Class 11

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 16 Probability Ex 16(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 16 Probability Exercise 16(b)

Question 1.
A school has six classes 1, 2, 3, 4, 5, and 6. Classes 2, 3, 4, 5, and 6 each have the same number of students, but there is twice this number in class 1. If a student is selected at random from the school, what is the probability that he(she) will be in
Solution:
A school has six classes 1, 2, 3, 4, 5, and 6. Classes 2, 3, 4, 5, and 6 each have the same number of students, but there is twice this number in class 1.
Let the number of students in class 2, 3, 4, 5, and 6 is x each and the number of students in class 1 is 2x.
∴ The total number of students = 7x.
A student can be chosen from 7x students in ^7xC₁ = 7x ways.
∴ |S| = 7x.

(i) class 1
Solution:
Probability that the student belongs to class 1, is \(\frac{2 x}{7 x}=\frac{2}{7}\)

(ii) class 2
Solution:
Probability that the student belongs to class 2, is \(\frac{x}{7 x}=\frac{1}{7}\)

Question 2.
Let a die be weighed in such a way that the probability of getting a number n is proportional to n.
Solution:
Let a die be weighed in such a way that the probability of getting a number n is proportional to n.
Let the constant of proportionality be k.
∴ P(n) = nk so that P(1) = k
P(2) = 2k, P(3) = 3k,…. P(6) = 6k
∴ P(1) + P(2) +…….+ P(6) = 1
or, k + 2k +……..+ 6k = 1
or, 21 k = 1 or, k = \(\frac{1}{21}\)

(i) Find the probability of each elementary event.
Solution:
P(1) = \(\frac{1}{21}\), P(2) = \(\frac{2}{21}\), P(3) = \(\frac{3}{21}\), P(4) = \(\frac{4}{21}\), P(5) = \(\frac{5}{21}\) , P(6) = \(\frac{6}{21}\)

(ii) Find the probability of getting an even number in a single roll of the die.
Solution:
= P(2) + P(4) + P(6)
= \(\frac{2}{21}+\frac{4}{21}+\frac{6}{21}=\frac{12}{21}\)

(iii) Find the probability of getting a prime number in a single roll of the die.
Solution:
= P(1) + P(3) + P(5)
= \(\frac{1}{21}+\frac{3}{21}+\frac{5}{21}=\frac{9}{21}\)

(iv) Find the probability of getting a prime number in a single roll of a die.
Solution:
Probability of getting a prime number = P(3) + P(5) + P(2)
= \(\frac{3}{21}+\frac{5}{21}+\frac{2}{21}=\frac{10}{21}\)

Question 3.
Five boys and three girls are playing in a chess tournament. All boys have the same probability p of winning the tournament and all the girls have the same probability q of winning. If p = 2q, find the probability that
(i) a boy wins the tournament.
(ii) a girl wins the tournament.
Solution:
5 boys and 3 girls are playing a chess tournament. All boys have the same probability P of winning the tournament and all the girls have the
same probability q of winning.
We have P(B) =p, P(G) = q.
As there are 5 boys and 3 girls,
we have 5p + 3q = 1
Now putting p = 2q,
we have 10q + 3q = 1
or, q = \(\frac{1}{13}\) ∴ p = 2q = \(\frac{2}{13}\)
∴ P(B) = 5p = \(\frac{10}{13}\),
∴ P(G) = 3p = \(\frac{3}{13}\)

Odisha State Board CHSE Odisha Class 11 Invitation to English 3 Solutions Writing Argument or Persuasion Textbook Activity Questions and Answers.

CHSE Odisha 11th Class English Writing Argument or Persuasion

2.4 Argument And Persuasion

Argument is that form of writing the main purpose of which is to persuade your readers (or listeners) to adopt a certain attitude, point of view, or course of action.

Read the following views, expressed by six different speakers, on the importance of English in India, in a debate in Femina.

a. Years ago the sun did not set on the British Empire, but the sons and daughters of India still speak English. ‘Please’ and ‘sorry’ are very much a part of our vocabulary. In most’states higher education is imparted in the English language. The white man’s language still holds the same fascination today as they did a century ago. More Indians are speaking and writing in English than ever before. A separate class of Indo-English writers, acclaimed internationally, exists today. Telephone directories, advertisements, films, music, etc. are in English. Hence, the language has been integrated into our culture.

b. English is an important language in India today. For all important business transactions, paperwork and documentations is in English (like banking, shares, certificates). The gifts we have received from the British are the postal and telegraph services, railways and the English language. As the industrial revolution first took place in England, most of the mechanical engineering terminology is in English. For instance, there is no Hindi equivalent for the term ‘internal combustion’. It is very important to know English.

c. Knowledge of English language has helped me to communicate not only with my audience abroad but even with Indians of various states. English is an Indian language. If Indian states try and promote their languages, there is nothing wrong in it. But at the same time, English language and literature should not be neglected. It is an interesting language with a rich literature.

d. English is an Indian language. Any Indian who is slightly educated understands English, It is the langauge of science and technology. It connects us with the world. In India, people who know English often dominate non- English speaking Indians. There is no harm in learning and speaking in English, but to follow western culture along with the language is not appropriate.

e. English is one of the languages spoken by Indians. But it is wrong to believe that to achieve or to get a job one must know English. Most people in India feel that to earn their bread they should know English. In Germany, China and Japan people hardly understand English. Among the Indians the ‘mental slavery’ to English still exists.

f. It is a wrong belief that English is an important Indian language. Only two percent of Indian speak it. In fact, it is a language that often leads to complexes. I remember very well when the well-known Russian writer. Rasool Humzatov came to Delhi and narrated his poems, not in English or Russian, but in the regional language. Because he was proud of it. We Indians do not have enough respect and love for our language. Personality, even when I meet people who are well-versed in English, I speak in Hindi.

It is important to dispel the guilt complexes regarding Indian languages, that all of us have.
The main points raised by the speakers are noted below.
(i) English is the language of higher education.
(ii) The language of international communication.
(iii) Only 2% Indians speak English.
(iv) The language of science and technology.
(v) The belief that one can easily get a job or achieve success is not always true.
(vi) People in China, Japan and Germany hardly understand English.
(vii) Self-respecting people respect their mother tongue/dialect.
(viii) People in India need English.
(ix) Early education of a child must be in the mother tongue.
(x) Indian languages including Indian culture get neglected.
(xi) Language of communication inside India.
(xii) Language of business, commerce and advertisement.

Note that some of the arguments are in favour of English and others against English. Put them in two separate columns, as suggested below. The first one has been done for you. Think, and add your own points.

Answer:

Activity 36

We have a number of arguments here, both for and against English. Can you now reach a definite position of your own, after considering both sets of arguments ? Try to produce your own arguments to counter those presented by the speakers : for example, you could argue that English can be replaced by Hindi for the purposes of communication within India, etc. Write a paragraph on any one of these points.

Answer:
One of the main arguments in favour English is that people in India need English. But, in my view, this is not correct. We should know that people in China, Japan and Germany hardly understand English. Nevertheless, they are more prosperous than India. Of course, lately China has felt the importance of English. English is a foreign language and not one of the soil. Only 2% Indians speak English. English has become a medium of education in our colleges and universities.

This is doing an incalculable harm to the proper intellectual growth of students. A fast majority of students fail to understand the lessons imparted through English. The very thinking and understanding of the student is stunted under the weight of an incomprehensible language. The spread of English also hinders the growth of Indian culture. Lastly, though not the least, it can be said that there should be an end to ‘the mental slavery’ that still exists among the Indians.

Activity 37

(i) Given below are some of the views expressed by different speakers on the topic “The Reading habit is dying out” in Femina. Read through each of them.
(ii) Note that some speakers accept the proposition while others reject it. There is one speaker who offers suggestions to improve the reading habits of children. Try to identify the main points in each speech and arrange them under three headings :
(1) in favour of the proposition
(2) against the proposition and
(3) suggestions.
(iii) Add your own points. Be clear about the points you support and those which you do not support.
(iv) Before you start writing on the topic, think of an appropriate beginning. For this, see how the speakers begin their speeches. It will help you in starting your paragraph.

Now read the following speeches.

(a) I agree that reading is a dying habit. A lot has been already written about how television is rapidly stealing a march over reading. The sale of books is diminishing, while the launching of a new television channel has become a regular affair. A lot of children find other ways of passing their leisure hours because they have simply not discovered the wonderland of books and the pleasure it offers. At the age of two or three, they are taught how to read, but as they grow older, they are not taught to use reading for entertainment, information, and knowledge.

Brought up on a diet of textbooks, the child does not get to read anything else. Naturally, when a child finds that the textbooks he/she reads are dull and boring, he/she never feels like reading anything else. There is no addiction more pleasurable than getting hooked on books. Parents should encourage their children to read, but let me point out that most adults don’t read themselves; a cursory glance at the day’s newspaper is all the reading they seem to do. How can they expect their children to develop the habit of reading, when they themselves sit down in front of the TV set in their free time ?

(b) It is definitely true that reading is a dying habit, and one of the major reasons for this decline is the advent of the electronic medium. Even the reading of newspapers has been limited to that headlines and few introductory paragraphs. If one gets the news and can watch a few soap operas for entertainment just by pressing a few buttons, why should anyone then take the trouble of reading? But that’s very sad for we’re losing the very flavor of life.

Just sitting like robots in front of a box that gives us information like robots, like listening to it, watching it — these things kill our intellectual faculties. We’ve failed to realize that the lasting impact on the mind can be provided by the written word alone. Reading gives one time to ponder over things and it enriches our vocabulary too.

(c) The habit of reading is increasing day by day. There is a boom in publishing in India, and our sales have doubled in the last few years. Indian authors are creating ripples in the international literary scene. Our company has linked up with Harper Collins and Pan Macmillan, so international books are being made available to Indian readers at a reasonable price.

Access to technology and infrastructure has made things easier for publishers. It has led to innovations in packaging and graphics. Focused designs have made the appearance of books much more attractive. Printing quality too has improved vastly. The reader today has a good variety to choose from.

(d) I don’t totally agree with the statement that reading is a dying habit. As a librarian for nearly 27 years, I’ve seen students and research scholars. I feel that my reading habit has changed a lot. Students prefer to read magazines and newspapers rather than books. Earlier, during the summer vacations, many students did come to the library for general reading.

today, they have various other options like listening to music and watching television programs. But the library is never empty. Light reading may have declined, but academic reading related to assignments, references, and research, has not.

(e) I don’t think that reading is a dying habit – but that parents and teachers have to play a very important role in inculcating this habit, for they are the role models for children. Since the child has more grasping power than an adult, it is the right age to develop this habit. It is important for parents to spend quality time with their children, to read aloud to children, to listen to what they’ve to say, and answer their questions.

For the proposition	Against the proposition
(i) Television has adversely affected reading	(i) Students are not being encouraged to read
(ii) Children pass leisure hours in other ways than reading.	(ii) Reading leaves a lasting impression on the mind and enriches one’s vocabulary.
(iii) Dull text books discourage the reading habit.	(iii) Habit of reading is incresasing and sale of books proves this.
(iv) Adults don’t read them selves and thus are not good role models.	(iv) Books of varied kinds are being read now.
(v) Reading materials are prohibitive in costs.	(v) Parents should spend. their time with children; reading is not a dying habit.
	(vi) Light reading has declined but not academic reading.

The Reading is a dying habit:
Most people believe that the reading habit is dying out and they are right about it. Even a cursory survey among students reveals that they spend more time watching television than reading books, except during examinations. Besides, children spend their leisure in many other ways rather than reading books. In addition to this, today’s textbooks are so dull and boring and studying has been made such a burden that children or students don’t have the motivation to read books.

Moreover, adults themselves do not read many books. They don’t serve as role models, instead they too spend more time on the T.V. Last but not the least, the cost of books have today become prohibitive. On an average, a book costs seventy-five to hundred rupees. It is all these factors that have made reading a dying habit. It is right that students are not being encouraged to read, that reading is something worthwhile, but suggestion that since sale of books have increased and therefore reading has increased is to miss the point.

A comparative study of sales of electronic consumer items and that of books reveal that the sale of electronic goods is twice as much as those of books. Moreover, those engaged in academic reading are a very negligible minority and they can’t be counted with those who read for pleasure. Similarly the contention that varied books are 1 being read does not prove that there are many readers. This attests the fact that today interests of people have become diversified and therefore to cater to their needs various kinds of books are being published and sold.

For example, a century back we had no books on computers but today there isn’t any library or bookshop which does not possess books on computers. Thus, we can safely conclude that reading is a dying habit. The television is now reining supreme over the minds. The T.V. is ubiquitous even in the smallest of homes while illiteracy is rampant in a place like India.

Activity 38

1. The following are the main points that emerged in a debate on the topic “The presidential form of government is more suitable for our country than the parliamentary form”. But the points are all mixed up. Arrange them under two separate heads for and against.

a. Will ensure strong centre…. curb divisive tendencies.
b. Deprives people of power to elect, recall, approach representatives,
c. Will quicken change towards removal of poverty, equal opportunity, greater production, prosperity.
d. Makes ruling sections/groups more powerful….discourages loc*t! or minority talents, culture, distinctions,
e. Concentrates authority….leads to dictatorship.
f. Reduces expenditure on wasteful elections, political propaganda, party politics.
g. Denies fundamental freedom….curbs human rights; builds fear, cowardice.
h. Simplifies decision making and brings about uniformity, can lead to greater discipline, better economic achievements. Present system breeds inaction, indiscipline, strikes, poor results.
i. Suited to Afro-Asian temperament; recent events prove it too.
j. Is against Indian democratic traditions.

2. First, make up your mind regarding the line of argument that you would like to follow. Second, think how to begin. Then, develop the outline into a paragraph : you are free to add your own points to the given ones.

Answer:
For:
a. Will ensure strong centre… curb divisive tendencies.
b. Will quicken change towards removal of poverty, equal opportunity, greater production, prosperity.
c. Concentrates authority.., leads to dictatorship.
d. Denies fundamental freedom… curbs human rights: builds fear, cowardice.
e. Suited to Afro-Asian temperament; recent events prove it too.

Against:
a. Deprives people of power to elect, recall, approach representatives.
b. Makes ruling sections more powerful… discourages local or minority talents, culture, distinctions.
c. Reduces expenditure on wasteful elections, political propaganda, party politics.
d. Simplifies decision making and brings about uniformity, can lead to greater discipline, better economic achievements. Present system breeds. inaction, indiscipline, strikes, poor results.
e. Is against Indian democratic traditions.

The presidential form of government is more suitable for our country than the parliamentary form.

It is just about 50 years since our country has been an independent nation. And numerous problems have been plaguing our nation. This has set people thinking in some quarters that there is a need to change our form of government. That would be like throwing the baby with the bathwater. The nation is just a baby with a particular structure and it need not be changed just because it has not grown and matured. In short, the parliamentary form of government does not need to go.

It is argued that the presidential form of government will ensure a strong centre, curb divisive tendencies, quicken changes in economic, social and political spheres, avoid wasteful expenditure on elections and party politics, simplify decision making and lead to greater discipline. There is no denying this fact. A presidential system does quickly bring about such changes but in the long run, as history has time and again shown, proves counter-productive and disastrous.

The rules of Mussolini, Napoleon, Stalin and Hitler are all outstanding examples of this trend. The presidential form of government makes the state larger than the individual, makes personal freedom a dream and gradually stamps out human rights. Finally, it leads to totalitarianism and dictatorship. The fear of facing a 1984-like scenario is ever alive in a presidential form of government. Oligarchy, plutocracy, stratocracy, autocracy and despotism are ominous realities in a presidential form of government.

History amply records this truth. The KGB and the communist party in USSR, the Nazi Party and the storm troppers in Germany are good examples of what happens when power is concentrated in the hands of a few or in one man’s hand. Moreover, a presidential form of government will gradually crush minority talent and minority culture and impose a cultural homogeneity. This would be disastrous in a multiracial, multicultural, multi-lingual, pluralistic society like India.

Its ethos would take the beating and its beauty will be lost. india has existed for ages as a pluralistic society whose greatness has been its power to assimilate and unite in its fold diverse cultures and religions. Tolerance and non-violence have been its mainstay and to abandon them would mean going against the grain of our character as a nation. Such a forced change would prove disastrous for the nation. Hence the parliamentary form of government with its respect for individual right, and its inclination towards unity in diversity, should be given the thumbs up.

Activity 39

In several cities, television has come to nearly all homes. Some people welcome this while others find it a bad influence and an expensive addition to the drawing-room. Some believe it creates problems – indiscipline, loss of sleep, reduced attention to homework, the danger of bad movies as bad models. Others consider it a good ‘teacher’ – brings vividly a lot of new information, helps farmers, makes stories interesting, provides both entertainment and instruction, saves money spent on bad/indifferent films, food at restaurants, etc., keeps the family together at home. A television company has organised an “essay competition” on the subject ‘Television, your new friend’. At the same time, the ‘Society of Cinema-goers’ has invited essays criticising television. Write on each topic, presenting your views on television, and its uses/abuses.

Points for	Points against
i. ______________	i. ______________
ii. ______________	ii. ______________
iii. ______________	iii. ______________
iv. _______________	iv. _______________

Answer:

Points for	Points against
(i) A good teacher	(i)Creates problem, indiscipline, loss of sleep etc.
(ii) Provides both entertainment and instruction	(ii) Reduces attention towards homework
(iii) Leads to the togetherness of the family members	(iii) Bad movies act as bad models
(iv) Saves money spent on food at restaurants	(iv) An expensive addition to the drawing room

Answer:
Television: its uses and abuses :
Television has truly made the world a global village. Its all-encompassing reach to the remote comers of the globe has made omnipresent medium. Moreover, the fact that it is an audio-visual medium, makes it all the more effective as well as alluring. Thus, it could be put to a wide variety of use. But it is more abused than used. In a developing country like India, television has become the medium by which literacy is spread all over the nation.

