Class 11

Odisha State Board CHSE Odisha Class 11 Alternative English Solutions Grammar Prepositions Exercise Questions and Answers.

CHSE Odisha Class 11 Alternative English Grammar Prepositions

What is a Preposition?
Answer:
A Preposition is a word like on, at, to, up, off, by about etc. Which is used to establish a relationship between words in a sentence.
However, without the Preposition the sentence becomes meaningless. That is why the use of appropriate preposition is so important.
Examples:
1. The train left at 2 O’clock.
2. I am sorry for my mistake.
3. They talked about the plan.
4. Don’t sit on that broken chair.
5. He was not born of rich parents.
In the above sentences, at, for, about, on, and of are prepositions.

Kinds of Prepositions :
The Prepositions can be classified as the following five kinds, such as
1) Simple Preposition: as- at, to, on, by, for, of, with etc.
2) Compound Preposition: as- about, within, until, into, before etc.
3) Participle Preposition: as- during etc.
4) Phrasal Preposition: as- along with, by virtue of, by way of, on behalf of, on account, of etc.
5) Double Preposition: as, from among, from beneath, from under, out of etc.

Use Of certain Prepositions :
1. The use of ‘At’

1) To show definite time.
Ex- I get up at 6 A.M.
2) To show definite location.
Ex-My mother, is at home.
3) Used before the name of a village.
Ex- I live at Pratapur.
4) Used before the name of a city.
Ex- I was born at Cuttack.
5) It is used before the name of a colony.
Ex- Priya lives at Basanti Colony.
6) Used, before dawn, noon and night.
Ex- I go to the temple at dawn, at noon and at night.
7) To show the rates. Ex-Petrol is selling at fifty rupees a litre.

2. The use of ‘In’’

1) To indicate a definite place.
Ex- The Principal is in his office.
2) Used before the name of a province.
Ex-I was bom in Odisha.
3) Used before the name of a big city.
Ex-I study in Kolkata.
4) Used before the name of a country.
Ex- Utkal University is in India.
5) To show the duration of an action.
Ex-1 shall finish my break-fast in ten minutes.
6) To show context.
Ex- In my opinion, she is quite blank.
7) To show financial condition.
Ex- Mamata was born in poverty.
8) To show the month and year which prolong for some time.
Ex- Gandhiji was bom in October in 1869.
9) Used before morning, evening and afternoon.
Ex- I study in the morning and in the evening, but rest in the afternoon.

3. The uses of ‘To’

1) Used before destination.
Ex- I go to College daily.
2) To tell/show time.
Ex- It is ten minutes to two.
3) Used before an infinite verb.
Ex-1 want to buy a pencil
4) To show relation.
Ex- What is she to you?

4. The use of ‘Into’

1) To show movement towards a place.
Ex- She fell into a well
2) To change the form.
Ex- Translate this passage into English.

5. The use of ‘On’

1) To classify the position of something.
Ex-1 have written a book on translation.
2) To show contact with a place.
Ex- We sleep in the roof.
3) Used before a day.
Ex-I shall visit your house on Monday.
4) Used before a date.
Ex- India became a Republic on 26th January, 1950.

6. The use of ‘Upon’

1) To show movement towards a higher position.
Ex- The cat pounced upon a rat.

7. The use of ‘After’

1) To show sometime or position meaning later than.
Ex- It was after 10 p.m., when we ran after the thief.

8. The use of ‘Behind’

1) To show some place ‘at the back of.
Ex- Who is hiding behind the wall.

9. The use of ‘Within’

1) To show the position of time in between the specified limit.
Ex- He will return within a week.
2) To show the boundary/boundlessness of a place.
Ex- Women live within the four walls of the house.

10. The use of ‘Before

1) It is used prior to some time.
Ex-I shall finish my work before Sunset.

11. The use of ‘Above’ and ‘Over’

1) To show upper position.
Ex- Keep your head above water.
2) To show a much higher position;
Ex- The sky is over pur head.

12. The use of ‘Between’

1) Used with two persons.
Ex- My book is between Kaberi and Supriya.
2) Showing the intervening places.
Ex- There is a distance of 30 km. between Cuttack and Bhubaneswar.
3) Showing two pronouns.
Ex- There is no secret between him and you.
4) Showing two tilings/items. Ex- There is
no similarity between your book and my book.

