5) = 0 – 30 = -30

(ii) \(\left|\begin{array}{ll}
2 & -1 \\
3 & 2
\end{array}\right|\) = 2 × 2 – 3 (-1) = 4 + 3 = 7

(iii) \(\left|\begin{array}{ll}
0 & 4 \\
5 & -1
\end{array}\right|\) = 0(-1) – 5 × 4 = 0 – 20 = -20

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

(iv) \(\left|\begin{array}{ll}
\frac{1}{2} & 1 \\
\frac{3}{4} & \frac{1}{5}
\end{array}\right|\) = \((\frac{1}{2})(\frac{1}{5})-(\frac{3}{4})(1)=\frac{1}{10}-\frac{3}{4}=\frac{2-15}{20}=\frac{-13}{20}\)

Question 6.
Cramer ଙ୍କ ନିୟମ ପ୍ରୟୋଗ କରି ନିମ୍ନ ସହସମୀକରଣମାନଙ୍କର ସମାଧାନ କର ।
(i) 2x + 3y = 5, 3x + y = 4
(ii) x + y = 3, 2x + 3y = 8
(iii) x – y = 0, 2x + y = 3
(iv) 2x – y = 3, x – 3y = -1
ସମାଧାନ :
(i) \(\Delta=\left|\begin{array}{ll}
a_1 & b_1 \\
a_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
2 & 3 \\
3 & 1
\end{array}\right|=2 \times 1-3 \times 3=2-9=-7\)
ଏଠାରେ ∆ ≠ 0 ତେଣୁ ସମୀକରଣର ସମାଧାନ ସମ୍ଭବ ।
\(∆_x=\left|\begin{array}{ll}
-c_1 & b_1 \\
-c_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
5 & 3 \\
4 & 1
\end{array}\right|=5 \times 1-4 \times 3=5-12=-7\)
\(∆_y=\left|\begin{array}{ll}
a_1 & -c_1 \\
a_2 & -c_2
\end{array}\right|=\left|\begin{array}{ll}
2 & 5 \\
3 & 4
\end{array}\right|=2 \times 4-5 \times 3=8-15=-7\)
x = \(\frac{∆_x}{∆}=\frac{-7}{-7}=1\), y = \(\frac{∆_y}{∆}=\frac{-7}{-7}=1\)
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (1, 1)

(ii) \(\Delta=\left|\begin{array}{ll}
a_1 & b_1 \\
a_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
1 & 1 \\
2 & 3
\end{array}\right|=1 \times 3-2 \times 1=3-2=1\)
ଏଠାରେ ∆ ≠ 0 ତେଣୁ ସମୀକରଣର ସମାଧାନ ସମ୍ଭବ ।
\(∆_x=\left|\begin{array}{ll}
-c_1 & b_1 \\
-c_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
3 & 1 \\
8 & 3
\end{array}\right|=3 \times 3-8 \times 1=9-8=1\)
\(∆_y=\left|\begin{array}{ll}
a_1 & -c_1 \\
a_2 & -c_2
\end{array}\right|=\left|\begin{array}{ll}
1 & 3 \\
2 & 8
\end{array}\right|=1 \times 8-2 \times 3=8-6=2\)
x = \(\frac{∆_x}{∆}=\frac{1}{1}=1\), y = \(\frac{∆_y}{∆}=\frac{2}{1}=2\)
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (1, 2)

(iii) \(\Delta=\left|\begin{array}{ll}
a_1 & b_1 \\
a_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
1 & -1 \\
2 & 1
\end{array}\right|=1 \times 1-2 \times -1=1+2=3\)
∆ ≠ 0 ତେଣୁ ସହ-ସମୀକରଣର ସମାଧାନ ସମ୍ଭବ ।
\(∆_x=\left|\begin{array}{ll}
-c_1 & b_1 \\
-c_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
0 & -1 \\
3 & 1
\end{array}\right|=0 \times 1-3 \times -1=0+3=3\)
\(∆_y=\left|\begin{array}{ll}
a_1 & -c_1 \\
a_2 & -c_2
\end{array}\right|=\left|\begin{array}{ll}
1 & 0 \\
2 & 3
\end{array}\right|=1 \times 3-2 \times 0=3-0=3\)
x = \(\frac{∆_x}{∆}=\frac{3}{3}=1\), y = \(\frac{∆_y}{∆}=\frac{3}{3}=1\)
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (1, 1)