Students tune into educative programmes like the country-wide classrooms of the University Grants Commission and Krishi Darshan Programmes cater to the needs of farmers. Similarly programmes on family planning, health awareness, AIDS, nutrition baby care are beamed across the country. Forecasting of weather and climate helps fishermen, farmers and all kinds of people to plan out their future course of action. Storm warning, earthquake warnings and flood warmings have had a greater impact because of visual and graphic details of facts.

Above all, television has become the supreme medium of infotainment. Watching the news or watching a soap opera, a cookery special or a sports channel, a movie or an engaging group discussion, a sermon or a song, the television has it all, controlling and dispersing knowledge all over the world. And yet unconsciously the television is ruling us, stealing our time and making morons out of us.

A couch potato is no more a rarity. A great thinker enumerates the abuses of television as follows. First, television makes people emotionally insensitive. The images of sex and violence that are projected on the screen gradually drive out all human feeling from us and renders us indifferent to such incidents in real life. We accept them as normal. A murder, a rape, a dead body no more shocks us as it did earlier generations. We are gradually being denuded of humane feeling.

Second, television makes viewers morally uncritical and impairs their sense of judgement. With a book, one reads and then ponders over what it has stated but the television gradually impairs this sense of evaluation in us. It hits us so powerfully and forcefully that it bypasses our head and rules our heart. Third, television destroys our ability to concentrate for long on anything. Kids who are brought up on fast moving scenes and cartoon characters thus do not find their teachers exciting, their books seen dull and boring.

Quickfix solutions, capsule presentations, ready-made notes, fast food are the order of the day and television is one great factor in enhancing the pace of life and thereby reducing concentration spans of people. Fourth, television sets up such role models and projects such lifestyles which young people follow with zeal. They are led to believe that all that life is about is having girl-friends, wealth, fame and power. Finally, T.V. is creating dislocations in centres of authority.

Most often a person becomes authoritative because he or she is well- known. Thus a cricket star or a hero tells you to keep away from AIDS and has your attention no matter what he does in his personal life. Thus, his voice is powerful while that of a celibate priest’s is not. As a result there is total psychological, moral and academic confusion in our culture. T.V. is not bad just as money is not bad. It’s the way one uses it that matters. Let the T.V. be our servant and not our master.

Activity 40

Here are a few more topics for argumentative writing. Prepare outlines and write on each topic.
i. Men and women should/should not be paid equal wages for equal work.
ii. Prohibition will save the country from destruction/Prohibition goes against individual freedom. (Prohibition-disallowing by law the making and sale of alcoholic drinks.)
iii. Cricket commentaries are a national evil./ Cricket commentaries provide entertainment and education.
iv. History breeds narrow-mindedness. It should not be taught in schools/colleges.
v. Driving licenses should not be issued to students in schools/colleges.
vi. Girls should not marry before they are twenty, boys before they are twenty-five.
vii. College education must be made free.

Answer:
(i) Men and women should be paid equal wages for equal work.
For:
(a) Equal pay for equal work ensured in the Indian Constitution.
(b) Women do not work lesser than men/women do equally good work as men.
(c) It is the quality of work which matters and not who did it/wages are given for task completed, and not because someone did the task.
(d) Pay hike and promotions are made on grounds of merit and not on basis of gender.

Against:
(a) Women are less intelligent than men.
(b) Women work less than men.
(c) Women cannot do certain kinds of work because they are not physically fit to do it.

Gender differences have curbed the rights of women in a patriarchal and male dominated society. As a result, in some quarters it is still held that women should not be given equal wages as men. This kind of primitive thinking is a result of male chauvinism and is not justified by facts at hand. It has nothing to do with the question of women receiving equal wages as men. Patriarchal society has always held women as inferior to men. As a result, women were thought to be less intelligent than men.

This argument was thus put forth in favour of giving lesser wages to women. The contention is however not borne out by facts. Women have proved themselves the equals of men in almost all professions and spheres of life whether in science and techlology or in the humanities and social science. As more and more opportunities are being given to them women are proving themselves equal for men in every sphere of life.

Admittedly they are biologically made less strong than men but now-a-days work requires more brain and, therefore, the question of equal pay for equal work arises in the context of what work woman is doing and not what she is not. Besides, women Boxers, wrestlers, athletes, weightlifters. Marathoners etc. have proved that they too can do things like men. However, a strong case can be made for the question of equal pay for equal work for women.

First of all, just as equal opportunity for all is enshrined in our Constitution, so also equal pay for equal work is enshrined in our Constitution. A just and fair society will always provide equal pay for equal work for that is the universal law of natural justice. Considerations of caste, creed, race and sex should never come in way of a person’s wages. Secondly, it is another natural axiom that the meritorious be rewarded. If the woman is equally qualified as man, if she does work equal to man, then she deserves a wage equal to it, as men do.

Pay hike and promotions are decided on merits of individuals and not on considerations of caste and creed or sex. Finally, it may be argued that women in many ways are better than men. They are more sincere, committed, honest, responsible and hard-working than men. Case studies of working men and women has proved this. Thus, women deserve equal pay for equal work because they are in no way inferior to men in their qualifications and in their work.

(ii) Prohibition will save the country from destruction / prohibition goes against individual freedom.
For:
(1) Drinkers are bread winners, drinking therefore denudes the bread supply.
(2) Drinkers are physically violent; they indulge in wife beating and also a general nusiance.
(3) Drinking leads to hazardous health problems, the cost of which has to be borne buy family / govt.

Against:
(1) Prohibition curbs freedom of an individual.
(2) Prohibition breeds illegal trade in liquour.
(3) Prohibition results in loss of revenue to state.

Prohibition will save the country:
Drinking and smoking are two-sides of the same coin. They are equally dangerous and hazardous not only for the individual but also for the nation as well. Therefore, it is necessary to implement and ensure prohibition, for this alone can save the country from destruction. The opponents of prohibition are of the view of that it curbs freedom of the individual. They are right but of course individual freedom has always been curbed by social limitations to ensure that every other individual enjoys his or her liberty.

A man has the right to walk on the road as long as he does not infringe anybody else’s right to walk on the road. If drinking results in social disharmony, then it must be prohibited. A doctor prescribes a bitter pill to heal a person in spite of the protests of an individual. A whole individual can be a useful citizen. Secondly, anti-prohibitionists talk of the breeding of illegal trade in liquor.

True indeed: prohibition breeds an illegal trade in sale of liquor and the very purpose of prohibition is thereby defeated. But illegal trade can be prevented, an alert police, a cooperative public can detect and stop this trade. This has been proved earlier in Andhra Pradesh where women enforced prohibition and curbed illegal trade. Finally, there is the loss of revenue to the state. This too is true. But it can be argued that the cost of having host of diseased drinkers is higher than that of loss on revenue due to prohibition.

It is fallaciously thought that the cost of treating a man with drinking related health hazards is borne by families of those individuals but the national loss in this context is not taken into account. Moreover, less corruption and generation of revenues in other trades can nullify the loss accruing from prohibition. Non-prohibition on the other hand, has high costs in terms of familial, societal and national loss.

Consumption of country liquor by males who are bread winners in lower income groups have left families bereft of the basic needs of food, shelter and clothing. Broken families, loss of childhood, denial of education and health are the result. The social costs in terms of crime, prostitution, child labour, drug addiction, and a host of other problems emerging from such households, are immense.

Moreover, drinkers gradually lose self-esteem, self-confidence and slowly lose skills. They become irresponsible and unfit for work. This happens even among people of higher income group. Their erratic behaviour, tendency to shimk from duty and going on unauthorised leave hurts sectors in which they work thereby adding to the national loss. Finally, it may be reiterated that the cost of rehabilitating a person with drink- related health hazards is exorbitant.

Whether it is the government that finances this, the company or the individual, all of them result in a national loss. On the other hand, the money saved by individuals on enforcement of prohibition results in per capita gain though it may not accrue to the revenue of the state. Prohibition is therefore a better option than the freedom to drink. For prosperity of the family leads to prosperity of the nation.

(iii) Cricket commentaries are a national evil / Cricket commentaries provide entertainment and education.
For:
– Is a waste of time
– A hobby of the leisure class
– Take too much air time and T.V. time.
– Does not benefit the state or nation.
– Denies equal weight to other sports.

Against:
– Commentary is an art.
– Commentary provides entertainment and education.
– Commentaries provide job and earn revenue.

The very mention of cricket commentaries as a national evil gives rise to passions because the game of cricket is the favourite of a large majority of the upper and middle classes of people. Nevertheless a reasoned analysis of its pros and cons reveals that cricket as well as its commentary is a national evil. First of all cricket commentaries involve a colossal waste of time. During a cricket match, offices are deserted and so are schools and colleges.

People in factories and business establishments slow down work and sometimes even stop working. Moreover, a game of cricket takes a lot of time. A test match spans three to five days while the one day game consumes 8 hours. An avid fan of cricket who listens to its commentary pays little attention to work because the match is held mostly during office hours, school and college hours from 9.00 a.m. to 4.00 p.m.

Time is money and therefore the damage to the economy during a cricket match is irreversible. On an average if a man watches cricket for 4 hrs. a day for 60 days, there is a waste of 24 hrs or a total of 10 days in a year. If the number of those watching or listening to commentaries is even a minimum of 2 million then there is an astounding waste of 20 million days.

The corresponding loss to the economy is therefore colossal. Besides this, cricket commentaries occupy too much of air space as well as as visual space on the T.V. The radio and the television could be used to broadcast other | programmes of social interest during this time. An even greater lacunae is the unequal media coverage that other sports receive. The priority that is given to cricket by the media and T.V. networks does not encourage sportspersons of other games.

While sponsorers are available to- support cricket matches there are very few sponsorers to support the broadcasting of other sports. Further, the revenue generated from commentaries on cricket matches is mostly 1 deposited in the offices of the T.V. Network which has bought the rights to brodcast the match. Revenue to the state in this context is paltry. Opponents of this view that commentaries are a national evil hold that they are educative and entertaining.

But it may be reasonably shown that their educative value is minimal and marginal. As for entertainment that is a very transitory form Of entertainment. The same can be said of its value as an art. It is art of transitory value and does not have any permanent or lasting effect. As for the contention that it provides jobs, it can be said that employment opportunities as commentators are very minimal, limited only to a few individuals and that it is not to be taken as a profession. Thus after weighing the pros and cons it may be emphatically said that cricket commentaries are a national evil.

(iv) History breeds narrow-mindedness. It should not be taught in schools/colleges.
For:
(1) History breeds crude nationalist.
(2) It is full of crimes.
(3) It provides a confused heap of facts.
(4) It records popular beliefs.

Against:
(1) History is interesting and useful.
(2) It helps us to escape the burdens of life.
(3) It is a sound teacher.
(4) It provides us moral inspiration.
(5) It widens our intellectual outlook.

History generated crude nationalism among the students. It records the glory and achievements of some countries and the failures of others. Germany under Hitler was a case in a point. The students who read it learn nothing. History is a record of war and blood-shed. If we scan the pages of history, we learn a lot about many bloody battles fought among different nations. History takes us to a world where lies a confused heap of facts. It is difficult to understand and analyse them. These facts lack colour.

Above all, it acquaints us with some popular beliefs. There is nothing innovative about them. All these facts mentioned above adversely affect the minds of the people. Therefore, history should not be taught in schools/colleges. We should see the bright side of history. It launches man on a thrilling adventure of a journey to the past. It awakens in him the racial memories that he slumbering in the depths of time. The study of history strengthens one’s faith, however, wavering, in the ultimate decency of things.

History must not be read as a collection of dry and old facts and dates, but as living representation of the past which has a significance for the present. The study of history is interesting, useful and amusing. It helps us to escape the burdens of life. Moreover, history is a sound teacher. The records of the past interpreted in practical by noble men and women, supply moral tonic which must be administered to each generation. Study of this subject widens our outlook. Besides, history makes our intellectual horizon touch new heights. It also sensitizes our minds. Therefore, history should be taught in schools and colleges.

(v) Driving licenses should not be issued to students in schools/colleges.
For:
(1) Driving licenses make the students wayward.
(2) They become law-breakers.
(3) They live in a world of fancy.

Against:
(1) Issuing driving licences to school/college makes them responsible.
(2) They save their time.
(3) They become law-abiding.

Issuing driving licenses make school/college students carefree. They move freely in their bikes/four-wheelers without caring anybody. They become liberty drunk. They never feel the importance of why they have been issued driving licenses. They make use of their vehicles for a constructive purpose. They are young. In the full flush of their youth, they drive recklessly, flouting the traffic rules.

Sometimes they meet with accidents. Some die premature deaths, some escape with a miracle and others suffer fractures. These students find themselves cut off from the outside world when they drive their bikes or cars. On the other hand, we must not be blind to the other side of these facts. School/college students should be issued driving licenses, because they are mature. Fear of parents and accidents makes them responsible. They do not want to waste the latter’s money by misusing driving licenses.

They drive their vehicles very carefully. Time is precious. They save it as a result of using bikes or cars. These students become law- abiding. They are alive to the traffic rules. They understand why they have been given bikes/four wheelers by their parents. In view of these facts, driving licenses should be issued to school/college students.

(vi) Girls should not marry before they are twenty, boys before they are twenty- five.
For:
(1) Girls become highly educated.
(2) They get a chance to fulfil their dreams. .
(3) They enjoy empowerment.
(4) They become independent and are free from the drudgery of household work.
(5) They become ideal mothers and wife.
(6) Boys are no different.
(7) They want higher education.
(8) They become independent.

Against:
(1) They should be educated.
(2) Marriage before 20 makes them typical house-wives.
(3) They are immature to understand the ways of the world.
(4) They go astray.
(5) They are deprived of enjoying impowerment.
(6) Boys cannot be highly educated.
(7) They cannot be independent to the core.

Girls should be highly educated in word and spirit. Very few girls continue their studies after their marriage. They try their best to fulfil their dreams and achieve then- goals. Today we see many a woman enjoy empowerment. They have become high- profile entrepreneurs, bureaucrats and academicians. They are now successful political leaders. They brim with confidence. They become independent by earning their livelihood. Educated wives get a respite from the monotany of their household works.

Education makes them conscious of their duties to their husbands and children. They never become a burden on society. Boys are no different from the girls. A certain age is indispensable for building their career, but marriage before 25 puts bars in fulfilling the dreams, hopes and aspiration. Failures to achieve their goals drive them to a state of frustration. As a result of higher education, they earn handsome income and become assets to their families.

On the other hand, if the girls marry before twenty, they cannot enjoy the things they want. They become neither highly educated nor enjoy real empowerment. They become typical house-wives and don’t get a chance to experience what is happening in the external world. Frustration grips them. They don’t understand the language of independence. They often go astray and as a result, bring disgrace to society. Boys suffer the same fate.

Their marriage before twenty-five seldom allow them to go for higher education according to their will. They soothe with frustration for not achieving their goals. They fail to rise to the expectations of their parents. They are shorn of confidence. They can’t be fiercely independent. Therefore, girls should not marry before they are twenty, boys before they are twenty-four.

(vii) College education must be made free.
For:
(1) Scope for higher education, irrespective of caste, creed or colour.
(2) It makes everyone confident.
(3) It leads to independent among the students.
(4) It provides broader exposure to the outside world.

Against:
(1) Ordinary students have no value.
(2) Free college education creates indiscipline.
(3) Wastage of public money.
(4) There is no room for further academic development, there is no much fund for research.

Free college education provides a scope for higher education for all sorts of students, irrespective of caste, creed and colour. They all feel a state of what higher education is. This makes them brim with confidence. Some of the poor students get a chance to dream big and are determined to achieve someting in life. College education makes them independent, because, they get a chance to earn their livelihood.

They are now exposed to the happenings of the external world. As a result, they can contribute to the well-being of their country and fellow-beings. On the other hand, the issue has a darker side. Free college education encourages many ordinary students to sit in their classes. They should have been given vocational education. Instead of reading sincerely, they create indiscipline in the college and as a result, spoil the academic environment.

Besides, free college education costs our public exchequer beyond imagination. The common tax-payer’s money is injudiciously spent. Academic development suffers a serious jolt as a result of paucity of finance. Research work lags far behind. In view of these facts, college education should not be free.

Odisha State Board Elements of Mathematics Class 11 Solutions CHSE Odisha Chapter 14 Limit and Differentiation Ex 14(e) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 14 Limit and Differentiation Exercise 14(e)

Question 1.

Find derivatives of the following functions from the definition :
(i) 3x² – \(\frac{4}{x}\)
Solution:

(ii) (4x – 1)²
Solution:

(iii) 2 + x + √x³
Solution:

(iv) x – \(\sqrt{x^2-1}\)
Solution:

(v) \(\frac{1}{x^{2 / 5}}\) + 1
Solution:

Question 2.
(i) cos (ax + b)
Solution:
Let y = cos (ax + b)
Then \(\frac{d y}{d x}\) = -sin (ax + b) × \(\frac{d}{d x}\) (ax + b) by chain rule.
= -sin(ax + b). a = -a sin (ax + b)

(ii) x² sin x
Solution:
Let y = x² sin x
Then \(\frac{d y}{d x}=\frac{d}{d x}\) (x²). sin x + x² \(\frac{d}{d x}\)
[ ∴ \(\frac{\mathrm{d}}{\mathrm{dx}}(u \cdot v)=\frac{d u}{d x} \cdot v+u \cdot \frac{d v}{d x}\)
= 2x sin x + x² cos x

(iii) \(\sqrt{\tan x}\)
Solution:
Ley y = \(\sqrt{\tan x}\) = \((\tan x)^{\frac{1}{2}}\)
Then \(\frac{d y}{d x}=\frac{1}{2}(\tan x)^{-\frac{1}{2}} \times \frac{d}{d x}\)(tan x)
= \(\frac{1}{2 \sqrt{\tan x}}\) sec² x.