13. The use of ‘Among’

1) Used in between more than two places.
Ex- There is no difference of culture among Cuttack, Bhubaneswar and Puri.
2) Used in between more than two persons.
Ex- Divide these bananas, among these ten boys.

14. The use of ‘By’

1) Shows persons as doers.
Ex- Tea has been taken by the guests.
Used to refer according to.
Ex- What is the time by your watch?
To show last limit of time.
Ex- You have to finish this work by 6 p.m.
4) To show means of an action.
Ex- We go to school by train.
5) To show the way of an action.
Ex- She caught you by the collar.
6) To show measuring instruments.
Ex- Apples are sold by the kilogram.

15. The use of ‘With’

1) Showing harmful instrument.
Ex- Why did you stab him with a knife?
2) To show a companion doing same action.
Ex- Who was playing with you.

16. The use of ‘Till’

1) To show time limit.
Ex-I shall wait for you till Sunset.

17. The use of ‘Under’ and ‘Below

1) To show a lower position in place.
Ex- A .cat set under the table.
2) To show a lower rank in service.
Ex- Kamala is below Sarita in the office.

18. The use of ‘Besides’ and ‘Besides’

1) Used to refer by the side of.
Ex- The baby has slept beside it mother.
2) Used to refer in addition to.
Ex- Besides being punished, he was expelled from the college.

19. The use of ‘Of’

1) To show relationship.
Ex- She is the daughter of a rich man

20. The uses of ‘Off’

1) Used to disconnect the function.
Ex- Switch off the light.
2) To show separation from upwards to downwards.
Ex- She ft off the tree.

21. The uses of ‘from’

1) To show the starting point.
Ex- She has come direct from home
To show time.
Ex-I shall start my revision from tomorrow.
To show the source.
Ex- This is a quotation from Kalidas.

22. The uses of ‘Since’

1) To show reason.
Ex- I cannot take exercise since I am ill.
To show point of time.
Ex- I have been reading since morning.

23. The uses of ‘For’

1) To show an indefinite period of time.
Ex- She has been reading for five hours.
2) To show exact period of time.
Ex- Lend me your book for day.

24. The use of ‘Towards’

To show direction.
Ex- She went towards the post office.

Exercise For Practice
1 Fill in the following blanks with suitable prepositions:

1. Your house is __________ the road.
2. She is __________ the thumb of her mother-in-law.
3. The water on the road is __________ my knees.
4. I shall return __________ at 8 O’clock.
5. Should I wait for you __________ 9 O’clock
6. Ram beat his daughter __________ a stick.
7. We are Brahmins __________ caste.
8. Sit_________ me for a while.
9. It has been drizzling __________ morning.
10. The kidnappers left Rajeswari __________ for years.
11. My house is __________ the Super Market.
12. The ornaments were divided equally the two daughters.
13. She jumped_____________ the river.
14. Return the library books___________ a week
15. The tiger jumped __________ the goat.
16. You can stay with us ___________ a month.
17. Where are you coming __________?
18. A pen is to write __________?
19. I shall ring to you__________ 7 O’clock
20. There is no hair___________ his head.
Answer:
1. Your house is above the road.
2. She is under the thumb of her mother-in-law.
3. The water on the road is below my knees.
4. I shall return by 8 O’clock.
5. Should I wait for you till 9 O’clock?
6. Ram beat his daughter with a stick.
7. We are Brahmins by caste.
8. Sit beside me for a while.
9. It has been drizzling since morning.
10. The kidnappers left Raieswari after four years.
11. My house is behind the Super Market.
12. The ornaments were divided equally between the two daughters.
13. She jumped into the river.
14. Return the library books within a week.
15. The tiger jumped upon the goat.
16. You can stay with us for a month.
1 7. Where are you coming from?
18. A pen is to write with.
19. I shall ring to you at 7 O’clock.
20. There is no hair on his head.