BSE Odisha 10th Class Maths Solutions Algebra Chapter 1 ସରଳ ସହସମୀକରଣ Ex 1(b)

(iii) \(\Delta=\left|\begin{array}{ll}
a_1 & b_1 \\
a_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
2 & -1 \\
1 & -3
\end{array}\right|=2 \times (-3)-1 \times (-1)=-6+1=-5\)
∆ ≠ 0 ତେଣୁ ସହ-ସମୀକରଣର ସମାଧାନ ସମ୍ଭବ ।
\(∆_x=\left|\begin{array}{ll}
-c_1 & b_1 \\
-c_2 & b_2
\end{array}\right|=\left|\begin{array}{ll}
3 & -1 \\
-1 & -3
\end{array}\right|=3 \times -3-(-1) \times -1=-9-1=-10\)
\(∆_y=\left|\begin{array}{ll}
a_1 & -c_1 \\
a_2 & -c_2
\end{array}\right|=\left|\begin{array}{ll}
2 & 3 \\
1 & -1
\end{array}\right|=2 \times -1-1 \times 3=-2-3=-5\)
x = \(\frac{∆_x}{∆}=\frac{-10}{-5}=1\), y = \(\frac{∆_y}{∆}=\frac{-5}{-5}=1\)
∴ ନିର୍ଣ୍ଣେୟ ସମାଧାନ (x, y) = (2, 1)

BSE Odisha 10th Class Hindi Solutions Poem 1(c) तुलसीदास के दोहे

Odisha State Board BSE Odisha 10th Class Hindi Solutions Poem 1(c) तुलसीदास के दोहे Textbook Exercise Questions and Answers.

BSE Odisha Class 10 Hindi Solutions Poem 1(c) तुलसीदास के दोहे

प्रश्न और अभ्यास (ପ୍ରଶ୍ନ ଔର୍ ଅଭ୍ୟାସ)

1. निम्नलिखित प्रश्नों के उत्तर दो-तीन वाक्यों में दीजिए।
(ନିମ୍ନଲିଖୂ ପ୍ରଶ୍ନୋ କେ ଉତ୍ତର ଦୋ-ତୀନ୍ ୱାର୍କୋ ମେଁ ଦୀଜିଏ।)
(ନିମ୍ନଲିଖ ପ୍ରଶ୍ନର ଉତ୍ତର ଦୁଇ-ତିନୋଟି ବାକ୍ୟରେ ଦିଅ।)

(क) कठोर वचन का क्यों परिहार करना चाहिए?
(କଠୋର୍ ବଚନ୍ କା ର୍ଯ୍ୟା ପରିହାର୍ କର୍‌ନା ଚାହିଏ?)
उत्तर:
कठोर वचन सबको दुःख पहुँचाता है। परिवेश को अशान्त कर देता है। कठोर वचन से दूसरों को पीड़ा पहुचती है इसलिए कठोर वचन को परिहार करके मीठे वचन बोलना चाहिए।

(ख) मीठे वचन से क्या लाभ होता है?
(ମୀଠ ବଚନ୍ ସେ କ୍ୟା ଲାଭ୍ ହୋତା ହୈ ?)
उत्तर:
मीठे वचन सबको प्रिय होते हैं। मीठी वाणी से हम सबको अपने वश में कर सकते हैं। मीठी वाणी से चारों ओर शांति बनी रहती है। सबको सुख मिलता है।

(ग) सन्तोष धन के सामने कौन-कौन से धन धूरि के बराबर माने जाते हैं?
(ସନ୍ତୋଷ୍ ଧନ୍ କେ ସାମ୍‌ନେ କୌନ୍-କୌନ୍ ସେ ଧନ୍ ଧୂରି କେ ବରାବର୍ ମାନେ ଜାତେ ହୈ ?)
उत्तर:
सन्तोष धन के सामने गोधन, गजधन, बाजीधन, रतनधन आदि धन धूरि के बराबर माने जाते हैं। क्योंकि इस प्रकार के धन से सुख शांति नहीं मिलती। मन चिंतित रहता है।

(घ) रोष या गुस्से के समय क्या नहीं खोलना चाहिए और क्यों?
(ରୋଷ୍ ୟା ଗୁସ୍‌ କେ ସମୟ କ୍ୟା ନହୀ ଖୋଲ୍‌ନା ଚାହିଏ ଔର୍ କ୍ୟା?)
उत्तर:
रोष या गुस्से के समय जीभ नहीं खोलनी चाहिए। क्योंकि क्रोध में मनुष्य कड़वी बातें बोल जाता है। कड़वी बातें तलवार से भी अधिक घाव कर देती है।