(iv) cot x²
Solution:
Let y = cot x²
Then \(\frac{d y}{d x}=-{cosec}^2 x^2 \times \frac{d}{d x}\left(x^2\right)\)
= – cosec² x². 2x
= -2x. cosec² x²

(v) cosec 3x
Solution:
Let y = cosec 3x
Then \(\frac{d y}{d x}\) = -3 cosec 3x . cot 3x

Question 3.
(i) √x sin x
Solution:
Let y = √x sin x
Then \(\frac{d y}{d x}=\frac{d}{d x}\)(√x) sin x + √x. \(\frac{d}{d x}\)(sin x)
= \(\frac{1}{2 \sqrt{x}}\) sin x + √x. cos x

(ii) \(\sqrt{x^2+1}\)cos x
Solution:

(iii) tan x – x² – 2x
Solution:
Let y = tan x – x² – 2x
\(\frac{d y}{d x}\) = sec² x – 2x – 2

Odisha State Board CHSE Odisha Class 11 Invitation to English 3 Solutions Writing Exposition Textbook Activity Questions and Answers.

CHSE Odisha 11th Class English Writing Exposition

Expository Writing

Exposition is an orderly presentation of facts and ideas. It exposes or shows. All exposition is informative. In an exposition, you answer various questions that might be asked of an object, an event, or an idea – questions like these:
What is it?
What does it consist of?
What is it for?
How is it put together?
What good is it?
What does it mean?
What is the cause of it?
What will be the result of it?
There are several methods of writing an exposition of these, exposition by definition and exposition the rough analysis are the most important.

Activity 31

Develop paragraphs of your own, using the following plans. The given topic should form part of the opening sentence.
(a) Topic: There were several things I liked (disliked) about my high school.
Sentence 1: Topic sentence
Sentences 2, 3, 4, 5: The things I liked (disliked)
Sentence 6: Conclusion

(b) Topic: It is easier for someone to express himself in speech than in writing.

Answer:
(a) There were several things I liked in my high school. Firstly, we had good teachers who not only taught us well but were also very friendly with us. Secondly, we were never burdened with homework. Instead, we were asked to read what was taught in the class at home. Thirdly, there were a lot of extra-curricular activities which helped in developing our personality. Finally, we had an Old Boys Association which helped us keep in touch with our classmates and to know about the development of our school. Thus, my high school was really unique in many ways.

(b) Is it easier for someone to express himself in speech than in writing? Or is writing easier than speech? Linguists are divided in their views. Some say that speech is easier than writing because one learns to speak spontaneously without having to attend school. They also argue that speech takes less time to learn than writing. Others, however, dispute these views.

They contend that writing is easier than speech because it involves graphic images which the child can easily learn even before imitating speech. They also are of opinion that writing is accessible to speech-disadvantaged children and therefore, more universal. Thus, linguists are equally divided over the question of which is easier, speech or writing.

Activity 32

Write a paragraph on each of the following topics, using Chesterton’s model at page 39.
(a) Types of students
(b) Types of teachers
(c) Kinds of books we read
(d) Kinds of friends

Answer:
(a) Types of students :
Roughly speaking, there are three kinds of students in our college. The first may be called bookworms. They can always be seen pouring over books in the library when they travel by bus while having food and so on. This kind has no interest in games and most often they love to be indoors rather than play outside. The second sort may be called truants. These students take pleasure in not attending classes. They bunk college, go to films, play cricket and create a nuisance on the campus.

To them, we owe all the strikes and indiscipline in the college. The third kind is called Casanova’s. You can see them talking in hushed whispers with girls under a tree, in the corridors, accompanying them to the bus stop, or shadowing others who are not yet in their hold. The studies are secondary and they end up as unemployed youth who dream of their golden day in college.

(b) Types of teachers :
There are different types of teachers. Firstly, there are teachers who are dedicated to the core. They inspire their students to reach newer heights in the future. Their devotion to teaching is matchless. Secondly, there are teachers who just teach students for the sake of teaching. They are never serious about it. They lack dedication to their profession. Thirdly, there are those who pretend to be ideal teachers. They are dull. They always aim at earning money by paying lip service to their profession. These teachers bring disgrace to society.

(c) Kinds of books we read :
Books are of many types but they can be generally divided into good and bad. Good books are man’s most important teachers. They instruct and entertain, make men wise and ignorant, men of knowledge. Bad books, on the other hand, waste men’s time and introduce evil thoughts into their minds. They neither enlighten the mind nor broaden the imagination in the right direction. Thus good books ought always to be chosen over bad ones.

(d) Kinds of friends :
We have friends of several kinds. First, there is gossip. He can never keep our secrets and always lets us down by telling everything about us to others. Second, there is the coward. He is seldom able to stand on his own feet but that is not any danger. Keep him in the team for any enterprise and he’ll take off whenever he smells any danger to himself. Third, there is the flatterer. He always sings your praises and never tells you the truth. He is neither dependable nor trustworthy. He stays with one as long as he profits from his company and then he changes loyalty. Fourth, there is the slanderer.

This kind of friend feigns friendship but behind your back, he talks ill of you. Then there is the follower. This kind rarely takes his own initiative in doing anything for you. He’s a good supporter, a loyal disciple but you can’t hand him any responsibility and sit quietly. He needs nudging and guiding. There’s yet another kind called the parasite. He feeds on you, eats of you, borrows your notes, your money, your cycle, etc. He is always dependable. Finally, there is the one and only true friend. He is rare to find. But this is the kind of friend who is dependable, responsible, and trustworthy.

Activity 33

1. Write a paragraph ending with the sentence: “I’m afraid I didn’t like the film at all and wouldn’t recommend it to anyone.”
2. Write a short paragraph beginning with the sentence: “I had a very happy childhood.”
3. Write separate paragraphs from the point of view of the taxi driver and the truck driver, using the following outline. An accident between a truck and a taxi – an old man was killed – a buffalo was seriously injured – a policeman arrived on the scene – a doctor drove the dead body to the hospital.
4. Write a paragraph to be included in a letter to a pen-friend telling him/her how you celebrate Diwali.

Answer:
(1) Refugee is not worth watching. Its story is a stock one: Laila-Majnu, Romeo-Juliet like and perhaps borrowed from Daruwalla’s “Love in the Salt Desert.” There is no life in Abhishek Bacchan’s acting. As for action, there is not much that it has to boast off. Walking like a shepherd with a staff in his hand and a band around his head. Bacchan evokes pity rather than empathy, he does not inspire and he does not display much emotion, seems so wooden. Besides, photography, music, and choreography aren’t great either. In short, I’m afraid I didn’t like the film at all and wouldn’t recommend it to anyone.

(2) I had a very happy childhood. Father, Mother, Grandpa, and Grandma, all of us lived together. Every morning, Grandma would play with me and tell me tales. In the evening Grandpa would take me on walks and in the night I used to huddle in my mother’s lap and sleep. Those days were wonderful. It was all play and no work, no worries, no fears, only love. And every summer we went off to Puri to frolic in the sun and sand, I wasn’t afraid of the sea. Daddy put me on his shoulders and walked into the sea. The smell of the surf and the thundering of the waves excited me then as it excites me now. Truly I can never forget the joys of my childhood days.

(3) The Truck-driver’s point of view: It was almost noon as I carried a truckload of bricks to be delivered at the Institute of Physics. I was on N.H.5 and had already neared Acharya Vihar Square. I was to take a right turn at the square to get into the road leading to Sainik School. Traffic was thin and a buffalo was standing right in the turn and urinating. A taxi was coming from the Sainik School road. I put on the dippers indicating a left turn. I slowed down as I had to avoid the buffalo.

Suddenly, the taxi emerged, flashing its lights. I had already taken the turn while the taxi was speeding straight ahead. I applied the brakes but the vehicle did not halt because of the load. Instead, it careened past the taxi, hit an old man standing serenely and rammed into the ditch beside the N.H.5. My head hit the steering wheel and I became unconscious. When I woke up I was in the capital hospital. The Taxi driver’s point of view: I was returning from Sainik School after dropping a fare.

It was noon and I was supposed to pick up my little children from the convent school. I should have been there by 11.30 a.m. but it was already half an hour behind. Hence I was rushing with thoughts of my children waiting hungrily at school. As I was approaching Acharya Vihar Square, I saw a truck coming toward me. It was turning into the road. I was in a hurry. I did not want to wait till the truck had turned and so did not slow down my speed.

Instead, I flashed my headlights requesting priority of way but the adamant truck driver did not heed to my signal, it was turning. I applied the brakes but it was too late, I rammed into- a buffalo, swerved sharply to the right, grazed past the rear of the truck’s body, and then hit a telephone pole against which the car stopped. Fortunately, I escaped unhurt with only minor pain in my back. But then my problems were, not over. A policeman arrived from nowhere, accosted me, and asked me to get out of the car.

Meanwhile, people who were crowded around informed us that an old man had fallen down unconscious. There was a doctor among them and he suggested that we take him to the hospital. As the old man was brought to my taxi, the doctor noted that he had already died. However, I requested the doctor to keep quiet and immediately drove to the hospital with the dead body. I was lucky not to have been manhandled by people. But I must say it is all the truck driver’s fault. I did not kill the old man.

(4) Paragraph included in the letter

121, Kharavel Nagar,
Bhubaneswar
20 August 20

Dear Joseph,
Greeting from India!
I received your letter and your picture postcard at the same time. I will cherish the card for a long time to come. The picture of the Millennium Dome is crystal clear. It looks very beautiful. Well, you had written to me about how everyone in England celebrates Guy Fawkes day. You did have a lot of fun, really. I could see that from your letter. Do you know, here, back in India we too celebrate something similar to Guy Fawkes? There it commemorates the gunpowder plot but in India, we celebrate a festival called Diwali, the festival of lights.

It symbolizes the victory of good over evil, of light over darkness commemorating the victory of the forces of Shri Rama over the evil forces of Ravana. The festival falls every year in the month of October or November. On that day, we offer Puja to Shri Rama, distribute sweets among friends and neighbors and prepare for the night. We purchase crackers of all sorts and dry them in the sun. We also prepare wick lamps. The lamps and wicks are purchased from the market.

Then oil is poured into the lamps and the wick is set on it. These are then kept in a row on terraces, the boundary wall, on window sills, and everywhere where there is space to keep them. When night falls, these lamps are lit. There must be thousands and thousands of lamps lit in every house, in every street, town, city, district, and state. The house is thus lit like a Christmas tree. It looks beautiful and gay. After this starts the ceremony of lighting fire-crackers. Everyone, from a child to an old man enjoys lighting fire-crackers and bursting them.

This goes on till the last hours of the morning. Often, Diwali is celebrated for two days. Of course, one of these days is only declared a national holiday but then there is no holding back for persons who enjoy Diwali. They take leave and enjoy this festival. This reminds of Guy Fawkes day, isn’t it? Well, do write to me about how you celebrate Christmas. I am eager to hear from you.

With warm regards.
Your loving friend,
Subrat Das.

Activity 34

Do you have friends whose mothers are working? What problems do they have? Put these problems in the blanks in the list ‘
1. Getting pampered
2. Bad company
3. Neglecting studies
4. Aggressive attitude
5. Too much TV
6. Psychological problems.
7. Widening communication gap
_______________________
_______________________
_______________________
_______________________
Answer:
They have a widening communication gap.
They have psychological problems.
They are getting pampered.
They neglect studies.
They have bad company.

The list below contains some advantages that children of working mothers enjoy.
Now think of other advantages and add them to the list. Are these advantages real? If not, why?
1. Complete freedom
2. No nagging for homework
3. Enjoy yourself freely
4. Have full privacy
5. Gain in confidence
6. Be more, independent
7. Do what you like
_______________________
_______________________
_______________________
Answer:
These advantages are not real, because, without the mother’s presence at this stage, the children never feel the importance of their formative years which shape their future in a great measure.
They develop adaptability. 
They develop a sort of creativity.
They are free from worries.

Now write a passage of 2 or 3 paragraphs on ‘ Working mothers and their children
2. Dear ………………..,
My mother started working seven years ago. My first problem is that I have to keep ringing her up to find things in the house. Second, living with a ten-year-old sister is not as easy as it seems. My younger sister is supposed to take permission from me, but most of the time she doesn’t listen to me. Then I get angry and she rings up my mom who scolds me. Third, I don’t really have much freedom because I have to call my mother to take her permission. She has placed so many restrictions on me that I feel caged in. Fourth, Let me confess that at home I listen to music, watch TV and spend a lot of time with my friends, neglecting my studies. Besides, although my parents never pamper me, they always pamper my sister, my be because she is much younger. Very often I feel neglected when they do that. Lastly, I really wish that my mother or father were at home, especially some months before the boards.
3. Dear…………………,
I think it’s the best way. I don’t think I’d like to see more of my parents at home. I like my free time. At home I read, listen to music, fiddle around with the computer, play badminton and tennis, and even I have started writing because I don’t have any other entertainment. The other definite plus is that 1 get my own privacy, and I have also become more independent, in fact, when my maternal or paternal grandparents come over, then I feel closed in somehow. Since I do my own things, I am pretty confident about everything. But having someone at home is obviously a big advantage. I can never tell myself to study. I often wish my mother were at home to tell me
and help me. Worst of all, 1 waste a lot of my time worrying about security and about meals.

Answer:
Passage 3 throws light on the impact of a working mother on her child. Here the latter likes to be away from its parents. At home, the child enjoys reading, listening to music, playing badminton and tennis, and so on. Lack of any other entertainment makes the child start writing something. The most remarkable thing about it is its own privacy. As a result of its working mother, the child somewhat develops | closeness with its maternal or paternal grandparents. It becomes confident still, the child wishes the mother were at home for help. Worrying about security and about meals takes a lot of its time.

Activity 35

Read the following letters published in an issue of India Today. These letters \ tell us what is wrong with sports in India.

(a) The story on Indian sports (“A Shocking Mess”, August 15) reveals only the tip of the problem. Officialdom and corruption have so spoiled our system that every effort is made to stall an achievement. While sportsmen live like beggars, deprived of quality gear, the managers live like kings.
R. SINGH, NEW DELHI

(b) With neither motivation nor money to galvanize them, it’s no wonder that many players bid goodbye to sports once they get a sound footing elsewhere. It is high time that those who actually know about different sports are appointed at the helm of affairs.
MANI NATRAJAN, CHENNAI

(c) The fact that only 22 of the 46 probables for the hockey team reached the coaching camp shows the lack of commitment of the players. Though official mismanagement can be blamed, the athletes have to accept part of the responsibility.
B.C. PRAKAS, BANGALORE’

(d) If the story on India’s preparation for the Hiroshima Games had been published a year or two ago, it might have had some effect. To an extent, it is this lack of media coverage of sports, other than cricket and tennis, that is also responsible for India’s debacle in various events. MANISH PATHAK, NEW DELHI

(e) The sports mess is hardly surprising. After all, sports are also managed by the bureaucracy and the bigwigs. Like other plans and programs they implement, how could they deviate from their time-honored practice here – plan with fanfare, implement with nonchalance, forget the monitoring, and don’t worry about the results?
K G JAIN, NEW DELHI

(i) Read the letters again and make a list of the factors that are responsible for the sorry state of Indian sport is in.
(ii) If possible, think of and add your own points to the list.
(iii) Try to write 3 or 4 sentences on each point.
(iv) Write a short paragraph incorporating suggestions for improvement This should ideally conclude your topic. Now write on the topic “The Sorry State of Indian Sports.”

Answer:
Indian sports is in an extremely sorry state today. It is plagued by manifold problems to which there seems no end in sight. Officialdom and corruption have tarnished our sports bodies so much so that, every achievement is stalled. Moreover, while officials grab the limelight and the financial benefits accruing from an event, sportspersons who made it all possible, are handed over the crumbs. With such a state of affairs presiding, our sportsmen do not have any motivation to shine.

Leave alone prize money, they are often not even paid their due. And so, when they get a good job, they bid goodbye to the sports that they so much loved. After all, they also have to earn their livelihood to feed their families. Budding talents too are not spared. Companies would rather have an established player endorse their products than choose a greenhorn. As a result, young sportspersons take the help of their parents, friends, and relatives to hone their skills at meets both at home and abroad.

But when the money they had diminished to a trickle, they turn their back on sports and look for other options. Besides, the media is at fault too. Come cricket or tennis and they run to cover it. What about football, hockey, polo, kabaddi, handball, basketball, Choko, badminton, table tennis, chess, etc? Are they receiving equal coverage? This is a question that is better not asked by the media. They would shrink and then vanish. Then there’s the ubiquitous red-tapism of the bureaucracy and the official bigwigs.

Their plans for the development of sports in the country sound grand, but they are seldom implemented. They go “bang”, and “bang” in speeches but their implementation always ends in a whimper. However, all blame cannot be laid at the doors of others. Sportspersons too are responsible for this state of affairs. They lack commitment and professionalism. A foreign trip is coveted more for the glamour and the sightseeing than as an opportunity to bring home medals.

Most often, groups lack team spirit and this is very obvious in their game. How can these problems be solved? It is easier said than done. Solutions may be suggested but who will implement them? First, perhaps there should be an attitudinal change among the people who run the sports in this country. They should take it seriously as something concurring with national honor and national pride. Secondly, eminent sportspersons should run sports bodies.

Third, sportspersons must be encouraged by monetary rewards, and their achievements recorded and honored by sports bodies as well as the government. Fourth, the government must ensure the sponsorship of budding talents for national and international meets. Fifth, media coverage should be given equally to all sports and finally, sportspersons must be inspired to total commitment and professionalism. If and only when these changes are implemented in India, will the scene of Indian sports change for the better?

Odisha State Board Elements of Mathematics Class 11 Solutions CHSE Odisha Chapter 14 Limit and Differentiation Ex 14(d) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 14 Limit and Differentiation Exercise 14(d)

Question 1.