Words followed by appropriate Prepositions:

1. Abide by: She failed to abide by her promise.
2. Absorb in: My mother is absorbed in household duties.
3. Abstain from: A wise man should abstain from drink.
4. Accede to: I cannot accede to your silly request.
5. Access to: We have an easy access to the librarian.
6. Accuse of: He was accused of murder.
7. Admitted to: I have been admitted to +2 Science.
8. Agree to: She did not agree to my proposal.
9. Agree with: Do you agree with me or not?
10. Aim at The fowler aimed at the crow.
11. Alarmed at: I was alarmed at the sight of a snake.
12. Amuse with: I amused him with titbits.
13. Angry with: Why are you angry with me?
14. Afraid of: I am afraid of my teachers.
15. Appeal to The red colour does not appeal to me.
16. Apologise to, for: He apologised to you for my folly.
17. Apply to, for: He applied to the Principal for leave.
18. Approve of: I never approve of her conduct.
19. Arrive at: The train arrived at the station in time.
20. Annoyed with: You were annoyed with me at my misbehavior.
21. Associate with: You will ruin yourself if you associate with bad girls.
22. Assure of: The teacher assured us of help.
23. Astonished at: I was astonished at your failure.
24. Ask of, for: I asked of my neighbour for a loan of five hundred rupees.
25. Abound in: The pond abounds in fish.
26. Attend to: Attend to what your mother says.
27. Attend upon: You should attend upon your aged parents.
28. Believe in: I believe in Godly help.
29. Beg for: The beggar begged a rupee of me.
30. Beware of: Beware of your neighbour’s dog.
31. Bark at: Dogs bark at the strangers.
32. Back out: Never back out of your promise.
33. Belong to Prakash belongs to the family of writers.
34. Bent on: Our neighbour is bent on harming us.
35. Bless with: Prakash has been blessed with a son.
36. Blind of: Mohan was blind of one eye.
37. Blind to: You are blind to the defects of your brother.
38. Boast of: Never boast of your riches.
39. Born in: Sukanti was born in Gautam family.
40. Born of: I was not born of rich parents.
41. Born to: A daughter was born to Krishna.
42. Busy with: Always remain busy with your work.
43. Borrow from: You had borrowed a pen from me
44. Call at: I shall call at your house tonight.
45. Call on: Will you call on me today?
46. Care for: Nobody cars for a poor man.
47. Charge with: Jaggu was charged with murder.
48. Cheat of: Hari Chand cheated me often rupees
49. Complain of: She always complains of headache.
50. Complain to: I have complained to the Postmaster against the postman.

51. Come by: How did you come by this suitcase?
52. Collide with: Two buses collided with each other.
53. Cling to: The body is clinging, to its mother.
54. Comply with: I cannot comply with your request.
55. Compare to: Eyes are compared to a Lily.
56. Compare with : Compare Lal Bahadur with Jawahar Lal.
57. Control over The teacher has no control over his class.
58. Confident of: I am confident of my success.
59. Congratulate on: I congratulate you on your success.
60. Conscious of: You are not conscious of your weakness.
61. Consist of: This exercise book consists of one hundred pages.
62. Contented with: Nobody is contented with his lot.
63. Cured of: She .could not be cured of cancer.
64. Deal in: I deal in tea leaves.
65. Deal with: He does not know how to deal with others.
66. Depend upon: Never depend upon others.
67. Deprive of: Nobody can deprive me of my share.
68. Desire for: I have no desire for health.
69. Die of: He died of Pneumonia.
70. Die from: He died from overwork.
71. Differ with: The two brothers differ with each other in their views.
72. Different from: Your younger brother is totally different from you.
73. Devoid of: You are devoid of common sense.
74. Disgusted with: I am disgusted with overwork.
75. Dispense with: The mill owner has dispensed with his services.
76. Dispose of: I want to dispose of my scooter.
77. Distinguish between: I cannot distinguish between gold and brass.
78. Eligible for: I am not eligible for this post.
79. Equal to One kilometre is equal to one thousand meters.
80. Envious of: Don’t be envious of others’ success.
81. Enquire of: Enquired of him about his parents.
82. Escape from: The thief escaped from the police station.
83. Essential to Good health is essential to success in life.
84. Expect of: She never expected this of him.
85. Exception to: There is an exception to every rule.
86. Exempt from: The Principal has exempted Akash from the payment of fine.
87. Familiar to: Her face is familiar with Mukesh.
89. Faith in: Have you no faith in me?
90. Famous for: Agra is famous for the Taj Mahal.
91. Feed on: The tiger feeds on flesh.
92. Feel for: The rich should feel for the poor.
93. Free from: Nobody is free from worries.
94. Free with: I am not free with my teachers.
95. Fight for: We should fight for our rights.
96. Filled with: His brain is filled with dirt.
97. Fond of: Children are fond of toys and toffees.
98. Furnished with: Your house is not furnished with modem items.
99. Gifted with: Mohit is gifted with a sweet voice.
100. Give up: Give up smoking.