(ङ) मीठे वचन की तुलना वशीकरण मन्त्र से क्यों की गई है?
(ମୀଠ ବଚନ୍ କୀ ତୁଲନା ବଶୀକରଣ୍ ମନ୍ତ୍ର ସେ କୈ କୀ ଗଈ ହୈ ?)
उत्तर:
मीठे वचन की तुलना वशीकरण मन्त्र से की गई है क्योंकि मीठे वचन से हम सबको अपने वश में कर सकते हैं। मीठे वचन सबको प्रिय होते हैं, इससे सबको शांति और सुख मिलता हैं।

(च) हमें सोच विचार कर क्यों बोलना चाहिए?
(ହର୍ମେ ସୋଚ୍ ବିଚାର୍ କର୍ ଜ୍ୟୋ ବୋଲନା ଚାହିଏ ?)
उत्तर:
हमें सोच विचार कर हमेशा बोलना चाहिए। क्योंकि क्रोध में मनुष्य कड़वी बातें बोल जाता है। ये कड़वी बातें तलवार से भी अधिक घाव करती है। इसका प्रहार सीधे हृदय और मन पर होता है। मधुर वचन का परिणाम मधुर होता है।

निम्नलिखित अवतरणों का आशय दो-तीन वाक्यों में स्पष्ट कीजिए।
(ନିମ୍ନଲିଖ୍ ଅବତରର୍ଡୋ କା ଆଶୟ ଦୋ-ତୀନ୍ ୱାର୍କୋ ମେଁ ସ୍ପଷ୍ଟ କୀଜିଏ ।)
(ତଳଲିଖ୍ ଅବତରଣଗୁଡ଼ିକର ଆଶୟ ଦୁଇ-ତିନି ବାକ୍ୟରେ ସ୍ପଷ୍ଟ କର ।)

(क) तुलसी मीठे वचन ते, सुख उपजत चहुँओर।
(ତୁସୀ ମୀଠେ ବଚନ୍ ତେ, ସୁଖ୍ ଉପଜତ୍ ଚହୁଁଓର ।)
उत्तर:
इस पंक्ति में तुलसीदास यह बतलाते हैं कि मीठ वचन से सबको सुख मिलता है। चारों ओर शांति बनी रहती है। मीठे वचन सबको प्रिय होते हैं।

(ख) जब आवे सन्तोष धन, सब धन धूरि समान।
(ଜବ୍ ଆୱେ ସନ୍ତୋଷ୍ ଧନ୍, ସବ୍ ଧନ୍ ଧୂରି ସମାନ୍ ।)
उत्तर:
इस पंक्ति में कवि ने यह कहा है कि सन्तोष धन के सामने सब धन धूल के समान है। क्योंकि इस प्रकार के धन से सुख शांति नहीं मिलती, मन चिंतित रहता है।

(ग) रोष न रसना खोलिए, बरु खोलिओ तलवारि।
(ରୋସ୍ ନ ରସ୍‌ନା ଖୋଲିଏ ବରୁ ଖୋଲିଓ ତଲବାରି ।)
उत्तर:
गुस्से में जीभ नहीं खोलनी चाहिए। क्योंकि गुस्से में मनुष्य आपे से बाहर हो जाता है और कड़वी बातें बोल जाता है। ये कड़वी बाते दिल और मन को घायल करके अधिक कष्ट देती है।

3. निम्नलिखित प्रश्नों के उत्तर एक-एक वाक्य में दीजिए।
(ନିମ୍ନଲିଖତ୍ ପ୍ରକ୍ଷ୍ନୌ କେ ଉତ୍ତର୍ ଏକ୍-ଏକ୍ ୱାର୍କୋ ମେଁ ଦୀଜିଏ ।)
(ତଳଲିଖ ପ୍ରଶ୍ନଗୁଡ଼ିକର ଉତ୍ତର ଗୋଟିଏ-ଗୋଟିଏ ବାକ୍ୟରେ ଦିଅ ।)

(क) किससे चारों ओर सुख उपजता है?
(କିସ୍‌ ଚାର୍ରେ ଓର ସୁଖ୍ ଉପଚ୍ଚତା ହୈ ?)
उत्तर:
मीठे वचन से चारों ओर सुख उपजाता है।