Find the derivative of the following functions ‘an initio’, that is, using the definition.
(i) 2x³
Solution:

(ii) x⁴
Solution:

(iii) x² + 1
Solution:

(iv) \(\frac{1}{x}\)
Solution:

(v) \(\frac{1}{3 x+2}\)
Solution:

(vi) \(\frac{1}{x^2}\)
Solution:

(vii) \(\frac{x}{x+1}\)
Solution:

(viii) t(t – 1)
Solution:

(ix) s² – bs + 5
Solution:

(x) √x
Solution:

\(\frac{1}{\sqrt{z}+\sqrt{z}}=\frac{1}{2 \sqrt{z}}\)

(xi) tan θ
Solution:

(xii) cos 2θ
Solution:

(xiii) x sin x
Solution:

Question 2.
Find the derivative of the following function from the definition at the indicated points. Test whether the following functions are differentiable at the indicated points. If so find the derivative.
(i) x⁴ at x = 2
Solution:

(ii) 2x² + x + 1 at x = 1
Solution:

(iii) x³ + 2x² – 1 at x = 0
Solution:
Let x³ + 2x² – 1
Then \(\left.\frac{d y}{d x}\right]_{x=0}\) = \(\lim _{h \rightarrow 0}\left[\frac{\left(h^3+2 h^2-1\right)-(-1)}{h}\right]\)
= \(\lim _{h \rightarrow 0}\) (h² + 2h) = 0

(iv) tan x at x = \(\frac{\pi}{3}\)
Solution:

(v) \(\sqrt{3 x+2}\) at x = 0
Solution:

(vi) In x at x = 2
Solution:

(vii) \(e^x\) at x = 1
Solution:

(viii) sin² θ at θ = \(\frac{\pi}{4}\)
Solution:

Question 3.
\(\frac{x+1}{x-1}\) at x = -1
Solution:
We know that a function f(x) is differentiable at a point
x = c if (i) L.H.D. exists
(ii) R.H.D. exists
(iii) L.H.D. = R.H.D
Let f(x) = \(\frac{x+1}{x-1}\)

Thus L.H.D. and R.H.D. both exist and L.H.D. = R.H.D.
Hence f(x) is differentiable at x = -1 and the derivative is –\(\frac{1}{2}\)

Question 4.
√x at x = 0
Solution:
Let f(x) = √x
Then f(0) = 0

Question 5.
f(x) = \(\left\{\begin{array}{r}
1-x, x \leq \frac{1}{2} \\
x, x>\frac{1}{2}
\end{array} \text { at } x=\frac{1}{2}\right.\)
Solution:

Question 6.
f(x) = \(\left\{\begin{array}{r}
\sin \frac{1}{x}, x \neq 0 \\
0, x=0
\end{array}\right.\) at x = 0
Solution:
f(0) = 0

Question 7.
f(x) = \(\left\{\begin{array}{r}
x^2 \sin \frac{1}{x^{\prime}}, x \neq 0 \\
0, x=0
\end{array}\right.\) at x = 0
Solution:
f(0) = 0

Odisha State Board CHSE Odisha Class 11 Invitation to English 3 Solutions Telegram, E-mail Writing Textbook Activity Questions and Answers.

CHSE Odisha 11th Class English Telegram, E-mail Writing

Telegram

An ordinary letter may take two or three days to reach the addressee; if the message is urgent we send a telegram. Telegrams are the most common means of sending urgent messages if has an advantage over the telephone in that a written communication will be available for future reference. When you write a telegram, you have to limit your meaning to, the fewest possible words, since the amount you have to pay depends on the number of words you use in your telegram. In reducing the length of a message, you should not make it vague.

Remember the following points :
1. You can leave out articles, prepositions, and similar words that do not carry meaning in themselves but help to construct grammatical sentences.
2. Time or quantity or number could be clearly specified.
3. The address must be complete.
4. When in doubt, add a word rather than omit it.
5. Use capital letters.

Activity 1

Here are some messages which need to be sent as telegrams. Go through them carefully, strike off the words you think unnecessary and rewrite each one in the form of a telegram.
The first one has been done for you.
1. (My) bag (has) (been) stolen. (I) (have) no money send Rs. 1000 immediately (in) (the) care (of) ELTI Hostel.

Hence, the telegram is to be written in the following manner:

Now convert the following messages into telegrams :
2. Money has been sent. You should contact the Warden on Wednesday. Write back. Father.
3. I am unable to arrive on Tuesday. There is a meeting on Wednesday. You may postpone it to Friday.
4. I am reaching you with my family on 20th February by the Konark Express.

Answer:
(2) MONEY SENT (.) CONTACT WARDEN WEDNESDAY (.) WRITE BACK. FATHER
(3) NOT ARRIVING TUESDAY (.) MEETING WEDNESDAY (.) POSTPONE TO FRIDAY
(4) REACHING WITH FAMILY TWENTIETH FEBRUARY KONARK

Activity 2

Here are some letters which you have to convert into telegrams. Go through them carefully and identify the main ideas, which the telegrams should contain. The main ideas of the first letter have been identified and underlined.

1. “We haven’t heard from you for more than two months. We have written a number of letters to you. but you haven’t written us back. We are extremely worried. We hope and pray you are not ill. Please send a wire immediately about your welfare. If we do not hear from you this week, we will come to
Rourkela.”
2. “There is nothing to worry. I’m perfectly well. I couldn’t write because I had gone to IIT, Kharagpur on a study tour. Then I visited a friend in Calcutta for a few days. I am sorry for not writing.”
3. “Last evening Grandmother complained of severe pain in the stomach. We sent for a doctor. He gave her an injection and asked us to move her to hospital. He said her appendix had to be removed. The operation is on 10th. Mother wants you to come.”
4. “Our college is organising an educational tour to South India for 15 days. The tour will be very useful. We will be visiting many temples, museums and art galleries. All my friends are going. Please send Rs. 3,000 immediately. On my return I’ll write about the places we have visited.”

Answer:
(1) NOT HEARD FROM YOU EXTREMELY WORRIED SEND WIRE IMMEDIATELY ABOUT YOUR WELFARE
(2) DON’T WORRY PERFECTLY WELL HAD GONE STUDY TOUR AND COULD NOT WRITE SORRY
(3) GRANDMOTHER HOSPITALISED APPENDIX OPERATION TENTH COME
(4) COLLEGE ORGANISING SOUTH INDIA EDUCATIONAL TOUR ALL FRIENDS GOING SEND THREE THOUSAND IMMEDIATELY

Activity 3

A number of situations have been described below. You are required to draft a telegram to suit each situation. A part of each telegram is given. Can you complete the telegram?
1. Three months ago, that is, on 15 October, you ordered a dictionary from the Modem Book Depot, Station Square, Bhubaneswar. You have not received the book. You want the shop to send the book without further delay.
2. You are appearing for the +2 Examination. Unfortunately, you have not received your Admit Card. You want the council authorities to allow you to take the examination pending receipt of the Admit Card.
3. You are returning home (from Bangalore) for the holidays. You had written to your father that you would arrive on Sunday morning, but as berths are not available, you have to change your travel plans. You will now arrive two days later, by a different train. Draft a telegram informing your father of the change.
4. Prof. Mishra is in Delhi on tour. He was supposed to return to Bhubaneswar for an important meeting but has been held up in Delhi because of bad weather. He wants to inform his office of what happened and to apologize for not attending the meeting. Draft a telegram for him.

Answer:
(1) DICTIONARY ORDERED FIFTEEN OCTOBER NOT RECEIVED SENT IMMEDIATELY
(2) PLUS TWO ARTS ADMIT CARDS NOT RECEIVED PERMIT APPEARING EXAMINATION PENDING RECEIPT
(3) BERTHS NOT AVAILABLE CHANGED PLANS ARRIVING TUESDAY HOWRAH MAIL
(4) STRANDED DUE TO BAD WEATHER AND UNABLE TO ATTEND MEETING APOLOGIES

Activity 4

Read the following situations and draft suitable telegrams for each.

1. Your brother has booked tickets by the Howrah Mail and will arrive from Madras on Saturday morning. On Thursday, there is an announcement on TV that a cyclone is likely to hit coastal Orissa in the next 48 hours. Draft a telegram to be sent to your brother asking him to cancel the journey.
2. You have received a 13-volume set of Brilliant Tutorials Elite 2009. But when you unpack the parcel you find that volume 10 is missing. Draft a telegram to the bookseller.

Answer:
(1) POSTPONE JOURNEY CANCEL TICKETS DANGEROUS CYCLONE HITTING ORISSA COAST SATURDAY
(2) RECEIVED BRILLIANT ELITE SET. VOLUME TEN IS MISSING SEND IT IMMEDIATELY

E-MAIL

E-mail is a medium that has revolutionized the way in which we communicate with each other. It is relatively now very popular E-mail makes it possible to communicate cheaply and almost instantly with people anywhere in the world – provided they have access to a computer. You can send any type of message, from a single word to a book-length document complete with pictures and sound files. The recipient can respond at once or think carefully before replying. You can communicate just with one person or with a large group, every member of which can participate as much or as little as they wish. E-mails inhabit a shape somewhere between personal meetings, telephones, and letters. Like telephones, they are quick and inexpensive. They are a fairly new technology. The format of e-mail is quite simple, just like the telegram form, but there is no room for capital letters in the former. Write e-mail IDs after TV: and from :

Now write e-mails for the 4 situations given in Activity 3.
Answer:
(1)
To: mbd@yahoomail.com
CC :
From: bckhuntia; g mail.com
Date: 20.11.2009
Re: Request for dictionary
Sir,
Despite my order to you in connection with a dictionary on 15 October, you haven’t sent it yet. I would request to despatch the same as soon as possible.
BC Khuntia

(2)
To : secretary council @ g mail.com
SC :
From : kunal patnaik@yahoo.mail
Date: 14.2.20
Re: Request for Admit card
Sir,
Since I have not received my admit card for the +2 Final Examination, I would request you to allow me to take the examination pending the receipt of Admit Card.
Kunal Patnaik

(3)
To : sckhuntia®yahoo mail.com
From : vedadya khuntia@g mail.com
Date : 11.9.20
Papa,
Since berths are not available, I cannot reach home on Sunday morning. I will arrive two days later, by a different train.
Ved

(4)
To: vice-chancellor, Ravenshaw college@yahoo mail.com
CC :
From: pmishra@g mail.com
Date: 4.11.20_
Re: Apology for not attending the meeting
Sir,
Since I have been stranded in Delhi, due to bad weather, I am unable to attend the meeting and beg apology for the same.
P Mishra

Odisha State Board CHSE Odisha Class 11 Invitation to English 3 Solutions Business Letter Writing Textbook Activity Questions and Answers.

CHSE Odisha 11th Class English Business Letter Writing

Business Letters

A business letter is written for a particular purpose. Its aim is to transact some particular business. For example The letter you write to a sports-goods firm asking for information about their products and the reply they send you are business letter.
A business letter normally has seven parts some of which are not found in personal letters.
1. Sender’s address at the top right-hand comer.

2. The Date:
As in the personal letter, the date is written or typed on the right below the sender’s address.

3. The Inside Address:
The address is placed on the left, two or three lines below the line of the date (which is on the right). Each line of the address begins on the left margin. Here are some examples :
Shenai and Shenai
Auditors
Court Chambers
Chennai – 400020
The Divisional Superintendent
Central Railway
Vijayawada – 520001

4. The Salutation:
Dear Sir, Dear Sirs, and Madam – are the most common forms.

5. The body of the letter:
This part contains the actual message to be conveyed – make your letter brief, clear and courteous. The letter need not be stiff or cold. Avoid the old formulas which were fashionable. Here are some old phrases that are no longer used : Yours of ever date to hand at your earliest convenience.

6. The subscription of the complimentary close:
The most common forms in business letters are ‘Yours truly’, and ‘Yours faithfully’. In very formal letters such as letters to high dignitaries, you will find ‘Yours respectfully’, ‘Yours obediently’ or ‘Your obedient servant’. If you have used a personal name in the salutation, the subcription should be ‘Yours sincerely’.

7. The Signature:
The formal letter requires your full signature. Characteristics of a good business letter
1. A business letter must be courteous and considerable
2. It should be precise and clear.
3. It must be complete.
4. A business letter must be brief.

Activity 9

Here is a letter about the introduction of a new mosquito-repellant. Read it carefully, paying attention to the various points.

Quality Marketing Agency
27 Janpath, Bhubaneswar

4 March, 20

To
Mr. M.K. Pradhan
Managing Director
Home Products India Ltd.
Industrial Estate, Mancheswar, Bhubaneswar.
Dear Mr. Pradhan,
As requested by you, vide your letter No. MD/NS/2233 dated 2.2.20 we have carried out a market survey to check the public’s acceptance of the new mosquito repellant which your company plans to manufacture. We conducted an opinion poll covering 1000 families in the coastal districts of Orissa. Forty percent of these families use mosquito repellants, but most of them are unhappy with the existing products in the market. They find the electronic repellants too expensive while the coil-based ones emit too much smoke.

The preference is for an expensive product, preferably one that produces no smoke. Our study suggests there may be a good market for a new repellant, provided these requirements are kept in mind. We recommend that your company should concentrate on manufacturing an improved kind of smoke-free mosquito coil, preferably one that produces a pleasant fragrance.
Yours sincerely,
S.K. Patnaik Director of
Research Quality
Marketing Agency

Answer the following questions.
1. Who made the request for the study?
2. By whom was the study made?
3. What was the purpose of the study?
4. What kind of procedure was used for the study?
5. What were the findings from the study?
6. What was the conclusion arrived at?
7. What was the recommendation made?
Did you observe that Mr. S. K. Patnaik did not use the official letter format as he was using a printed letterhead?

Answer:
1. Mr. A. K. Pradhan, the Managing Director, of Home Products India Ltd, had made the request for the study.
2. The study was made by the Quality Marketing Agency.
3. The purpose of the study was to test the public’s acceptance of a new mosquito repellant.
4. The Quality Marketing Agency conducted an opinion poll covering a thousand families in the coastal district of Orissa to know their opinion on mosquito repellants available in the market.
5. The study revealed that people were not satisfied either with electronic repellants or coil-based ones. They showed a preference for a less expensive product and that which produces no smoke.
6. It was concluded that there is a market for a new repellant that is less expensive. Besides, it produces no smoke.
7. It was recommended that Home Products Ltd. should manufacture a smoke-free mosquito coil and one that produces a pleasant smell.

Activity 10

Imagine that you are the President of the Literary Society of your College. Your Society plans to publish a journal. You have asked the Secretary of the Society to contact all the printing firms in the town and to select one of them to print your journal.
Here is the letter that the Secretary submitted to you. Some parts of the letter are missing. Supply the missing parts.

LITERARY SOCIETY
………………… COLLEGE

5 February,

To
Prof. B. Pujari
President
Literary Society
Sir,
______________________________________
______________________________________
______________________________________
A team consisting of the Secretary and the Assistant Secretary of the Society contacted all five printing firms in the town and obtained quotations from them for the printing of the proposed journal. All the firms quoted the same price, that is, Rs. 5000/- for 1000 copies. Rasmita Printers, however, offered a discount of ten percent, provided we allowed them an extra period of fifteen days for printing.
___________________________________________________________________________________________________
___________________________________________________________________________________________________
______________________________________________________
Yours faithfully,
S. Pujari
Secretary

Answer:

Literary Society
B.J.B. College, Bhubaneswar

5 February, 20

To
Prof. B. Pujari
President
Literary Society
Sir,
As desired by you a team consisting of the Secretary and Assistant Secretary of the society contacted all five printing firms in town and obtained quotations from them for the printing of the proposed journal. A team consisting of the Secretary and the Assistant Secretary of the Society contacted all five printing firms in the town and obtained quotations from them for the printing of the proposed journal.

All the firms quoted the same price, that is, Rs. 5000/- for 1000 copies. Rasmita Printers, however, offered a discount of ten percent, provided we allowed them an extra period of fifteen days for printing. Since we do not need the copies of the journal till a month later, we could consider the offer of Rasmita Printers as it will cost us Rs. 500/- less than the offers quoted by other printing firms.
Yours faithfully,
Puja Udgata
Secretary

Activity 11

A customer approached a bank for a house-building loan. Before sanctioning the loan, the Branch Manager asked the Field Officer to examine the application and suggest whether the loan should be sanctioned. The following is the letter that the Field Officer wrote. Some parts of the letter are missing. Re-write the missing parts, using the hints supplied.