101. Glad at: I am glad at your success.
102. Good at: I am not good at painting.
103. Grateful to: I am grateful to you for your help.
104. Grumble at: Never grumble at your lot.
105. Guard against: Guard yourself against silly companions.
106. Guilty of: You are guilty of misbehaviour.
107. Glance at: Don’t glance at strangers.
108. Hard up: My father is hard up these days.
109. Hanker after: Do not hanker after wealth.
110. Heir to: The eldest son used to be the heir to his father’s property.
111. Hinder from: Don’t hinder me from doing graduation.
112. Hatred for: I have a great hatred for smugglers.
113. Honest in: Try to be honest in your dealings.
114. Hope for: Always do your very best and hope for the best.
115. Hopeful of: I am quite hopeful of my success.
116. Ignorant of: Man is ignorant of his success.
117. Ill with: Today, I am ill with fever.
118. Inform of: I shall inform you of my arrival.
119. Indifferent to: He is indifferent to his health.
120. Inferior to Madan is inferior to me in caste.
121. Injurious to: Drinking is injurious to health.
122. Interest in: I have no interest in painting.
123. Introduce to: I shall introduce you to my sister.
124. Insist on: She insisted on accompanying me.
125. Intimate with: I am not intimate with Priyanka.
126. Invite to: I am inviting you to a tea party.
127. Jealous of: Why is he jealous of my success?
128. Junior to: I am junior to Rahul in service.
129. Kind to: Be kind to all the creatures.
130. Knock at: Who is knocking at the door?
131. Known by: We are known by the company we keep.
132. Known for: Birbal was known for his witty remarks.
133. Known to: She is not known to me.
134. Lame of Priti is lame of one leg.
135, Laugh at Never laugh at the poor.
136. Lead to: Thus road will lead you to the hospital.
137. Lean against: Do not lean against the wall.
138. Listen to: Listen to what your teacher says.
139. Long for Who does not long for a long life?
140. Look at: Look at this silly fellow.
141. Loyal to: Be loyal to your master.
142. Match for: Dimple is no match for John.
143. Meddle with: Don’t meddle with
144. Mix with: Don’t mix with bad children.
145. Need of: I am in need of a housemaid.
146. Notorious for: Rajeswari is notorious for pick-pocketing.
147. Obedient to: Be obedient to your elders.
148. Object to: I object to your proposal.
149. Oblivious of: I am not oblivious of my surroundings.
150. Oblivious to: I was quite oblivious to the risk.

151. Part from: The bride parted from her girl friends in tears.
152. Part with: I cannot part with this costly pen.
153. Pity on: Take pity on this poor body.
154. Play upon: I cannot play upon the harmonium.
155. Pray to: I shall pray to God for success.
156. Preside over: He presided over the function.
157. Prevent from: Don’t prevent your sister from studying further.
158. Pride in: Your pride in your achievement is justified.
159. Pride of: The new car was the pride of the whole family.
160. Popular with: Our library incharge is popular with the students.
161. Profit by: You should profit by others experience.
162. Proud of: Deepti was not proud of her beauty.
163. Qualified for: I am fully qualified for the post of Superintendent.
164. Quarrel with: Never quarrel with anybody on trifles.
165. Quarrel over: The two ladies quarreled over their children.
166. Recover from: I have recovered from illness.
167. Refer to: Please refer to my application dated the 8th instant.
168. Refrain from: You should refrain from telling a lie.
169. Rejoice at: She rejoiced at her success.
170. Rely on: I cannot rely on that fair-weather friend.
171. Related to: I am not related to her.
172. Remember to: Remember me to your parents.
173. Remind of: Should I remind you of my application again.
174. Repent of: Sandeep repented of his meanness.
175. Reply to: Why did she not reply to your letter?
176. Respect for: I have no respect for cheats.
177. Rob of: A drunkard is robbed of his health and wealth.
178. Send for: Send for the doctor at once.
179. Search for: I am searching for my lost diary.
180. Search of: He is in search of a suitable job.
181. Satisfied with: I am not -satisfied with my present job.
182. Shiver with: Everyone shivers with cold in winter.
183. Shocked at: I was shocked at my uncle’s death.
184. Sick of The beggar is sick of his wretched life.
185. Sony for: I am sorry for being late.
186. Stare at: Why are you staring at that gentle lady?
187. Stare in: Death ever stares us in the face.
188. Superior to My watch is superior to yours.
189. Sure of: Everyone is sure of death.
190. Surprise at: Everybody was surprised at my success.
191. Suspect of: The police suspected him of murder.
192. Sympathy for: I have no sympathy for mean fellows.
193. Sympathise with: I sympathised with the old woman and gave her some money.
194. Take for: I took Rina for Meena.
195. Talk about: Let us talk about modem politicians.
196. Taste for: I have no taste for painting.
197. Teem with: Our farmhouse teems with rats.
198. Think over: I am thinking over my problems.
199. Tired of: I am tired of this miserable life.
200. Tremble with: He was trembling with fear.