(ख) वशीकरण का मंत्र क्या है?
(ବଶୀକରଣ୍ କା ମନ୍ତ୍ର କ୍ୟା ହୈ ?)
उत्तर:
मीठे वचन वशीकरण का मंत्र है।

(ग) हमें क्या परिहार करना या छोड़ना चाहिए?
(ହର୍ମେ କ୍ୟା ପରିହାର୍ କର୍‌ନା ୟା ଛାଡୁନା ଚାହିଏ?)
उत्तर:
हमें कटु वचन को परिहार करना या छोड़ना चाहिए।

(घ) कवि ने सन्तोष की तुलना किस से की है?
(କବି ନେ ସନ୍ତୋଷ୍ କୀ ତୁଲନା କିସ୍ ସେ କୀ ହୈ ?)
उत्तर:
कवि ने सन्तोष की तुलना धन से की है।

(ङ) कब रसना नहीं खोलनी चाहिए?
(କବ୍ ରସ୍‌ନା ନହୀ ଖୋଲ୍‌ନୀ ଚାହିଏ?)
उत्तर:
अधिक गुस्से में रसना नहीं खोलनी चाहिए।

(च) किस धन के सामने सारे धन तुच्छ माने जाते हैं ?
(କିସ୍ ଧନ୍ କେ ସାମ୍‌ ସାରେ ଧନ୍ ତୁଚ୍ଛ ମାନେ ଜାତେ ହେଁ ?)
उत्तर:
संतोष धन के सामने सारे धन तुच्छ माने जाते हैं।

(छ) सन्तोष धन के सामने सब धन किसके समान होते हैं?
(ସନ୍ତୋଷ୍ ଧନ୍ କେ ସାମ୍‌ ସବ୍ ଧନ୍ କିସ୍କେ ସମାନ୍ ହୋତେ ହେଁ ?)
उत्तर:
सन्तोष धन के सामने सब धन धूल के समान होते हैं।

(ज) विचार करके वचन कहने से क्या होता है?
(ବିଚାର୍ କର୍‌କେ ବଚନ୍ କହନେ ସେ କ୍ୟା ହୋତା ହୈ ?)
उत्तर:
विचार करके वचन कहने से उसका परिणाम मधुर होता है।

भाषा-ज्ञान (ଭାଷା-ଜ୍ଞାନ)

1. निम्नलिखित शब्दों के विपरीत शब्द लिखिए । ( 160 61 ।)
(ନିମ୍ନଲିଖ୍ ଶବ୍ଦଗୁଡ଼ିକର ବିପରୀତ ଶବ୍ଦ ଲେଖ ।)
मीठा, सुख, कठोर, छोड़ना, समान, खोलना
उत्तर:
मीठा – कड़वा/खट्टा
कठोर – मृदु/कोमल
समान – असमान
सुख – दुःख
छोड़ना – पकड़ना
खोलना – बंद करना

2. निम्नलिखित शब्दों के समानार्थक शब्द लिखिए।
(ନିମ୍ନଲିଖତ୍ ଶବ୍ଦା କେ ସମାନାର୍ଥକ ଶବ୍ଦ ଲିଖିଏ।)
(ନିମ୍ନଲିଖ୍ ଶବ୍ଦଗୁଡ଼ିକର ସମାନାର୍ଥୀ ଶବ୍ଦ ଲେଖ )
वचन, सुख, कठोर, उपजना, गो, गज, बाजि
उत्तर:
वचन – वाणी/बात
कठोर – निर्दयी
गो – गाय/गऊ
सुख – आनन्द
उपजना – पैदा होना/जन्म होना
गज – हाथी

3. निम्नलिखित शब्दों के प्रयोग से सार्थक वाक्य बनाइए।
(ନିମ୍ନଲିଖତ୍ ଶବ୍ଦା କେ ପ୍ରୟୋଗ୍ ସେ ସାର୍ଥକ ବାକ୍ୟ ବନାଇଏ ।)
(ନିମ୍ନଲିଖ୍ ଶବ୍ଦଗୁଡ଼ିକର ପ୍ରୟୋଗ କରି ସାର୍ଥକ ବାକ୍ୟ ଗଠନ କର।)
वसीकरण, कठोर, गोधन, सन्तोष, तलवार
उत्तर:
वसीकरण – मीठे वचन तो वशीकरण मंत्र के समान हैं।
कठोर – राहुल अत्यन्त कठोर स्वभाव का है।
गोधन – यशोदा गोधन की कसम खाकर कहती हैं कि कृष्ण ही उनका पुत्र है।
संन्तोष – सन्तोष रूपी धन के सामने बाकी सारा धन तुच्छ है।
तलवार – तलवार शरीर पर घाव करती है मगर कड़वी बातें दिल पर घाव कर देती हैं।