SBI PD BRANCH
CRP Square
Bhubaneswar

3rd March,

To
Mr. M. Mishra
Branch Manager
SBI PD Branch
CRP Square
Bhubaneswar.
Sir,
1. As described by you in your letter No. 254 dt. 24 February, I examined the application of Mr. J. K. Panda for a house-building loan. (inspection of the site – examination of documents – Mr. Panda interviewed)
2. My examination of the application and the relevant documents reveals : (ownership and size of the plot – whether the plot is a disputed one – Mr. Panda’s monthly income, and whether any other loan has been taken by Mr. Panda – Conclusion).
3. As Mr. Panda is a deserving party, the sanction of the loan is recommended.
Yours faithfully,
K.C. Panigrahy
Field Officer

Answer:

SBI PD BRANCH
CRP Square
Bhubaneswar

3 March, 20.

Prof. M. Mishra
Branch Manager SBI
PD Branch
CRP Square
Bhubaneswar
Sir,
1. As desired by you in your letter No. 254 dt. 24 February 20, I examined the application of Mr. J.K. Panda for a house-building loan. I also personally inspected the site, interviewed Mr. Panda, and examined the documents relating to the plot.
2. My examination of the application and the relevant documents reveal that the site is an undisputed one. To date, all land cess has been paid and the plot is litigation free. Mr. J.K. Panda is the owner of the plot and he has clear papers certifying its ownership. The plot is 112 decimals in size and its market value is around Rs. 8.00 lakhs. Mr. Panda also has a regular income of Rs. 15,000 and has no outstanding loan in his account.
3. As Mr. Panda is a deserving party, the sanction of the loan is recommended.
Yours faithfully,
K.C. Panigrahy
Field Officer

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 16 Probability Ex 16(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 16 Probability Exercise 16(a)

Question 1.
A coin was tossed twice. Find the probability of getting.
(i) exactly one head
Solution:
A coin is tossed twice.
∴ S = {HH, HT, TH, TT}, |S| = 4
Let A be the event of getting exactly one head.
∴ A = {HT, TH} ⇒ |A| = 2
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{2}{4}=\frac{1}{2}\)

(ii) at least one head
Solution:
Let B be the event of getting at least one head.
∴ B = {HT, TH, HH}
∴ |B| = 3
∴ P(B) = \(\frac{|\mathrm{B}|}{|\mathrm{S}|}=\frac{3}{4}\)

(iii) at most one head
Solution:
Let C be the events of getting at most one head
∴ C = {HT, TH, TT} ⇒ |C| = 3
∴ P(C) = \(\frac{|C|}{|S|}=\frac{3}{4}\)

Question 2.
A coin is tossed three times. Find the probability of getting.
Solution:
A coin is tossed three times.
∴ S = {HHH, HTT, HTH, THH, TTH, THT, HHT, TTT}
∴ |S| = 8

(i) all heads
Solution:
Let A be the event of getting all heads.
∴ A = {HHH} ⇒ O(A) = 1
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{1}{8}\)

(ii) at most 2 heads
Solution:
Let B be the event of getting at most 2 heads.
∴ B = {HTT, HTH, THH, TTH, THT, HHT, TTT} ⇒ |B| = 7
∴ P(B) = \(\frac{|\mathrm{B}|}{|\mathrm{S}|}=\frac{7}{8}\)

(iii) at least 2 heads.
Solution:
Let C be the event of getting at least 2 heads.
∴ C = {HTH, THH, HHT, HHH} ⇒ |C| = 4
∴ P(C) = \(\frac{|\mathrm{C}|}{|\mathrm{S}|}=\frac{4}{8}=\frac{1}{2}\)

Question 3.
List all possible outcomes when a die is rolled twice or a pair of dice is rolled once. Then find the probability that
Solution:
A die is rolled twice
∴ S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
∴ |S| = 36

(i) Sum of points is 10
Solution:
Let A be the event of getting the sum 10.
∴ A = {(4, 6), (5, 5), (6, 4)} ⇒ |A| = 3
∴ P(A) = \(\frac{3}{16}=\frac{1}{12}\)

(ii) sum of points is at least 10
Solution:
Let B be the event of getting the sum at least 10.
∴ B = {(4, 6), (5, 5), (6, 4) (5, 6) (6, 5) (6, 6)} ⇒ |B| = 6
∴ P(B) = \(\frac{|\mathrm{B}|}{|\mathrm{S}|}=\frac{3}{36}=\frac{1}{6}\)

(iii) sum of points is at most 10.
Solution:
Let C be the event of getting the sum 11 or 12.
∴ C = {(5, 6), (6, 5), (6, 6)} ⇒ |C| = 3
The C is the event of getting the sum at most 10.
∴ P(C’) = 1 – P(C’) =  1 – \(\frac{3}{36}=\frac{33}{36}\)

Question 4.
A die rolled twice. Find the probability that the result of the first roll exceeds the result of the second roll by
Solution:
A die rolled twice S = \(\left\{\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
1 & 2 & 3 & 4 & 5 & 6
\end{array}\right\}\)
∴ |S| = 36

(i) 3
Solution:
Let A be the event of getting the 1st roll exceeds the result of the 2nd roll by 3.
∴  A = {(4, 1), (5, 2), (6, 3)} ⇒ |A| = 3
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{3}{36}=\frac{1}{12}\)

(ii) at least 3
Solution:
Let B be the event of getting the 1st roll exceeds the result of the second roll by at least 3.
∴ B = {(4, 1), (5, 2), (6, 3), (5,1), (6, 2), (6, 1)}
∴ P(B) = \(\frac{|\mathrm{B}|}{|\mathrm{S}|}=\frac{6}{36}=\frac{1}{6}\)

(iii) at most 3
Solution:
Let A be the event of getting the 1st roll exceeds the result of the 2nd roll by 4 or 5.
∴ A ={(5, 1), (6, 2), (6, 1)}
P(A’) = 1 – P(A) = 1 – \(\frac{|A|}{|S|}\)
= 1 – \(\frac{3}{36}=\frac{33}{36}=\frac{11}{12}\)

Question 5.
A card is selected from 100 cards numbered 1 to 100. If a card is selected at random, find the probability that the number on the card is
Solution:
A card is selected from 100 cards numbered 1 to 100.
∴ |S| = 100

(i) divisible by 5
Solution:
Let A be the event of getting the card whose number is divisible by 5.
∴ A = {5, 10, 15, 20, ….. 10} ⇒ |A| = 20
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{20}{100}=\frac{1}{5}\)

(ii) divisible by 2
Solution:
Let B be the event of getting the card whose number is divisible by 2.
∴ B = {2, 4, 6, 8,…., 100} ⇒ |B| = 50
∴ P(B) = \(\frac{|B|}{|S|}=\frac{50}{100}=\frac{1}{2}\)

(iii) divisible by both 2 and 5
Solution:
If a number is divisible by both 2 and 5 then it is divisible by 10. Let A be a such an event.
∴ A ={10, 20, 30,……,100} ⇒ |A| = 10
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{10}{100}=\frac{1}{10}\)

(iv) divisible by either 2 or 5.
Solution:
Let A be the event of getting the number divisible by 2 and B be the event of getting the number divisible by 5.
∴ A = {2, 4, 6,……… 100}
B = {5, 10, 15, 20, ……, 100}
∴ A ∩ B = {10, 20, 30, ….., 100} ⇒ A ∩ B = 10
∴ P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= \(\frac{|\mathrm{A}|}{|\mathrm{S}|}+\frac{|\mathrm{B}|}{|\mathrm{S}|}-\frac{|\mathrm{A} \cap \mathrm{B}|}{|\mathrm{S}|}\)
= \(\frac{50}{100}+\frac{20}{100}-\frac{10}{100}=\frac{60}{100}=\frac{3}{5}\)

Question 6.
Eight persons stand in a line at random. What is the probability that two person X and Y don’t stand together?
Solution:
Eight persons stand in a line at random.
∴ |S| = 8!
Let A be the event that two persons X and Y stand together. Considering X and Y as one person, the total number of persons is 7, who can stand in 7 ! × 2 ways.
∴ |A| = 2 × 7 !
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{2 \times 7 !}{8 !}=\frac{1}{4}\)
∴ P(A’) = 1 – P(A) = 1 – \(\frac{1}{4}=\frac{3}{4}\)

Question 7.
What is the probability that four aces appear together when a pack of 52 cards is shuffled completely?
Solution:
Let A be the event of getting four aces appearing together. Then considering the four aces as one card, the total number of cards is 49, which can be shuffled in 49! × 4! ways.
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{4 ! \times 49 !}{52 !}\)

Question 8.
If 8 persons are to sit around a table, what is the probability that X and Y don’t sit together?
Solution:
If 8 persons sit in a round table then the number of ways is (8 – 1)!
∴ |S| = (8 – 1)! = 7!
Let A be the event of getting that X and Y sit together. Considering X and Y as one person, the total number of persons is 7, who can be sit in 2 × 6 ! ways.
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{2 ! \times 6 !}{7 !}=\frac{2}{7}\)
P(A’) = 1 – P(A) = 1 – \(\frac{2}{7}=\frac{5}{7}\)

Question 9.
A die is rolled three times. Find the probability that the numbers obtained are in strictly increasing order.
Solution:
A die is rolled three times.
|S| = 6³ = 216
Let A be the event of getting the numbers in strictly increasing order.
A = {(1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6), (1, 3, 4), (1, 3, 5), (1, 3, 6), (1, 4, 5), (1, 4, 6), (1, 5, 6), (2, 3, 4), (2, 3, 5), (2, 3, 6), (2, 4, 5), (2, 4, 6), (2, 5, 6), (3, 4, 5), (3, 5, 6), (4, 5, 6), (3, 4, 6)} ⇒ |A| = 20
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{20}{216}\)

Question 10.
Three phonorecords are removed from their jackets, played with, and then returned to the jackets at random. Find the probability that
Solution:
Three phonorecords are removed from their jackets, played with, and returned to the jackets at random. Let the records be numbered 1, 2, and 3, and let their jackets be similarly numbered 1, and 2,3. The number of ways in which the records can be put in their jackets is 3! = 6.
S = \(\left\{\left(\begin{array}{lll}
1 & 2 & 3 \\
1 & 2 & 3
\end{array}\right),\left(\begin{array}{lll}
1 & 2 & 3 \\
2 & 3 & 1
\end{array}\right),\left(\begin{array}{lll}
1 & 2 & 3 \\
3 & 1 & 2
\end{array}\right),\left(\begin{array}{lll}
1 & 2 & 3 \\
1 & 3 & 2
\end{array}\right),\right.\)
\(\left.\left(\begin{array}{lll}
1 & 2 & 3 \\
3 & 2 & 1
\end{array}\right),\left(\begin{array}{lll}
1 & 2 & 3 \\
2 & 1 & 3
\end{array}\right)\right\}\)

(i) none of the records goes to the right jacket
Solution:
Let A be the event that none of the records goes to the right jacket.
∴ A = \(\left\{\left(\begin{array}{lll}
1 & 2 & 3 \\
2 & 3 & 1
\end{array}\right),\left(\begin{array}{lll}
1 & 2 & 3 \\
3 & 1 & 2
\end{array}\right)\right\}\)
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{2}{6}=\frac{1}{3}\)

(ii) just one record goes to the right jacket.
Solution:
Let A be the event that none of the records goes to the right jacket.
∴ A = \(\left\{\left(\begin{array}{lll}
1 & 2 & 3 \\
1 & 3 & 2
\end{array}\right),\left(\begin{array}{lll}
1 & 2 & 3 \\
3 & 2 & 1
\end{array}\right),\left(\begin{array}{lll}
1 & 2 & 3 \\
2 & 1 & 3
\end{array}\right)\right\}\)
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{3}{6}=\frac{1}{2}\)

(iii) just two records go to the right jackets.
Solution:
Let B be the event that just two records goes to the right jackets. When two records goes to the right jackets, then it is obvious that the 3rd jacket must go to the right jacket.
∴ B = Φ
∴ P(B) = 0

(iv) all three of them go to the right jackets.
Solution:
Let C be the event that all 3 of them go to the right jackets.
∴ C = \(\left\{\left(\begin{array}{lll}
1 & 2 & 3 \\
1 & 2 & 3
\end{array}\right)\right\}\)
∴ P(C) = \(\frac{|\mathrm{C}|}{|\mathrm{S}|}=\frac{1}{6}\)

Question 11.
Four records are taken out of their jackets, played and returned to the jackets at random. Find the probability that
Solution:
Four records are taken out of their jackets, played and returned to the jackets at random.
∴ The number of ways in which the records can be put is 4!
∴ |S| = 24

(i) none of the records goes into the right jacket.
Solution:
Let the records and jackets be denoted as R₁, R₂, R₃, R_4, and J₁, J₂, J₃, J₄, respectively.
Considering \(\left(\begin{array}{llll}
\mathrm{R}_1 & \mathrm{R}_2 & \mathrm{R}_3 & \mathrm{R}_4 \\
\mathrm{~J}_2 & \mathrm{~J}_1 & \mathrm{~J}_4 & \mathrm{~J}_3
\end{array}\right),\left(\begin{array}{llll}
\mathrm{R}_1 & \mathrm{R}_2 & \mathrm{R}_3 & \mathrm{R}_4 \\
\mathrm{~J}_2 & \mathrm{~J}_4 & \mathrm{~J}_1 & \mathrm{~J}_3
\end{array}\right)\)
\(\left(\begin{array}{llll}
\mathrm{R}_1 & \mathrm{R}_2 & \mathrm{R}_3 & \mathrm{R}_4 \\
\mathrm{~J}_2 & \mathrm{~J}_3 & \mathrm{~J}_4 & \mathrm{~J}_1
\end{array}\right)\)
∴ When R₁ be put in J₂, there are 2 such cases. Similarly when R₁ be put in J₃ and J₄ the number of such cases is 3 each.
∴ The total number of ways in which none of the records goes to the right jackets is 3 × 3 = 9.
∴ Its probability = \(\frac{15}{24}=\frac{5}{8}\)

(ii) at least one record is put in the right jacket.
Solution:
The number of ways in which at least one record goes to the right jacket, i.e. 1, 2, 3 of 4 records goes to the right jacket is 24 – 9 = 15.
∴ ItS probability = \(\frac{15}{24}=\frac{5}{8}\)

Question 12.
Let A and B be events with P(A) = \(\frac{3}{8}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{4}\). Find
(i) P(A ∪ B)
Solution:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= \(\frac{3}{8}+\frac{1}{2}-\frac{1}{4}=\frac{3+4-2}{8}=\frac{5}{8}\)

(ii) P(A^c) and P(B^c)
Solution:
P(A^c) = 1 – P(A) = 1 – \(\frac{3}{8}=\frac{5}{8}\)
P(B^c) = 1 – P(B) = 1 – \(\frac{1}{2}=\frac{1}{2}\)

(iii) P(A^c ∪ B^c)
Solution:
P(A^c ∪ B^c) = P(A ∩ B)^c = 1 – (A ∩ B)
= 1 – \(\frac{1}{4}=\frac{3}{4}\)

(iv) P(A^c ∩ B^c)
Solution:
P(A^c ∩ B^c) = P(A ∪ B)^c = 1 – (A ∪ B)
= 1 – \(\frac{5}{8}=\frac{3}{8}\)

(v) P(A ∩ B^c)
Solution:
P(A ∩ B^c)
= P(A – B) = P(A) – P(A ∩ B)
= \(\frac{3}{8}-\frac{1}{4}=\frac{3-2}{8}=\frac{1}{8}\)

(vi) P(A^c ∩ B)
Solution:
P(A^c ∩ B)
= P(B – A) = P(B) – P(A ∩ B)
= \(\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\)

Question 13.
Let A and B be the events with P(A) = \(\frac{1}{3}\) P(A ∪ B) = \(\frac{3}{4}\) and P(A ∩ B) = \(\frac{1}{4}\), Find
(i) P(A)
Solution:
P(A) = \(\frac{1}{3}\)

(ii) P(B)
Solution:
we have
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
or, \(\frac{3}{4}=\frac{1}{3}\) +P(B) – \(\frac{1}{4}\)
or, P(B) = \(\frac{3}{4}+\frac{1}{4}-\frac{1}{3}=1-\frac{1}{3}=\frac{2}{3}\)
P(A’) = 1 – P(A) = 1 – \(\frac{1}{3}=\frac{2}{3}\)

(iii) P(A ∩ B^c)
Solution:
P(A ∩ B^c) = P(A – B) = P(A) – P(A ∩ B)
= \(\frac{1}{3}-\frac{1}{4}=\frac{4-3}{12}=\frac{1}{12}\)

(iv) P(A ∪ B^c)
Solution:
P(A ∪ B^c) = 1 – P(A ∪ B^c)^c
= 1 – P(A^c ∪ B) = 1 – P(B – A)
= 1 – P(B) + P(A ∩ B)
= 1 – \(\frac{2}{3}+\frac{1}{4}=\frac{12-8+3}{12}=\frac{7}{12}\)

Question 14.
There are 20 defective bulbs in a box of 100 bulbs. If 10 bulbs are chosen at random what is the probability that
Solution:
There are 20 defective bulbs in a box of 100 bulbs. If 10 bulbs are chosen at random.

(i) there are just 3 defective bulbs
Solution:
|S| = ¹⁰⁰C₁₀
The number of defective bulbs is 20 so that the number of non-defective bulbs is 80.
Let A be the event of getting defective bulbs.
∴ |A| = ²⁰C₃ × ⁸⁰C₇
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{{ }^{20} \mathrm{C}_3 \times{ }^{80} \mathrm{C}_7}{{ }^{100} \mathrm{C}_{10}}\)

(ii) there are at least 3 defective balls.
Solution:
Let B be the event of getting at least 3 defective bulbs.
∴ B’ is the event of getting at most 2 defective bulbs.

Question 15.
A pair of dice is rolled once. Find the probability that the maximum of the two numbers
Solution:
A pair of dice is rolled once.
∴ S = \(\left\{\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6 \\
1 & 2 & 3 & 4 & 5 & 6
\end{array}\right\}\)
∴ |S| = 6² = 36

(i) is greater than 4
Solution:
A be the event of getting the maximum of two numbers greater than 4.
|A| = 20
∴ P(A) = \(\frac{20}{36}\)

(ii) is 6.
Solution:
Let A be the event of getting the maximum of two numbers is 6.
∴ A ={(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{IS}|}=\frac{15}{36}\)

Question 16.
4 girls and 4 boys sit in a row. Find the probability that
Solution:
4 girls and 4 boys sit in a row.
∴ |S| = 8 !