201. True to: I am always true to my word.
202. Trust in: Trust in God and do the right.
203. Trust with: Do not trust the stranger with your suitcase.
204. Treat as: I treated his remark as joke.
205. Unfit for: A lame person is unfit for military job.
206. Useful to, for: A morning walk is useful to us for our health.
207. Vie with: The two rivals vied with each other.
208. Vote for: I always vote for a suitable candidate.
209. Wait for: I was waiting for your letter.
210. Wait upon/on: The waiter waits upon the customers.
211. Wait in: I waited in all days but you did not come.
212. Want in: Puspa is wanting in common sense.
213. Warn of: I warned him of the results of drinking.
214. Weary of: I am weary of old age.
215. Wonder at: I wondered at the beauty of the Taj Mahal.
216. Worthy of: The one-eyed and ugly girl is not worthy of her husband.
217. Yield to: I shall not yield to
218. Zeal for: She has a great zeal for outdoor life.

Exercise For Practice

Supply suitable prepositions in the blanks below:
1. pratap is addicted __________ smoking.
2. She has np chance ____________ getting a good job.
3. I have no need __________ his help.
4. I am not in ___________ anybody’s help.
5. I am occupied ___________ an important job.
6. Why don’t you aim __________ becoming a good girl.
7. I have no difficulty ___________ learning English.
8. He prevented his son ___________ gambling.
9. Why are you bent ___________ teasing him.
10. I could not act __ her advice.
11. Have you applied __________ leave.
12. He was annoyed __________his mischief.
13. Believe ___________ what I say __________ you.
14. I have a passion __________ reading articles.
15. He-is not inclined ___________ agree with you ___________ this point.
16. The train is bound ____________ Mumbai.
17. She appealed __________ me __________ a railway concession form.
18. Aren’t you tired ___________ sitting idle’?
19. She is very ambitious __________name and fame.
20. You begged mercy ___________ your neighbour.
21. This man deals __________ vegetable.
22. I don’t rely ___________ you in this, matter.
23. He is ___________ God.
24. She shouted ____________ help.
25. She is longing __________ her dead mother.
Answer:
1. Pratap is addicted to smoking.
2. She has no chance of getting a good job.
3. I have no need for his help.
4. I am not in need of anybody’s help.
5. I am occupied with an important job.
6. Why don’t you aim at becoming good girl.
7. I have no difficulty m learning English.
8. He prevented his son from gambling.
9. Why are you bent on teasing him?
10. I could not act upon her advice.
11. Have you applied for leave?
12. He was annoyed at his mischief.
13. Believe Jn what I say to you.
14. I have a passion for reading articles.
15. He is not inclined to agree with you on this point.
16. The train is bound for Mumbai.
17. She appealed, to me for a railway concession form.
18. Aren’t you tired of sitting idle?
19. She is very ambitious of name and
20. You begged mercy of your neighbour.
21. This man deals in vegetables.
22. I don’t rely upon/on you in this matter.
23. He is against God.
24. She shouted for help.
25. She is longing for her dead mother.

Odisha State Board CHSE Odisha Class 11 Approaches to English Book 1 Solutions One-Act Plays Chapter 2 The Unexpected Textbook Activity Questions and Answers.