4. निम्नलिखित शब्दों के शुद्ध रूप लिखिए।
(ନିମ୍ନଲିଖତ୍ ଶବ୍ଦା କେ ଶୁଦ୍ଧ ରୂପ ଲିଖିଏ।)
(ନିମ୍ନଲିଖ୍ ଶବ୍ଦଗୁଡ଼ିକର ଶୁଦ୍ଧ ରୂପ ଲେଖ।)
चहुँओर, वसीकरण, धूरि, तरवारि, परिनाम
उत्तर:
चहुँओर – चारों ओर
तरवारि – तलवार
वसीकरण – वशीकरण
धूरि – धूल/धूलि
परिनाम – परिणाम

5. निम्नलिखित शब्दों के साथ करण कारक ‘से’ चिह्न का प्रयोग करके वाक्य बनाइए:
(ନିମ୍ନଲିଖ୍ ଶବ୍ଦା କେ ସାଥ୍ କରଣ୍ କାରକ୍ ‘ସେ’ ଚିହ୍ନ କା ପ୍ରୟୋଗ କର୍‌କେ ବାକ୍ୟ ବନାଇଏ)
(ନିମ୍ନଲିଖତ ଶବ୍ଦଗୁଡ଼ିକ ସହିତ କରଣ କାରକ ‘ସେ’ ଚିହ୍ନର ପ୍ରୟୋଗ କରି ବାକ୍ୟ ଗଠନ କର )
वचन, मंत्र, धन, तलवार
उत्तर:
वचन – मीठे वचन से सबको सुख मिलता है।
मंत्र – वशीकरण मंत्र से सभी को वश में किया जा सकता है।
धन – धन से सुख नहीं मिलता।
तलवार – तलवार से मत खेलो।

Very Short & Objective type Questions with Answers

A. निम्नलिखित प्रश्नों के उत्तर एक वाक्य में दीजिए।

1. तुलसीदास का जन्म कब और कहाँ हुआ?
उत्तर:
तुलसीदास का जन्म सन् 1532 में उत्तर प्रदेश के राजापुर में हुआ।

2. तुलसीदास के गुरु कौन थे?
उत्तर:
श्री नरहरि दास तुलसीदास के गुरु थे

3. तुलसी जी किस-किस भाषा में लिखते थे?
उत्तर:
तुलसी जी अवधी और ब्रजभाषा में लिखते थे।

B. निम्नलिखित प्रश्नों के उत्तर एक शब्द / एक पद में दीजिए।

1. संतोष-धन आ जाता है तो बाकी सब धन किसके समान हो जाते हैं?
उत्तर:
धूल के

2. किसका परिणाम हितकर होता है?
उत्तर:
वशीकरण का

3. तुलसी ने श्रेष्ठ धन किसे कहा है?
उत्तर:
संतोष

4. तुलसीदास क्या परिहार करने को कहते हैं?
उत्तर:
कठोर वचन

5. जो वाणी सुनने में मधुर लगती है, उसका परिणाम क्या होता है?
उत्तर:
हितकर

6. किस अवस्था में रसना नहीं खोलनी चाहिए?
उत्तर:
गुस्से के समय

7. कवि तुलसीदास के अनुसार वशीकरण मंत्र का अर्थ क्या है?
उत्तर:
मीठी वाणी से सबको वश में करना