(i) the four girls are together
Solution:
Let A be the event that 4 girls are together. Considering 4 girls as one, the total number of children is 5 which can be sit in 5! × 4! ways.
∴ |A| = 5! × 4!
∴ P(A) = \(\frac{\mid \mathrm{Al}}{|\mathrm{S}|}=\frac{5 ! \times 4 !}{8 !}\)

(ii) the boys and girls sit in alternate seats.
Solution:
When the boys and girls sit in alternate positions. So the arrangement can be as follows:
BC₁BC₁BC₁BC₁
C₁BC₁BC₁BC₁B
∴ The total number of ways = 2(4! × 4!)
∴ Its probability = \(\frac{2 \times 4 ! \times 4 !}{8 !}\)

Question 17.
A committee of 3 is to be chosen from among 10 people including X and Y. Find the probability that
Solution:
A committee of 3 is to be chosen from among 10 people including X and Y.
∴ |S| = ¹⁰C₃

(i) X is the committee
Solution:
Let A be the event that X is in the committee. So we have chosen 2 persons from 9 persons in ⁹C₂ ways
∴ |A| = ⁹C₂
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{{ }^9 \mathrm{C}_2}{{ }^{10} \mathrm{C}_3}\)

(ii) X or Y belongs to the committee
Solution:
Let B be the event that X or Y belongs to the committee,
When X is in the committee, its probability = \(\frac{{ }^9 C_2}{{ }^{10} C_3}\)
When Y is the in the committee, its probability = \(\frac{{ }^9 C_2}{{ }^{10} C_3}\)
When X and Y both are in the committee, its probability = \(\frac{8 \mathrm{C}_1}{{ }^{10} \mathrm{C}_3}\)
∴ Probability that X or Y is in the committee
= \(\frac{{ }^9 \mathrm{C}_2+{ }^9 \mathrm{C}_2-{ }^8 \mathrm{C}_1}{{ }^{10} \mathrm{C}_3}=\frac{2 \times{ }^9 \mathrm{C}_2-{ }^8 \mathrm{C}_1}{{ }^{10} \mathrm{C}_3}\)

(iii) X and Y belong to the committee.
Solution:
When X and Y are both in the committee, we have to choose 1 person from 8 persons in ⁸C₁ ways.
∴ Its probability = \(\frac{{ }^8 \mathrm{C}_1}{{ }^{10} \mathrm{C}_3}\)

Question 18.
A class consists of 25 boys and 15 girls. If a committee of 6 is to be chosen at random, find the probability that
Solution:
A class consists of 25 boys and 15 girls. A committee of6 is to be chosen at random.
∴ |S| = ⁴⁰C₆

(i) all members of the committee are girls.
Solution:
Let A be the event of getting all members of the committee are girls.
∴ |A| = ⁴⁰C₆
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{{ }^{15} \mathrm{C}_6}{{ }^{40} \mathrm{C}_6}\)

(ii) all members of the committee are boys.
Solution:
If all members of the committee are boys, then its probability = \(\frac{{ }^{25} \mathrm{C}_6}{{ }^{40} \mathrm{C}_6}\)

(iii) there are exactly 3 boys in the committee.
Solution:
Let A be the event of getting exact 3 boys in the committee.
∴ |A| = ²⁵C₃ × 1⁵C₃
∴ P(A) = \(\frac{{ }^{25} \mathrm{C}_3 \times{ }^{15} \mathrm{C}_3}{{ }^{40} \mathrm{C}_6}\)

(iv) there are exactly 4 girls in the committee.
Solution:
Let B the event of getting exactly 4 girls in the committee.
∴ |B| = ¹⁵C₄ × ²⁵C₂
∴ P(B) = \(\frac{{ }^{15} \mathrm{C}_4 \times{ }^{25} \mathrm{C}_2}{{ }^{40} \mathrm{C}_6}\)

(v) there is at least one girl in the committee.
Solution:
Let C be the event of getting at least one girl in the committee.
∴ C’ is the event of getting no girl in the committee.
∴ |C’| = ²⁵C₆ ∴ P|C’| = \(\frac{\left|\mathrm{C}^{\prime}\right|}{|\mathrm{S}|}\)
∴ P(C) = 1 – P(C’) = 1 – \(\frac{{ }^{25} \mathrm{C}_6}{{ }^{40} \mathrm{C}_6}\)

Question 19.
There are 20 boys and 10 girls in the class. If a committee of 6 is to be chosen at random having at least 2 boys and 2 girls, find the probability that
Solution:
There are 20 boys and 10 girls in the class. A committee of 6 is to be chosen at random having at least 2 boys and 2 girls.

(20) Boys	(10) girls
2	4
3	3
4	2

∴ |S| = (²⁰C₂ × ¹⁰C₄) + (²⁰C₃ × ¹⁰C₃) + (²⁰C₄ × ¹⁰C₂)

(i) there are 3 boys in the committee.
Solution:
When there are 3 boys in the committee, its probability = \(\frac{{ }^{20} \mathrm{C}_3 \times{ }^{10} \mathrm{C}_3}{|\mathrm{~S}|}\)

(ii) there are 4 boys in the committee.
Solution:
When there are 4 boys in the committee, its probability = \(\frac{{ }^{20} \mathrm{C}_4 \times{ }^{10} \mathrm{C}_2}{|\mathrm{~S}|}\)

Question 20.
There are 120 students in a class who have opted for the following MIL. English 20, Oriya 70, Bengali 30. If a student is chosen at random, find the probability that the student is studying.
Solution:
There are 120 students in a class who have opted for the English 20, Oriya 70, Bengali 30.
∴ |S| = 120.
Let Be be the event of getting Bengali and E be the event of getting English.

(i) Bengali or English
Solution:
Since B and E are mutually exclusive events.
P(B ∪ E) = P(B) + P(E)
= \(\frac{|\mathrm{B}|}{|\mathrm{S}|}+\frac{|\mathrm{E}|}{|\mathrm{S}|}=\frac{30}{120}+\frac{20}{120}=\frac{50}{120}\)

(ii) neither Bengali nor English.
Solution:
Let A be the event of getting neither Bengali nor English, i.e. A is the event of getting Odia only.
∴ P(A) = \(\frac{|\mathrm{A}|}{|\mathrm{S}|}=\frac{70}{120}\)

Question 21.
Sometimes, probability of an event A is expressed as follows. We say that odds in favour of A are x toy if P(A) = \(\frac{x}{x+y}\). Similarly, we say that odds against A are x to y if P(A) = \(\frac{y}{x+y}\). Find P(A) and P(A)^c if
Solution:
Odds in favour of A are x to y if P(A) = \(\frac{x}{x+y}\)
Odds against A are x to y if P (A) = \(\frac{y}{x+y}\)

(i) odds in favour of A are 2 to 5.
Solution:
P(A) = \(\frac{x}{x+y}\) = \(\frac{2}{2+5}=\frac{2}{7}\)
and P(A’) = 1 – P(A) = 1 – \(\frac{2}{7}=\frac{5}{7}\)

(ii) odds against A are 4 to 3.
Solution:
P(A) = \(\frac{3}{4+3}=\frac{3}{7}\)
P(A’) = 1 – P(A) = 1 – \(\frac{3}{7}=\frac{4}{7}\)

Question 22.
Six dice are rolled. Find the probability that all six faces show different numbers.
Solution:
Six dice are rolled once.
∴ |S| = 6⁶
Let A be the event that all six faces show different numbers.
∴ |S| = 6!
∴ P(A) = \(\frac{6 !}{6^6}\)

Question 23.
There are 60 tickets in a bag numbered 1 through 60. Ifa ticket is picked at random, find the probability that the number on it is divisible by 2 or 5 and is not divisible by any of the numbers 3, 4, 6.
Solution:
There are 60 tickets in a bag numbered 1 through 60. A ticket is to be chosen, whose number is divisible by 2 or 5 and is not divisible by 3, 4, 6.
∴ |S| = 6 !
Let A be the event of getting the numbers divisible by 2 but not divisible by 3, 4, 6.
B be the event of getting* the numbers divisible by 5 but not divisible by 3, 4, 6.
∴ A = {2, 10, 14, 22, 26, 34, 38, 46, 50, 58}
B = {5, 10, 25, 35, 50, 55}
A ∩ B = {10, 50}
∴ P(A ∪ B) = P(A) + P (B) – P (A ∩ B)
= \(\frac{10+6-2}{60}=\frac{14}{60}\)

Question 24.
Compute P (A Δ B) in terms of P (A), P (B) and P (A ∩ B) where A Δ B denotes the symmetric difference of A and B.
Solution:
P (A Δ B) = P[(A – B)∪ (B – A)]
= P (A – B) + P (B – A) as (A – B) n (B – A) = Φ
= P[A – (A ∩ B)]+ P[B – (A ∩ B)]
= P(A) – P(A ∩ B) + P(B) – P(A ∩ B)
= P(A) + P(B) – 2P(A ∩ B)

Question 25.
Three volumes of a book and five volumes of another book are placed at random on a book shelf. Find the probability that all volumes of both the books will be found together.
Solution:
Three volumes of a book and five volumes of another book are placed at random on a book shelf.
∴ |S| = 8 !
When all volumes of both the books will find together, then considering the volumes as one book each, we have the total number of books is 2, which can be arranged in 2 × 3! × 5!
∴ Its probability = \(\frac{2 \times 3 ! \times 5 !}{8 !}\)

Question 26.
2 black cards and 2 red cards are lying face down on the table, If you guess their colours, find the probability that you get
Solution:
2 black cards and 2 red cards are lying face down on the table.
∴ We can guess their colours in \(\frac{4 !}{2 ! 2 !}\) = 4 ways
Cards kept face down as:
A student can guess:

(a)	B	B	R	R
(b)	B	R	B	R
(c)	B	R	R	B
(d)	R	R	B	B
(e)	R	B	R	B
(f)	R	B	B	R

(i) none of them right
Solution:
A student can guess none of them right only in case (d).
∴ Its probability = \(\frac{1}{6}\)

(ii) two of them right
Solution:
A student can guess two of them right in (b), (c), (d), (f).
∴ Its probability = \(\frac{4}{6}=\frac{2}{3}\)

(iii) all four of them right
Solution:
The student can guess all 4 of them right in (a) only.
∴ Its probability = \(\frac{1}{6}\)

Odisha State Board CHSE Odisha Class 11 Invitation to English 3 Solutions Official Letter Writing Textbook Activity Questions and Answers.

CHSE Odisha 11th Class English Official Letter Writing

Official Letters

A letter written to an official, in most cases, deals with some problem that concerns the writer.
Characteristics of good official letters
(a) Introduction
(b) Information
(c) Conclusion
The problem of the writer is briefly introduced in the first person. It is then elaborated on and substantiated in the second section. concluding section throws light on a specific request for a solution to the writer’s problem.

Activity 5

Here is a letter written by a Ward Member of Berhampur Municipality to the local Police Station. Read it carefully.

From
Dr. N.T. Rao, Member
Berhampur Municipal Council
Ward – 1
Dated 1 June, 20
To
The Officer-in-Charge
Baidyanathpur Police Station
Komapalli Berhampur
Sub: Request for Night Patrol Sir,
I write to draw your attention to the frequent occurrence of thefts of house-breaking in our locality during the last couple of weeks. last night, my neighbor lost all his valuables in a case of house-breaking. After receiving an urgent call, he had gone to his village in the evening with his family. He had locked all the doors, but when he returned in the morning, to his dismay.

he found the back door broken and all his valuables stolen. Last week, another neighbor lost his scooter. Someone broke open the grill gate during the night and took away his scooter. Cases of bicycle lifting have rather become common in our locality. We have reasons to believe that there is a gang operating in this area. I request you to provide extra police patrol at night and take urgent steps to nab the gang.
Yours faithfully,
N.T.Rao

Now read the letter again and answer the following questions.

Who is it from?
What is the problem he is writing about?
In which paragraph does he provide the details?
What are they?
What is the request made?
Answer:
(a) The letter is from N. T. Rao.
(b) He is writing about frequent occurrences of theft and house-breaking in his locality.
(c) He provides the details in paragraph 2.
(d) They refer to his neighbor’s house-breaking and theft of valuables. Above all, Dr. Rao refers to frequent bicycle lifting and the theft of a scooter from his neighbor.
(e) He requests the police to provide extra patrolling at night to catch the gang involved in house-breaking and theft.

Activity 6

Complete this letter which Mr. Sahu writes to the Chief District Medical Officer about some problems in the local hospital.

From
Mr.Srinivas Sahu,
Sarapanch
Nua Patna Gram Panchayat
Tigiria, Cuttack
14 Mar, 20_
To
The Chief District Medical Officer,
Cuttack
Sub: Steps to improve facilities in the hospital Sir,
I wish to invite your attention to some serious problems that the local hospital in Nigeria has been facing for some time. (The problems: inadequate staff; vacant posts not filled; unsanitary conditions; garbage dumped all around; poor maintenance of buildings and equipment; shortage of essential medicines, etc.) (Action requested: Yours faithfully, (Srinivas Sahu)

Answer:

Nua Patna Gram Panchayat
Tigiria, Cuttack
14, March, 20

To
The Chief District Medical Officer
Cuttack
Sir,
I wish to invite your attention to some serious problems that the local hospital at Tigiria has been facing for some time. First of all, Tigiria has been plagued by a lack of adequate staff for the last five years. While the sanctioned strength of doctors is twelve, there are only two of them. Moreover, the two doctors now posted at Tigiria are only graduates. There is no one to man the different other departments established at the hospital’s foundation by the WHO.

One is tempted to ask what has happened to the funds/grants that are being sanctioned every year by the W.H.O. in lieu of the salary of doctors. Similarly, where there ought to be 20 nurses there are only 6; of 8 pharmacists only 2, and of 10 attendants only 1. With such a skeletal staff one wonders how such a large hospital with such a great inflow of patients, can be run.

Secondly, there is the unsanitary condition of the hospital. Wards are being cleaned only once a week. Sweepers complain about the non-availability of phenyl, bleaching powder, and other disinfectants. As a result, the environs of the hospital emit a foul smell. This is compounded by the garbage piled behind the hospital. Without an incinerator or some kind of waste disposal unit, the hospital is becoming a breeding ground for germs and viruses from which it is intended to protect people.

Thirdly, poor maintenance of buildings and equipment is having its toll on patients. The air-conditioner in the ICU is ‘under repair’ for the last year. The x-ray machine is out of order and so on. One does not know when the leaking wards will be repaired and how long it will be before the hospital is whitewashed. Finally, what is of great concern is the shortage of essential medicines.

Oral rehydration packets, Enteroquinol, Quinine, Primaquin, etc. are always in short supply thereby resulting in a number of deaths. I request you therefore to kindly visit the hospital and get a first-hand experience of the situation here. I would also request you ensure the supply of essential medicines immediately so that common deaths from dysentery and malaria do not recur. Doctors, nurses, and pharmacists may also be transferred from overstaffed city hospitals.
Yours faithfully,
(Srinivas Sahu)

Activity 7

Your friend wants to send a letter to the Chairman of the Municipality complaining about the neglect of roads and drains in your locality. As he is going out, he expects you to write a letter to him. He gives you the following points. Write a letter to him.

From
Mr. Sujit Mishra
Ward Member, Municipal Council
Sector – 3, Rourkela
Date – 20 Feb, 20
To
The Chairman Rourkela Municipality
Rourkela
Sub: Improvement of civil facilities.
Sir,
– neglect of roads and drains
– roads not swept
– piles of garbage
– drains blocked
– stagnant water
– mosquitoes and flies
– place unhygienic
– request to clean the roads and drains twice every week
Yours faithfully,
(Sujit Mishra)

Answer:

Sector – 3
Rourkela
20, February, 20

To
The Chairman
Rourkela Municipality
Rourkela
Sir,
I would like to draw your attention to the unsanitary conditions that plague our locality. There is complete neglect of roads and drains in our sector. The roads are seldom swept and piles of garbage can be seen at every comer. Moreover, as some of the garbage has been washed into the drains by the rains, the drains have been completely blocked.

As a result, there is at least two feet of standing water in the drain. This has thus become a suitable place for the breeding of mosquitoes and flies, thereby making the whole locality unhygienic. I request you therefore to kindly see that the roads and drains are cleaned and the garbage lifted regularly so that the place is free from mosquitoes and flies and a hygienic environment prevails.
Yours faithfully,
(Sujit Mishra)

Activity 8

(a) Write a letter to the District Transport Manager, OSRTC complaining about the rude behavior of bus conductors on your route.
(b) The walls of your locality are frequently disfigured by posters. Write a letter to the police authorities expressing your disapproval and giving suggestions for overcoming the problem.
(c) There are frequent unscheduled power cuts in your locality. It seriously affects your preparation for the ensuing CHSE Examination. Write a letter to the SDO (Electricals) of your locality requesting him to check these unscheduled power cuts.
Answer:
(a)

Plot No. 106,
Jaydev Vihar
Bhubaneswar
25 Sept., 20.

To
The District Transport Manager,
OSRTC
Cuttack
Sir,
I wish to invite your attention to the rude behavior of bus conductors on the BBSR-Cuttack route. I am a regular commuter to Cuttack as I study there. Every day I take the OSRTC Bhubaneswar-Cuttack ‘Students Special’ to Ravenshaw College. As a student I am entitled to a fifty percent concession in the fare which amounts to Rs. 3.50. But the conductor charges Rs. 4.00 every time. In spite of our repeated requests, he has been doing this regularly.

Yesterday, he stopped the bus mid-way and forced a few classmates of mine, out of the bus. He even threatened them with dire consequences if they reported him and did not pay Rs. 4.00 as fare. Moreover, he takes in passengers other than students on the bus and charges them Rs. 10.00/- for dropping them off near Ravenshaw. As a result, many bona fide students are deprived of this facility.

It is a well-known fact that this conductor is a goonda and therefore he treats the passengers with little respect and has the bus move according to his own whims and fancy with unscheduled stops and erratic timing. As a result other conductors to have become lackadaisical in their work and high-handed with passengers. I request you therefore to look into the matter and take action to transfer the conductor in question to some other zone so as to pacify and solve the problems of the students.
Yours faithfully,
Prabhat Mishra

(b)

College Square
Cuttack
30 July, 20

To
The Station House Officer Cantonment Police Station Cantonment Road Cuttack Sir,
I wish to invite your attention to the disfiguring of walls in our locality. As you are aware Cuttack Chandi is graced by the Chandi temple as well as many educational institutions like the Sailabala Women’s College and Christ College. It is sad that the walls of this temple that houses the goddess and the walls of these temples of learning are disfigured by posters of films, posters advertising meetings or Tutorials, etc. Right in front of the Chandi Temple, the wall of Sailabala College provides a convenient place for posters.