CHSE Odisha Class 11 Alternative English Solutions One-Act Plays Chapter 2 The Unexpected

Section-I

Questions For Discussion

Question 1.
What is the exciting piece of news Alec and Tom bring Mrs. Parker? How does Mrs. Parker react to it? How do Alec and Tom feel about the way she reacts to their information?
Answer:
The news that two convicts have escaped from prison cells has been brought to Mrs. Parker by Alec and. Tom. There is a sudden reaction in Mrs. Parker’s mind to have listened to their statement: The tea cozy she had in her hand dropped land she stood motionless. She became puzzled by the news.

Question 2.
Who is Joe? Why does he call at Mrs. Parker’s cottage? What is it about his manners that Tom and Alec object to? Would you say he is educated or uneducated?
Answer:
Joe Badger is a young man who says that he has just come to ask Mrs. Parker a few questions. He is on ‘.a helping mission to his constable uncle of the village. He calls Mrs. Parker to ask her a few questions as to the escape of the two criminals. Tom and Alec object to Joe’s calling them ‘kids’.Joe is not uneducated. He is not educated either. He says, “My education may not be so fine as yours (Tom’s), but he has been taking correspondence lessons from a school of detectives.

Question 3.
What makes Joe suspect Mrs. Parker’s activities? How does Mrs. Parker explain herself? Does Joe find her answers convincing? What does he threaten to do?
Answer:
Mrs. Parker’s living alone near the jail i.e. why she wants to be so private and keeping with her’ a Bentley sports car in an old shed where no one would be able to notice it makes Joe suspect Mrs. Parker’s activities. She explains that the sports car that Joe had seen belonged to her nephew. Joe does not find her answers convincing or satisfactory. He threatens her to get to the bottom of that.

Vocabulary

A. Say which parts of speech the following belong to:

luck, diurnal, fabulous
lie, velocity, ghost
look, vivacious, ghostly
last, violent, gullible
paper, write, gunpowder
pipe, belong, expertise
prologue, elope, expert
perseverance, conducive, exigency
cousin, catastrophic, jerk
callous, loathsome, jostle
cactus, logical, jump
curious,longevity, judicious
caricature, torrential, jeopardy
pen, tremendous, civilization
dirty, parsimonious, erosion
Answer:
luck – noun
look – verb, noun
paper – noun
prologue – noun
cousin – noun
cactus – noun
caricature – noun
duty – noun
velocity – noun
violent – adjective
belong – verb
conducive -adjective
parsimonious -adjective
catastrophic -adjective
loathsome -adjective
logical -adjective
longevity -noun
torrential -adjective
tremendous -adjective
fabulous – adjective
ghost – noun
ghostly – adjective
gullible – adjective
gunpowder – noun
expertise – noun
expert – adjective
exigency – noun
lie – verb, noun
last – adjective, adverb
pipe – noun
perseverance – noun
callus -adjective
curious – adjective
pen – noun
diurnal – adjective
vivacious -adjective
write – verb
elope – verb
erosion – noun
jerk – verb
jostle – verb
jump – verb
judicious – adjective
jeopardy – noun
civilization – noun

Section-II

Questions For Discussion

Question 1.
What is? Does the secret Mrs. Parker share with Alec and Tom? What was her object when she took the cottage? How does she propose to use the Bentley car? What is the real surname of Mrs. Parker?
Answer:
The secret which Mrs. Parker hares with Alec and Tom.Is that the convict’s none other than her son who had parted from her for years together? Her sole object in taking the cottage nearer to the jail was to help her sen escape from the jail. She proposed to make her son. escape in the Bentley car. The real name of Mrs. Parker is Mrs. Felton.

Question 2.
Why is Mrs. Parker reluctant to let Alec and Tom stay, with her?
Answer:
Mrs. Parker is reluctant to let Alec and Tom stay with her. She wants them to leave outright. Her son might get startled to see the strangers. He might not take them into confidence.

Question 3.
What does Mrs. Parker tell Joe about the ownership of the Bentley car? How does she explain her relationship with the convict? How does she explain her relationship with the convict? Does Joe believe her? Why do Tom and Joe fight?
Answer:
Mrs. Parker tells Joe that the Bentley car belonged to her nephew. She explains to him as to her relationship- with the convict that he was her nephew-who arrived from London that morning. Joe. does not believe her when Joe insisted that the convict’s clothes were hidden away in another room Which he wanted to search for. The convict asked him to get out of the house he was opposed. But he told that he was going to inform about it this constable under, and the occasion fighting started.