8. रोष के समय क्या नहीं खोलनी चाहिए ?
उत्तर:
रसना

9. हमे किस प्रकार की वाणी बोलनी चाहिए?
उत्तर:
मीठी

10. ‘परिनाम’ का अर्थ क्या है?
उत्तर:
परिणाम

C. रिक्त स्थानों की पूर्ति कीजिए।

1. विचार करके वचन बोलने से परिणाम ……………… होता है।
उत्तर:
हितकर

2. ………………… सी बात तलवार से अधिक घाव करती है।
उत्तर:
कड़वी

3. कड़वी बातें. ……………. घायल करती है।
उत्तर:
मन को

4. वशीकरण मंत्र ……………….. है।
उत्तर:
मधुर वाणी

5. तुलसी जी के गुरु ………………… है।
उत्तर:
रामानन्द

6. ………………… में रसना नहीं खोलनी चाहिए।
उत्तर:
अधिक गुस्से

7. तुलसी ने सन्तोष की तुलना …………………. से की है।
उत्तर:
धन

8. ………………. से चारों ओर सुख उपजता है।
उत्तर:
मिठे वचन

9. ………………. के सामने सारे धन तुछ माने जाते है।
उत्तर:
संन्तोष धन

10 ‘बरु’ का अर्थ है…………….. ।
उत्तर:
बल्कि

D. ठिक् या भूल लिखिए।

1. संतोष धन के आने से सारे धन धूल के समान हो जाते हैं।
उत्तर:
ठिक्

2. तुलसी के अनुसार विचार करके घूमना चाहिए।
उत्तर:
भूल

3. तलवार से रसना घातक होती है।
उत्तर:
ठिक्

4. चुटकुले चारों ओर सुख उपजाने में सहायक हैं।
उत्तर:
भूल

5. मीठे वचनों से सुख मिलता है।
उत्तर:
ठिक्

6. विचार करके कहानी कहना जरुरी है।
उत्तर:
भूल

7. ‘रामचरित मानस’ तुलसीदास ने लिखा है।
उत्तर:
भूल

8. बाजिधन के सामने सारे धन तुच्छ हैं
उत्तर:
ठिक्

9. ‘बाजी’ का अर्थ हाथी है।
उत्तर:
भूल

10. विनय पत्रिका तुलसीदास की रचना है।
उत्तर:
ठिक्

11. कवि ने संन्तोष की तुलना धन से की है।
उत्तर:
ठिक्

Multiple Choice Questions (mcqs) with Answers

सही उत्तर चुनिए : (MCQS)

1. संतोष-धन आ जाता है तो बाकी सब धन किसके समान हो जाते हैं?
(A) धूल के
(B) बाजि के
(C) रतन के
(D) प्राण के
उत्तर:
(A) धूल के

2. किसका परिणाम हितकर होता है?
(A) कटु वचन का
(B) रत्न-धन का
(C) वशीकरण का
(D) मधुर वचन का
उत्तर:
(C) वशीकरण का

3. तुलसी ने श्रेष्ठ धन किसे कहा है?
(A) रत्न-धन को
(B) राम – रत्न को
(C) संतोष-धन को
(D) सोने-चाँदीको
उत्तर:
(C) संतोष-धन को

4. तुलसीदास क्या परिहार करने को कहते हैं?
(A) कुसंग
(B) चिंत
(C) कामना
(D) कठोर वचन
उत्तर:
(D) कठोर वचन

5. जो वाणी सुनने में मधुर लगती है, उसका परिणाम क्या होता है?
(A) हितकर
(B) अहितकर
(C) भयानक
(D) खुशामद
उत्तर:
(A) हितकर

6. चहुँओर सुख उपजाता है।
(A) मीठे वचन से
(B) कटुवचन से
(C) अल्प वचन से
(D) धीमे वचन से
उत्तर:
(A) मीठे वचन से

7. तुलसीदास के अनुसार सबसे बड़ा धन है।
(A) गोधन
(B) गज धन
(C) संतोष धन
(D) रतन धन
उत्तर:
(C) संतोष धन

8. किस अवस्था में रसना नहीं खोलनी चाहिए।
(A) गुस्से के समय
(B) शान्ति के समय
(C) खाते समय
(D) राते समय
उत्तर:
(A) गुस्से के समय

दोहे (ଦୋହେ)

(i) तुलसी मीठे बचन ते, सुख उपजत चहुँओर।
वसीकरण यह मंत्र है, परिहरु बचन कठोर॥
ତୁଲସୀ ମୀଠେ ବଚନ୍ ତେ, ସୁଖ୍ ଉପଜତ ଚହୁଁଓର।
ବସୀକରଣ ୟହ ମନ୍ତ୍ର ହୈ, ପରିହରୁ ବଚନ୍ କଠୋର୍॥

हिन्दी व्याख्या:
तुलसीदास कहते हैं कि मीठे वचन सबको प्रिय होते हैं। मधुर वचन से हम सबको अपने वश में कर सकते हैं। मीठे वचन से चारों ओर शान्ति बनी रहती है। सबको सुख मिलता है। लेकिन कड़वी वाणी से सबको दुःख पहुँचता है। मीठे वचन तो वशीकरण मंत्र के समान है। इसलिए कड़वा वचन न बोलकर मीठे वचन बोलना चाहिए।