But the sight of nude film posters is not only disconcerting but also ugly to look at. Similarly, the walls of Christ College have been disfigured by posters. Walls of private houses paralleling the wall of Christ College also have not been left untouched. I, therefore, request you to kindly enforce the prohibition on pasting posters on the walls of the Chandi temple as well as the colleges and private houses. The citizens’ committee is also willing to provide bamboo screens at suitable sites chosen by you, for putting up the posters.
Yours faithfully,
Santanu Mohanty

(c)

Main Road
Angul
4 March, 20

To
The SDO
CESCO
Angul
Sir,
I wish to draw your attention to the unscheduled power cuts that frequently occur in Kunjakanta. I am a student appearing for die ensuing CHSE Examination. Like me, there are numerous other friends of mine here at Kunjakanta who are taking the CHSE Examinations. All of us are deeply concerned about the unscheduled power cuts that frequently occur in our area.

The power cuts occur so erratically and with such increasing frequency as well as for such long hours that our preparation for the examination is greatly hampered. Besides, we are not even able to sleep well so that we can appear for the Examination the following morning without feeling sleepy and tired. It would not be too far-fetched to say that the power cuts are indirectly affecting our performance in the examinations.

We are not against load-shedding but with unscheduled power cuts, we are unable to plan out when we could relax and when to give time to studies. On the other hand, if load-shedding is scheduled, even for a whole hour, we could spend that time relaxing, going on walks, and thereby refreshing our minds and body. I request you therefore to view this matter seriously and prevent unscheduled power cuts.
Yours faithfully,
Ramesh Jena

Odisha State Board CHSE Odisha Class 11 Invitation to English 3 Solutions Application Writing Textbook Activity Questions and Answers.

CHSE Odisha 11th Class English Application Writing

Applications

An important type of business letter is the letter of aplication. Usually it is written in reply to an advertisement. The following points should be borne in mind in writing a lttter of application.

A. Presentation:
The letter must be neatly written or typed. The envelope must be properly stamped and addressed.

B. Qualifications:
Your qualifications must be clearly stated, and related to the job you are applying for. You should not sound boastful, but, on the other hand, you should clearly show that you consider yourself eligible for the post.

C. Experience:
Here again give the information that is relevant to the post. If you have just completed your studies, don’t write – Experience : nil You should try to say something positive.

D. Testimonials:
These can be enclosed even if the advertisement does not ask for them.

Activity 1

Read the following advertisement and the letter of application that follows it.

Wanted Medical Representative (Male/Female) for various towns in Orissa. Write to Agrasen Laboratories Pvt. Ltd., Sharma Lane, Banka Bazar, Cuttack within 7 days.

College Street
Puri
9 March, 20

Sir,
I read your advertisement in The Samaj of 8 March for the post of ‘Medical Representative’. I wish to apply for the post. I am 21 years old. I have passed +2 Science in the First Division. At present I am doing B.Sc. in BJB College with Chemistry as my Honours subject. I shall take the final Examination in April this year. I hope to hold a rank in the university. I am sorry to tell you that I have no experience as a medical representative. I am, however, quite familiar with different medicines, including their names and brands. My uncle runs a small shop in Puri, where I have worked part-time during my vacations. I speak Oriya, Bengali and Hindi. Being convent educated, I am quite comfortable in English. I am enclosing copies of my certificates. If necessary I can produce a testimonial from the Principal, BJB College at the time of interview. I look forward to meeting you for a personal interview at a time convenient to you.
Yours faithfully,
S Patnaik
Sudhir Ku. Patnaik.

In the box on the left, you have the main points of the application. Notice that they are not in order. Arrange them as they occur in the letter. Also put all the points of each paragraph in separate boxes on the right. The first one has been done for you.

Answer:

Activity 2

Read the following advertisement which appeared in The Samaj on 5 August, 2009 and the application of Miss Rani Das which is left incomplete. Complete the application by writing sentences for the information provided.

Padma Commercial Institute

Applications are invited from young graduates the post Clerk-cum-Typist at Padma Commercial Institute, Bajra Kabati, Cuttack. Applications should be sent to the Administrative Officer to reach him on or before 25 August 2009. Preference will be given to candidates having experience.

Lane 2
Gajapati Nagar
Berhampur Ganjam
16 August, 20

To
The Administrative Officer
Padma Commercial Institute
Bajra Kabati
Cuttack.
Sir,
I wish to apply for the post of Clerk-cum-Typist as advertised in The Samaj of
5 August, 20.
H.S.C. : First Division from De Paul School, Berhampur
B.A: Second class Honours in Economics from Berhampur University
Course in typing : Speed 45 words per minute.
Age : 27 years
Health : Sound
Post held : Clerk-cum-Typist
Experience : 6 months
Organisation : NM Tutorials New Bus Stand Berhampur
Salary : Rs. 8500 pm. (consolidated)
I enclose a testimonial from the Managing Director of NM Tutorials, Berhampur, I can get relieved from my present job in two weeks if I am selected for appointment. Your faithfully (Rani Das)

Answer:

Lane 2, Gajapati Nagar
Berhampur, Ganjam
16 August, 20

To
The Administrative Officer
Padma Commercial Institute
Bajra Kabati
Cuttack
Sir,
I wish to apply for the post of Clerk-cum-Typist as advertised in The Samaj of 5 August 20. I am 27 years old and possess sound health. As far as my educational qualifications are concerned, I have passed H.S.C. in the First Division from the De Paul School and have graduated from Berhampur University with second-class honors in Economics. Besides this, I have completed a certificate course in typing from the Hindustan Commercial Institute, Berhampur. My typing speed is 45 words per minute. I am working for the NM Tutorials, Berhampur as a Clerk-cum-Typist and am drawing a salary of Rs.8500 p.m. (consolidated). I have been working in this position for the last six months. I enclose a testimonial from the Managing Director, NM Tutorials, Berhampur, and attested copies of my certificates. I shall be relieved in two weeks if I am selected for an appointment.
Yours faithfully
(Miss Rani Das)

Activity 3

Here is an advertisement which your friend Girish Chandra Mohanty brought to you along with his personal details. He would like to apply for the post advertised. Can you help him ? Draft a letter of application for the job for your friend.

WANTED
SECURITY OFICER
below 50 : Apply in 15 days to
HOTEL MAYFAIR, Bhubaneswar.

Girish Chandra Mohanty
Nuapatana
Cuttack District
Orissa

– 47 years (Date of birth: 07.04.1962)
– H.S.C. (1978) Second division
– B.Sc. (1980) Second division
– Security Officer at Shakti Sugar, Baramba from 1984 to 1992
– DSP in Orissa Police from 1993 – 2008 (voluntary retirement in 2008)
– can read, speak and write Oriya, Hindi, and English
– good health, good eyesight
– gun license

Answer:

Anand Vihar
Nuapatna
Cuttack
23 Oct., 20

The Chief Manager
Hotel Mayfair
Nandankanan Road
Bhubaneswar
Sir,
I wish to apply for the position of Security Officer as advertised in The Samaj on 15 Oct., 20. I am 47 years old. I passed my H.S.C. in the Second Division in the year 1978, and B.Sc. in Second Division in 1980. At present, I am working as Security Officer at Shakti Sugar, Baramba, and have been in this position for the last 5 years. Prior to that, I had been working with the State Government as a Sub-Inspector of Police for 17 years from 1990-2006 and D.S.P. from 2006 to 2008. I took voluntary retirement in 2008. I am proficient in Oriya, Hindi, and English which I can read, write and speak. Besides this, I possess a sound physique and good eyesight. I enclose a testimonial from the Chief Executive Officer. Shakti Sugar and copies of my certificate as well as service records as S.I. of Police and D.S.P.
I shall be relieved in two weeks if I am selected for an appointment.
Yours faithfully,
(Girish Ch. Mohanty)

Activity 4

Write applications in response to the following advertisements :

(a) Wanted an experienced Lady Stenographer with good knowledge of English. Contact Box No. 998, The Samaj, Cuttack.
(b) Students ! Earn your pocket money during the holidays. Door-to-door visits to promote the sale of our Washing Powder Henko. Only for residents of Sambalpur. Apply to Box No. 446, The Samaj, Sambalpur.
(c) Wanted Lady Tutor for 3 Children of Convent School : 4th, 5th and 6th standanrd. Contact Deepak Mishra, Lane-3, Gajapati Nagar, Berhampur.

Answer:
(a)

27, Kharvel Nagar
Bhubaneswar
8 Dec., 20

To
Box No 998
The Samaj
Cuttack
Sir,
I wish to apply for the post of Lady Stenographer as advertised in The Samaj of 10 Dec. 2009.
I am 22 years old. I have passed the H.S.C. in the First Division. Besides this, I have passed a certificate course in Stenography from the Padma Commercial Institute, Bhubaneswar. Presently, I am working as Steno to the Manager, Home Products Ltd., Bhubaneswar, and am drawing a consolidated pay of Rs. 5500 p.m. I have been working in this capacity for the last year. I can read, write and speak Oriya, Hindi, and English. I enclose a testimonial from the Manager, Home Products Ltd., and attested copies of my certificate. I can be relieved within a week if selected for an appointment.
Yours faithfully,
(Ms. Snigdha Mohanty)

(b)

Daleipara
Sambalpur
20 Dec 20

To
Box No. 446
The Samaj
Sambalpur
Sir,
I wish to apply for the position of Door-to-Door promotional salesman as advertised in The Samaj of 17 Dec., 20. I am 20 years old. I have passed +2 Arts in the Second Division. At present, I am doing B.A. at G.M. College, Sambalpur with Political Science as the honors subject. I am in the first year of my graduation. This summer for 45 days I shall be completely free as the college is closing for vacations. Last summer after my +2 finals I worked as a newspaper delivery man and so am familiar with the lanes and by-lanes of many areas of Sambalpur. This experience I hope will stand me in good stead in door-to-door visiting. I have a cycle at my disposal and therefore going from one place to another will pose no problems. Moreover, I am fluent in Oriya, Hindi, and English which I can speak, read and write. I am enclosing copies of my certificate as well as a testimonial from the manager, of The Today News Agency, Sambalpur. I look forward to meeting you for a personal interview at a time convenient to you.
Yours faithfully,
(Shakti Das)

(c)

Hill Patna
Berhampur
14 Dec 20

To
Mr. Deepak Mishra
Lane – 3
Gajapati Nagar
Berhampur
Sir,
I am writing in connection with the advertisement which appeared recently in ‘The Samaj’, for a lady tutor. I am a trained Secondary School teacher and have taught in English medium schools. I would be interested in knowing further details about the post. I would be grateful if you could tell me what subjects the children are to be taught, for how long you expect to employ the tutor, and what salary you intend to pay. I am willing to supply full details of my qualifications and exposure. I look forward to hearing from you shortly.
Yours faithfully
S. Mishra (Miss)

Odisha State Board CHSE Odisha Class 11 Invitation to English 3 Solutions Writing Personal Letters and Notes Textbook Activity Questions and Answers.

CHSE Odisha 11th Class English Writing Personal Letters and Notes

The art of Writing Letters

Letters form an integral part of inter-personal communication. There are different tyeps of letters – personal letters which may be informal or casual, business letters, letters of public concern which appear in the newspapers, etc. which are formal in nature.
The name ‘personal letter’, generally refers to letters written to friends and relations. Such letters are usually full of news, and are usually written in conversational style. It has six parts :
1. The address of the sender
2. The date
3. The salutation or greeting
4. The body of the letter
5. The subscription or complimentary close
6. The signature

Let us look at these parts one by one.

1. The Address of the sender
This is written on the top right-hand comer of the page. Look at the punctuation.
For example,

181, Saheed Nagar
Bhubaneswar.

2. The date is written below the sender’s address

8 August 20

3. The salutation
When writing to a friend, address him by name :
Dear Sarat,
Not Dear friend Sarat.
If you are writing to the parents or brothers or sisters or intimate friends, you could write
My dear Father,
My dear Mummy, etc.
The punctuation after the salutation agrees with the punctuation of the sender’s address. A comma can be placed after the salutation if you have used commas in writing your address at the top.

4. The body of the letter.
This is the most important part of the letter. A good personal letter must be simple and pleasant to read. It is full of small details which appeal to the person you are writing to. The tone of the letter must be personal: you should write as you would speak to him if he were present before you.

5. The Subscription.
The most eomon form of closing a letter to a friend is

Yours sincerely
Yours sincere friend
Yours ever, etc.

To both friends and relations you can write

Yours affectionately

Some other closng phrases that can be used in personal letters

Ever sincerely
Yours
Your loving son
Love

6. The Signature
A letter to a friend or a close relation does not require your full signature. You should write only the first name, or the name by which you are known to the friend you are writing to : not

Sarat Kumar Mohanty
but only Sarat

7. The Address on the Envelope
Usually the address is written towards the lower half of the envelop leaving space at the top for stamps. The titles, Mr, Mrs and Ms are used before the names. Sometimes postcards are used to write personal letters. Then it is not necessary to use all the six parts in the letter. The date, the message and the signature or initials of the sender will be enough.

Activity 1

The following letter has a few errors. Correct them in order to improve the letter.

_______________
(Fill in the date)

From,
Mr. Ashok Kumar Das.
Mandara Bagicha Para.
Bhabanipatna.
To,
Mr, Biswanath Mishra.
420, Kalpana Flats.
Old Town, Bhubaneswar.
Dear friend
Well and wish to hear the same. In particular, I passed the examination in the first class. I am applying for admission in the local government college. What are your plans ? What college do you intend to join. Hope, you will successful. Thanking you.

I remain
Your sincere friend,
A. K. Das

You must have marked that there are errors in every part of the letter. Could you correct them ? Show the revised version to a friend of yours and discuss the points of revision. If necessary, ask your teacher.
Answer:
Revised letter

Mandar Bagicha Para
Bhawanipatna
14 Dec. 20

Dear Bisu,
I passed the examination in first class. I wish to hear the same in particular, from you. I am applying for admission in the local governmental college. What are your plans ? Which college do you intend to join ? Hope, you will be successful.

Yours sincerely,
Surendra

Biswanath Mishra
420, Kalpana Flats
Old Town, Bhubaneswar – 2

Errors in the first letter:
(1) The addresses and names of the receiver have been wrongly placed.
(2) Address (excluding the name) and date should be written on the top in the right-hand comer.
(3) Salutation – Dear friend is wrong.
(4) Sentences in the main part are not in order.
(5) They are replete with grammatical errors.
(6) Ending is wrong.
All these errors have been corrected in the above letter.

Activity 2

The two paragraphs are given below from the body of a personal letter. Do you find anything odd about them? One part of the letter has to be rewritten in order to make it sound personal and informal. Which part is it? Identify the part and rewrite it. “I have just returned after a wonderful holiday with you. I thought I should write to you immediately and tell you how I enjoyed every minute of my stay with you. Your cousins are such jolly companions and I will never forget the fun we had together. However, I shall be failing in my duty if I do not express my profound gratitude to your parents who spared no pains to extend warm hospitality to me during my stay there.”
Answer:
The second paragraph lacks substance in the context of a personal letter which is informal, but here it is formal to the core. The ending should be ‘the hospitality of your parents has moved me. I look forward to visiting your home and staying there for some time.’

Activity 3

(a)

Angul
24 April, 20

Dearest Jeje,
How are you? You haven’t come to see us for a long time. We are going to be in Angul all summer. Why don’t you visit us? We would love to have you.
Lots of love,
Yours.

(b)

Cuttack
20 October, 20_

Dear Kunu,
Thanks ever so much for asking me to your party. Of course, I’ll be there! And I look forward to staying the night with you.
Cheers!
Yours,
Sikta

(c)
Mr. and Mrs. Kundu request the pleasure of your company at the wedding of their daughter Rani to Raja Mohanty at Nayapalli Kalyan Mandap, Bhubaneswar at
10.30 p.m. on March 16, 20.
R.S.V.P.

(d)

Sambalpur
15 May, 20_

Dear Omunu,
It was lovely hearing from my favorite grandson. Thank you, for inviting me to spend the summer with you but I’m afraid I have to go to Mumbai in June for a heart operation. If I’m all right, I’ll visit you in December.
All my love,

(e)

Sahid Nagar
Bhubaneswar
17 October. 20_

Dear Sikta,
Just a short note to say we’re having a party on Diwali night and were wondering if you could join us. You could stay the night with us if it gets late.
Do let us know soon.
Love,

(f)

Nayapalli
Bhubane swar
5.3.20__

Mr. and Mrs. R.K. Sahu thank Mr. and Mrs. Kundu for their kind invitation to the wedding of their daughter Rani on 16.3.2000 but regret their inability to attend, on account of a prior engagement

Which invitation and reply are the most formal? Why do you think so?
Answer:
a – d
b – e
c – f
Invitation ‘c’ and the corresponding reply ‘f are the most formal because they neither contain any salutation nor do they end with an expression of affection.

Activity 4

Look at the letters in activity 3 again. Which expressions in these letters can be used for the following purposes?
to open a letter ____________________________
to say thank you ____________________________
to close a letter ____________________________
to invite somebody ____________________________
to accept an invitation ____________________________
to decline (refuse) an invitation ____________________________
Answer:
to open a letter How are you? It was lovely hearing from you.
to say thank you Thank you for, thanks ever so much for
to close a letter Lots of love. Cheers! All my love.
to invite somebody Why don’t you visit us? Request the pleasure of your company. Wondering if you could join us.
to accept an invitation I look forward to
to decline an invitation I’m afraid I have. Regret their inability.

Activity 5

Work in pairs to produce letters of invitation to suit the situations suggested below.

(a) You are going on a holiday
to Ooty. You want to invite
a friend to come with you.

You are going away on holiday
day. Do you want to invite
someone to live in your
house while you are away.

You are starting a new
restaurant and you want
to invite some of your
friends to a party you are
arranging for the launch
of your new restaurant.

Send your letter to another pair of your classmates. Keep the layout below in mind while writing the letters.
(b)

Read the letters you get and decide whether you want to accept or decline the invitation. Then draft a reply, using the hints below :
(c)

Answer:
(a)

27, Krishna Nagar
Secunderabad
12.3.20

Dear Sameer,
How are you? It’s a long time since we met. This summer we are going to Ooty and will be spending the vacations there. We were wondering if you could join us at Ooty. We could all have an enjoyable time there.
Do let us know soon.
Love,
Sanjay

(b)

80, Kharavela Nagar
Bhubaneswar
2 January, 20

Dear Suman,
We would be very happy if you could join us for the dinner party on 12 January 2010 at 7.30 pm on the occasion of the launching of our new restaurant.
Do let us know soon.
Yours,
Sudhir,

(c)

Railway Colony
Mancheswar
Bhubaneswar
10.12.20

Dear Ravi,
How are you? When we met last time you were complaining about not having a quiet place to study. Would you like to have a whole house to yourself this summer? And a secluded one too. It would be great, isn’t it? Well, we are going to our granny’s for the whole summer. We would be very grateful if you could stay in our house while we are away. Our maidservant could cook for you and of course, Deepu will keep visiting you now and then to see what you need. Can you help?
Please let us know.
Love,
Mausi.

Replies:

(a)

Saheed Nagar
Bhubaneswar
18.3.20

Dear Sanjay,
Thank you very much for inviting me to Ooty for the summer. I would love to come but I am afraid I cannot because I have already enrolled in a computer course which will continue during the vacation. I hope to come and meet you during Christmas. Hope you will enjoy yourself.
Your loving friend,
Sameer.

(b)

28, Kalpana Area
Bhubaneswar
5 January 20

Dear Sudhir,
Thank you very much for asking me to your party. I would love to be there to taste all the delicacies of your new restaurant. And by the way, Congratulations! You have succeeded in making your dream come true.
With Best Wishes,
Yours,
Suman

(c)

HA, B.J.B. Nagar
Bhubaneswar
18.12.20

Dear Mausi,
Thank you very much for reposing so much confidence in me. I would have really liked to spend the summer at your place but I am afraid I cannot. Dad has already asked me to stay with him at Rourkela so that he can coach me in mathematics and science. I can’t put this off because I’ll have to appear for the entrance next month. Sorry to have disappointed you.
Your loving nephew,
Ravi

Activity 6

It is usual to send a ‘thank-you note’ when you receive an invitation, even if you do not want to accept the invitation. Draft a ‘thank-you note’ in reply to the invitation you received in Activity 5, which you may either accept or decline. Use the suggestions given below :

Answer:

Saheed Nagar
Bhubaneswar
18.3.20

Dear Prabhat,
Just a note to thank you for inviting me to spend the summer vacation at Ooty with your parents. It was so thoughtful and kind of you to do so. I am afraid I will be unable to join you because I am doing a computer course that will continue beyond the vacations. I hope you enjoy yourself thoroughly at Ooty. Anyway, excuse me for being unable to join you and convey the same to all.
Best Wishes,
Yours,
Submit.

Activity 7

Read the letter below, and write two similar letters of invitation.
(a) to an elderly aunt, asking her to visit you for the Dussera Festival:
(b) to a young nephew, asking him to stay for the month of June.

Answer:

Plot No. 201
Apamanagar
Chauliaganj
2 September

Dear Aunty,
If you have not made plans for your Dushera holidays this year, perhaps you would like to come and stay with us at Cuttack. It is a long time since we met and all my family members would like to see you again. During your stay here, we shall enjoy the famous puja festival here to the brim. Do come. We look forward to seeing you.
Yours affectionately,
Sarika

Saheednagar
Plot No. 202
Bhubaneswar
1 December 20

Dear Ravi,
I am happy to learn that your examination is over. Your school will be closed for a month. Instead of staying there, I would like you to come here for a month. I am sure you will have a wonderful time in our midst.
We look forward to meeting you soon,
Your affectionate uncle,
Sarbeswar

Activity 8

Study the letter below as a model letter of refusal.

Write two similar letters of refusal,
(a) because your sister (brother) is going into hospital;
(b) because you have arranged to go on holiday.

Answer:
(a)

Shantivihar
Plot No 105
1 September 20

Dear Aunty,
I am happy to learn that you have invited me to the Dussera festival with you. I am indeed thrilled. I would like to accept your invitation, but I am sorry that I cannot go to you. Unfortunately, my sister is going to the hospital every day for physiotherapy in connection with his acute ankle problem. This will continue for another month. I accompany her every day. I do hope you will realize my problem, and accuse me of declining your warm invitation.
Yours affectionately,
Rahul

(b)

Vinay Mahal
Main Road
Jatni
14 June 20

Dear Mohan,
Thank you very much for your invitation to lunch next Monday. I would like to accept it, but we have arranged much in advance to go on a holiday to some important places in India. We are leaving at 1 p.m. the very same day. I am sure you will understand my predicament and excuse me for not attending your lunch.
Yours sincerely,
Subrat

Activity 9

Imagine that you are writing to some friends from a well-known holiday resort and write a few sentences describing the weather, food, etc. You can choose suitable adjectives from the list below.

cold	delicious	boring	friendly	hot	awful
exciting	rude	nice	interesting	spicy	sunny
windy	beautiful	helpful	warm

Answer:

Panth Nivas
Pun
12.05.20

Dear Varun,
We arrived here today rather late in the night as the train was running late. However, we were given a warm reception by the Panth Nivas staff who served us spicy hot tandoori chicken and roil As we sit here in the open-air restaurant we can hear the roar of the waves background and the moonlight creating beautiful shadows on the casuarina trees that line the beach. It is a very pleasant, though a windy night. I can’t wait to sleep and get up early tomorrow to watch the sunrise. I am nervous with excited.
I hope to write to you again.
Love,
Suresh

Activity 10

Here is some pictures. Use the sentences which follow the pictures to write a letter to accompany each picture. Choose a beginning, a middle, and an end from among the ones given on the next page.

The beginning :

The middle :

The end:

Answer:
(1)

Sterling Resort
Doda Valley, Kashmir
12.05.20

Dear Rabi,
We arrived safely in Kashmir on Monday evening after a hectic bus journey. The weather is fantastic and the scene all around is snow-covered mountain peaks. Exhilarating! Truly it is a paradise on earth. Unfortunately, however, I broke my leg skiing yesterday. Now I can’t walk and I have to stay in the hotel all day. It’s extremely boring and I can’t stand lying down on the bed and reading books the whole day while others enjoy themselves. Anyway, we are going back home on Thursday.
Love,
Ratha

Answer:
(2)

Panth Nivas
Puri
12.05.20

Dear Miti and Niki,
Here we are on the beach!
It’s terrible here! It’s hot and there are thousands of people everywhere. There’s no place where you can have some privacy. The food is awful.
Will be back home on Saturday. Thank goodness!
Best wishes,
TitI

Answer:
(3)

Yemen
12.01.20

Dear Umesh,
This hill station is wonderful! The weather is gorgeous, the people are very friendly and the food is delicious. Yesterday, we went to a carpet market like the one in the picture. It was extremely beautiful.
I don’t want to come home!
Love,
Ramakanta

Activity 11

Here are some more pictures. Choose one and imagine that you have gone there for a holiday. What would you write to your friends about this place? You can write about:
– the people
– the food
– what you did/saw yesterday
– something interesting that happened to you

Answer:
(1)

Paris
10.10.20

Dear Pulin,
Paris is wonderful!
The weather is just fantastic. The food is bland and the people very helpful. The scenes and sights are extremely beautiful. Yesterday we had been to the Eiffel Tower which you can see in the picture. It is the most important landmark of Paris.
Will be back home on Tuesday.
With Best wishes,
Priya

Answer:
(2)

Rourkela
2.1.20

Dear Sukant,
Greetings from Rourkela!
Our tour of the steel plant proved disastrous. A fire broke out in the smelting plant and we had to vacate the premises immediately. That was a horrifying experience. The whole town is full of smog, and that makes it terribly hot and sticky out here. I can’t wait to get back home.
Love,
Supreeti

Answer:
(3)

Bombay
10.05.20

Dear Kuni,
We are here in Bombay!
The weather is hot and sultry and the city is extremely crowded. The food is very bad and not at all to our taste. However, it’s a wonderful shopping center here. Cotton is damn cheap.
Will be back home on Sunday.
Love,
Kusum

Activity 12

A. You will find the letter of a famous person below. Which of the people mentioned below the letter could have written the letter? Why do you think so?

(a) Neil Armstrong, the first person on the moon.
(b) Florence Nightingale, the famous Nurse in the Crimean War.
(c) Edmund Hillary, the first person to climb Mount Everest.
(d) Christopher Columbus in America
(e) Ronald Amundsen, the first person to reach the South Pole.
Answer:
Edmund Hillary, was the first person to climb Mount Everest and put up his country’s national flag on its top.

B. Now imagine that you are some other person (from the list of names above) and write a letter to a friend. Work in pairs. Do not sign your name. You can write about :
– the place
– the weather
– the food
– the people
– what you have done
– some things very interesting

When you are ready, give your letter to another pair. They have to guess who it is from.
Answer:
(a)

20 July, 20

Dear Bathsheba,
We landed here on the moon yesterday. It’s cold and eerie here with no gravitational pull. Today with my space suit on, I took a walk or rather jumped all over the moon’s surface collecting rock and soil samples. The silence is frightening.
Already feeling homesick.
Love,
Neil.

(b)

21 Oct., 20

Dear Roberts,
The war is getting bloodier day by day. Thousands of dead bodies lie on the battlefield, their stench filling the air. Tending to be sick and dying; almost every minute of the day is exhausting but I am glad to be of help to the soldiers.
Hoping that the war will end soon.
Cheer up.
Florence.

(d)

America
July 20

Dear Christina,
Landed here on Sunday. The land here is virgin and wild. There are dangerous-looking Indians here wearing colorful head-dresses. But there is nothing to fear. They flee at the sound of our guns being shot.
Missing you.
Yours,
Columbus.

(e)

South Pole
Feb 20

Dear Victor,
Made it! It’s extremely cold here and the food’s frozen but the sacrifices are small considering the achievement. Yesterday we sighted some polar bears. Fishes are plentiful. The vast desert of snow and mountains makes me lonely.
Missing you.
Yours,
Ronald.

Activity 13

A. Sometimes you can send a short letter to give a friend some news. Ravi Kumar has just moved house and he wants to give his friends his new address. His letter is given below, but some parts are missing. What do you think he wrote? Complete the letter.

Answer:

Kalpana Flats
Old Town
Bhubaneswar
26th November

Dear Niki,
I’m sorry I haven’t written for a long time. How are you? We have just moved house from Uttara Chhak to the Kalpana Flats. Our new address is given above. Tika has joined her new school. She finds it quite exciting. Some of her classmates from the old school have also joined her. So she has friends too and is enjoying herself. Otherwise, life is just the same. I get up, I go to school, I eat, I sleep, and I get up. Very boring.
Anyway, write soon and do visit us when you can.
Best wishes,
Kunu

B. Imagine that you have not seen the other students in your class for a long time. Write a letter to one of them. Tell him/her how you are and give some news about yourself. (You can invent something if you like. For example, you have won Rs. 10,000 in a lottery or you are going on a long trip to Delhi.) You can begin as follows :
Dear ………………………………..,
How are you? I haven’t seen you for such a long time …………………………………..,
Answer:

68, Metro Towers
Acharya Vihar
Bhubaneswar
30th Sept. 20

Dear Lovely,
How are you? I haven’t seen you for such a long time. Why haven’t you come to the classes for three weeks? Are you sick? A lot of progress has been made in Mathematics, Science, and Social Studies. Mrs. Das our Maths teacher has retired in the mean time school and another new teacher has joined the school in her place. She’s young and beautiful and she teaches well too. Well, you’ll be surprised to know that I have won first prize in the Debate Competition. Pratik stood second and Namrata third. I received prize money of 3000 rupees. Daddy is going to buy me a Yamaha synthesizer with it. Of course, he is going to add more than 1000 to it. That’s going to be my birthday gift. I can’t wait to get it and show it to you. Do write to me at the earliest and let me know if I can do anything for you.
Missing you a lot.
Love,
Pallavi.

Activity 14

(a) Using the following clues draft an invitation :
Mr. and Mrs. S. Pattnaik — eldest son Zubin — Enu — daughter of Mr. K. Mohantv — Purunapara. Bhawanipatna — Wednesday, 7 February, 20 — 8 a.m. — the bride‘s residence — reception — Thursday, 8 February — 7 p.m. — their residence — Mandar Bagichapara, Bhawanipatna. R.S. V.P.
(b) A neighbor, who is not very good at writing letters, asks for your help to reply to the invitation above. He would like to attend the wedding. Draft a reply for him.
(c) Your father has been invited to the wedding by Mr. and Mrs. Pattnaik. But as he has to go to Delhi on some urgent business, he is unable to attend the wedding. He has asked you to reply to the invitation as he has no time. Draft a reply.

Answer:
(a)
Mrs and Mr S. Pattnaik
request the pleasure of your company at the wedding of their eldest son Zubin with Enu, the daughter of Mrs. and Mr. K. Mohanty of Purunapara, Bhawanipatna on Wednesday, 7 February, 20_ at 8.00 a.m. in the bride’s residence and thereafter to the reception at our residence (Mandarba, Gichapara, Bhawanipatna) on Thursday, 8 February 20…, at 7.00 p.m.

R.S.V.P.

(b)

Acharya Vihar
Bhubaneswar
3.2.20

Mr. and Mrs. B. K. Sahu thank Mr. and Mrs. S. Pattnaik for their kind invitation to the wedding of their eldest son, Zubin on 7.2.20 and reception thereafter on 8.2.20. They would be indeed very happy to attend the wedding and the reception thereafter.

(c)

Niladrjvjhar
Plot No. 168
13 January 20

Mr. and Mrs. B. K. Mishra thank Mr. and Mrs. S. Pattnajk for their kind invitation to the wedding of their eldest son Zubin on 7.2.20(XJ but regret their inability to attend on account of a prior business engagement in Delhi.

Activity 15

Satrupa telephones her friend Anusuya. Anusuya’s brother Prakash takes the call. Here is the conversation.
Prakash : 1-yellow, this is 2543867.
Satrupa : Good morning. Is that Prakash? Satrupa here.
Prakash : Morning. Stupa. How are you?
Strupa : Oh, fine. Can I speak to Anusuya, please?
Prakash : Sorry, I am afraid she’s not around. She has gone to a friend’s house. Any message?
Strupa : Yes, you see there is a beautiful film on at the Maharaja. Use bought two tickets for the afternoon show for Anusuya and myself. The show begins at 3 p.m. Everyone says the opening scene is not to be missed. If Anusuya
doesn’t turn up on time, I’ll have to go in.
Prakash : Where did you say the film was?
Satrupa : At the Maharaja. Near Acharya Vihar.
Prakash : All right, I’ll give her the message.
Satrupa : Thanks, Prakash. Bye.
Prakash : Bye.

Anusuya does not return by 10 a.m. and as Prakash has to go to college, he leaves a note for his sister. Imagine that you are Prakash. Now write the note using the clues given below.

Anusuya,
Satrupa ______________________, _____________, ___________ two tickets _________. wants you __________. ____________ _________ till 2.45 p.m. If _____________________. Prakash

Answer:
Anusuya,
Satrupa had rung you this morning. She has bought two tickets for the afternoon show at the Maharaja. She wants you to join her. She will wait outisde the hall till 2.45 p.m. If you do not turn up, she will have to go in.
Prakash

Activity 16

Sikta was alone at home when the postman came. She ran up to the gate and talked to him.
Sikta : Good afternoon, Postman Uncle.
Postman: Good afternoon, Sikta. Is your daddy in?
Sikta : No, unice. He hasn’t returned from the office.
Postman: When do you think he’ll return?
Sikta : Around 7.30 p.m. Do you have anything for him?
Postman: Yes, A fat registered parcel.
Sikta : Where is it from?
Postman: I think it’s from EFLU, Hyderabad.
Sikta : I see. It must be important. Can I receive the parcel on my daddy’s behalf?
Postman: I’m sorry. It can’t be given to anyone else. Tell your daddy to collect it
tomorrow. I’ll be at the Post Office from 2 to 3 p.m.
Sikta : Okay, uncle. I’ll tell him to collect the parcel tomorrow. Bye.
Postman: Bye.

Sikta writes down the note for her father lest she should forget. She begins thus :
Daddy,
The postman came this afternoon around 5.30 pm. He had _____________________ Sikta.
Now complete the note.

Answer:
Daddy,
The postman came this afternoon around 5.30 p.m. with a fat registered parcel possibly from EFLU, Hyderabad for you. I asked him if I could receive it on your behalf, but he declined. He asked you to collect it from the Post Office from 2 to 3 pm.
Sikta

Activity 17

Write a note based on the following conversation as Ashutosh would report it to his father.

Asutosh : Good afternoon. Who would you like to speak to?
Stranger : I’m Satya Mohanty from Ritz Travels. I’ve come to see your father, Mr. Saroj Patnaik. He wanted me to call on him to discuss his travel plans to the States.
Asutosh : I’m afraid he won’t be back until the day after tomorrow. He had gone to Bangalore for a meeting. But I’ll let him know you called.
Mr Mohanty : Please do so and give him these forms. He should fill them in as early as possible. If he wants to travel in May, he must apply for a passport and a visa immediately. It usually takes three months to get everything ready.
Asutosh : Thank you, Mr. Mohanty. Fil gives him your message and the forms. I’ll also ask him to call you as soon as he comes.
Mr Mohanty : Thank you. Goodbye.
Asutosh : Goodbye, Mr. Mohanty.

Answer:
Daddy,
Satya Mohanty from Ritz Travels had come to see you. He wanted to meet you to discuss your travel plans to the States. When I said that you wouldn’t be back till the day after tomorrow, he left these forms for you to fill in and apply for the passport immediately if you want to travel in May. In this view, it usually takes three months to get everything ready. I also told him that I would tell you to call him back when you return.
Asutosh