ଓଡ଼ିଆ ଅନୁବାଦ:
ମିଠା କଥା ସମସ୍ତଙ୍କୁ ଭଲ ଲାଗେ। ମିଠା କଥା କହି ଆମେ ସମସ୍ତଙ୍କୁ ଆପଣେଇ ପାରିବା। ମିଠା କଥାଦ୍ଵାରା ସବୁଆଡ଼େ ଶାନ୍ତି ଲାଗି ରହିଥାଏ। ସମସ୍ତଙ୍କୁ ସୁଖ ମିଳେ। କିନ୍ତୁ କଟୁକଥା ସମସ୍ତଙ୍କ ମନକୁ ଆଘାତ କରେ ଓ ଦୁଃଖ ଦିଏ। ମଧୁର ବଚନ ବଶୀକରଣ ମନ୍ତ୍ର ପରି। ଏଣୁ ଆମକୁ କଟୁ କଥା ନ କହି ମିଠା କଥା କହିବା ଦରକାର।

(ii) गोधन, गजधन, बाजिधन और रतनधन खान।
जब आवे सन्तोष धन सब धन धूरि समान॥
ଗୋଧନ୍, ଗଜଧନ୍, ବାଜିଧନ୍ ଔର୍ ରତନଧନ୍ ଖାନ୍।
ଜବ୍ ଆୱେ ସନ୍ତୋଷ୍ ଧନ୍, ସବ୍‌ ଧନ୍ ଧୂରି ସମାନ୍॥

हिन्दी व्याख्या :
कवि कहते हैं कि साधारणतः हमारी धारणा है कि जिसके पास पर्याप्त गाय-भैंस, हाथी और घोड़े होते हैं या धन रत्न आदि होते हैं, वह इस संसार में सबसे अधिक धनी है। लेकिन कवि के अनुसार ये सारे धन होते हुए भी अगर मन में सन्तोष नहीं है तो ये सबकुछ मूल्यहीन होता है। सन्तोष धन के सामने ये सब धन धूल के समान तुच्छ हैं। क्योंकि इस प्रकार के धन से सुख शान्ति नहीं मिलती। मन चिंतित रहता है।

ଓଡ଼ିଆ ଅନୁବାଦ:
ସାଧାରଣତଃ ଆମେ ଭାବିଥାଉ ଯେ ଯାହା ପାଖରେ ଗାଈ, ମଇଁଷି, ହାତୀ-ଘୋଡ଼ା ବା ଧନରତ୍ନ, ହୀରା-ମୋତି ଅଛି, ସେ ଜଣେ ବଡ଼ ଧନୀ ବ୍ୟକ୍ତି। କିନ୍ତୁ ତୁଳସୀ ଦାସଙ୍କ ଅନୁସାରେ ଏତେ ସବୁ ଧନ ଥାଇ ମଧ୍ୟ ଯଦି ତା’ମନରେ ଶାନ୍ତି ନାହିଁ ତାହାହେଲେ ସେ ଧନ ସବୁ ତା’ପାଇଁ ମୂଲ୍ୟହୀନ। ସନ୍ତୋଷ ରୂପୀ ଧନ ପାଖରେ ଏସବୁ ଧନରତ୍ନ ଧୂଳି ସଙ୍ଗେ ସମାନ ଓ ତୁଚ୍ଛ। ଏପରି ଧନ ସମ୍ପଦରେ ସୁଖ ଶାନ୍ତି ମିଳେ ନାହିଁ। ମନରେ ଚିନ୍ତା ଲାଗି ରହିଥାଏ।

(iii) रोष न रसना खोलिए, बरु खोलिओ तरबार।
सुनत मधुर परिनाम हित, बोलिओ बचन बिचारि॥
ରୋସ୍ ନ ରସନା ଖୋଲିଏ, ବରୁ ଖୋଲିଓ ତରବାରି।
ସୁନତ ମଧୁର୍ ପରିନାମ ହିତ, ବୋଲିଓ ବଚନ୍ ବିଚାରି॥

हिन्दी व्याख्या:
कवि तुलसीदास कहते हैं कि जब क्रोध अधिक हो तो जीभ नहीं खोलनी चाहिए। क्रोध में मनुष्य कड़वी बातें बोल जाता है। ये कड़वी बातें तलवार से भी अधिक घाव करती है। कड़वी बात का प्रहार सीधे दिल और दिमाग पर होता है। तलवार तो शरीर पर घाव करती है, लेकिन कड़वी बातें दिल और दिमाग को घायल करके अधिक कष्ट देती हैं।

ଓଡ଼ିଆ ଅନୁବାଦ :
ଯେତେବେଳେ ରାଗ ଅଧ୍ବକ ବଢ଼ିଚାଲେ ସେତେବେଳେ ଜିଭକୁ ନିୟନ୍ତ୍ରଣ ରଖିବାକୁ ପଡ଼ିବ। ରାଗରେ ମଣିଷ କଟୁ କଥା କହି ଚାଲିଥାଏ। ଏହି କଟୁ କଥା ଖଣ୍ଡାଠାରୁ ମଧ୍ୟ ଅଧିକ ଆଘାତ କରିଥାଏ। କଟୁ କଥାର ପ୍ରହାର ସିଧା ମନ ଓ ହୃଦୟ ଉପରେ ପଡ଼ିଥାଏ। ଖଣ୍ଡାର ଚୋଟରେ ଶରୀରରେ କ୍ଷତ ହୋଇଥାଏ। କିନ୍ତୁ କଟୁ କଥା ମନ ଓ ହୃଦୟକୁ ଆଘାତ କରେ ଏବଂ ଅଧିକ କଷ୍ଟ ଦିଏ।

शबनार: (ଶରାର୍ଥି)

मीठे – मीठा/मधुर (ମିଠା/ମଧୁର )।

उपजत – उपजना/पैदा होना (ଜନ୍ମହେବା/ଉପୁଜିବା)।

चहुँओर – चारों ओर (ଚାରିଆଡ଼େ)।

परिहरु – त्यागना/परित्याग करना (ତ୍ଯାଗ କରିବା)।

गोधन – गाय रूपी धन (ଗୋଧନ)।

बाजि – घोड़ा (ଘୋଡ଼ା)

ते – से/द्वारा (ଦ୍ଵାରା)।

वसीकरण – वशीभूत (ହାତି)।

गज – हाथी (ରତ୍ନ)।

रतन – रत्न (ବଶୀଭୂତ)।

खान – भंड़ार (ଭଣ୍ଡାର)।

धूरि – धूल यूरिकि)। (ଧୂଳି)।

रसना – जीभ (ଜିଭ)।

खोलिओ – खोले (ଖୋଲିବା)।

परिनाम – परिणाम (ପରିଣାମ)।

सुनत – सुनकर (ଶୁଣି)।

विचारि – विचार करके (ବିଚାର କରି)।

आवे – आए (ଆସେ)।

रोष – गुस्सा (ରାଗ)।

बरु – बल्कि ( ବରଂ)।

तरवारि – तलवार (ଖଣ୍ଡା)।

हित – मंगल (ହିତମଙ୍ଗଳ)।

बोलिअ – बोलो (କୁହ)।

कवि परिचय

भक्त कवि तुलसी दास का जन्म सन् 1532 में उत्तर प्रदेश के राजापुर में हुआ था और देहांत सन् 1633 में। पितामाता के स्नेह से वंचित होकर बचपन में उनको बड़ा कष्ट उठाना पड़ा। सौभाग्य से गुरु नरहरिदास ने उनकी बड़ी मदद की। तुलसी रामभक्त थे और यौवन काल में ही साधु बन गये। रामानंद उनके गुरु थे। वे हिन्दी और संस्कृत के बड़े पंड़ित थे। उस समय मुगलों का शासन था। देश की सामाजिक और धार्मिक परिस्थितियाँ अस्तव्यस्त थीं।

तुलसी दास ने रामचरित मानस लिखकर लोगों के सामने निष्कपट जीवन और आचरण का उदाहरण रखा। आज भी यह देश का अत्यंत लोकप्रिय ग्रंथ है। जन साधारण उसे बड़े चाव से पढ़ते हैं। दुःखी, निराश तथा भक्त लोगों को रामचरितमानस पढ़कर सुख शान्ति मिलती है। विनयपत्रिका, कवितावली, दोहावली, गीतावली आदि उनके अनेक ग्रंथ हैं। वे अवधी और ब्रजभाषा दोनों में लिखते थे।