Vocabulary

Derive nouns from the following:

innocent, pitiable, kind
pretend, realize, probably
friendly, quick, melodramatic
clever, nervous, pleasant
suspect, monetary, narrate
circumstantial, frighten, good
monetary, expect, beautiful
difficult, dangerous, luxurious
remember, repeat, sorry
horrible, hopeful, systematic
Answer:
innocent – innocence
pretend – pretension/pretense
friendly – friendliness
clever – cleverness
suspect – suspicion
circumstantial – circumstances
monetary – money
difficult ‘ – difficulty
remember – remembrance
horrible – horror
pitiable – pity
realize – realization
quick ‘ – quickness
nervous – nerve
momentary – moment
frighten – fright
expect – expectation
dangerous – danger
repeat- repetition
hopeful- hope
kind- kindness
probably- probability
melodramatic- melodrama
pleasant- pleasure
narrate- narration
good- goodness
beautiful- beauty
luxurious- luxury
sorry – sorrow
systematic – system

Section-III

Questions For Discussion

Question 1.
What does the warder collect from Mrs. Parker’s house as pieces? evidence against the convict? How does he propose to use the car? What purpose do they really serve?
Answer:
The warder collects the prison clothes and a parcel in Mrs. Parker’s house as evidence against the convict. He proposes to take the convict in the Bentley sports car as evidence of his escaping in it. They really serve the purpose of escaping.

Question 2.
What is the password Joe tells the warder? How was Joe able to get it ? … it’s safe with me, he claims, Do you agree with him?
Answer:
The password is “Regent” which Joe tells the warder. Joe was able to get it from his Uncle, the constable of the village. He says that it is safe with him which gives a false sense of safety. It’s a false notion he carries.

Question 3.
What, as Mrs. Parker says, cream of joke? Who really are the convict and the warder? How does Joe unwillingly help them escape to safety?
Answer:
The cream of the joke is that Joe never believes any of his uncle’s secrets, but he told Roger the one thing he needed to know. He told him the password that will get him safely to freedom. Now, all she has to do is join him, and they are going to Australia to start all over again. The warder is Mrs. Parker’s .son Roger himself and the convict happens to be a stranger whom Mrs. Parker did not know. Joe does not know the secret that the warder is Roger himself whom he unwillingly tells the password “Regent” which Roger used in different situations and places and safely escaped as the roads are tightly watched.

Question 4.
“Where women are concerned, the unexpected always happens” who says this? How many times has this statement been repeated in The play? How is this statement relevant to the play?
Answer:
Tom repeatedly utters that in the context, women are concerned with unexpected happeningsÿ things become unpredictable statement “where women are Concerned, the unexpected always happens”. This statement is said by his father. The repetition takes place’ thrice in the play. This statement is relevant.

Composition

Question 1.
Who do you think is the central character of the play? Why? Unexpected” is written by Alia Adkins, an
Answer:
The one-act play “The eminent and outstanding playwright of our time. The playwright is a superb and excellent master in the art of .depicting attractive and fascinating characters. They are lovely, real, and lively in nature. Such a typical character is Mrs. Parker who is really considered the pivotal character of the play. She drags our attention automatically with a tint of rare intelligence and wit. In fact, a play has’ kaleidoscopic characters who cross and recross the stage throughout. The protagonist figure acts like the linchpin around whom the other characters revolve. In the play, “The Unexpected Mrs. Parker happens to be the central and pivotal character who dominates the plot of the play from the beginning to the end. She is the only female character whose importance is realized in every vein of the play.

The play without Mrs. Parker is like the proverbial play if we eliminate Mrs. Parker from the play, it becomes a meaningless piece of nothing else, However, the play opens with Mrs. Parker and the two young men who are found in the former’s house. He has been staying in a house close to the jail. It is because his innocent son has’ been imprisoned with no “Hamlet”.without the prince of Denmark. If the fault of his. Mrs. Parker has a tendency to help her son escape from jail. But she wants that all such things need be done secretly. She even does not take the young men into confidence lest her secret design should be exposed. As her son is likely to arrive at any time after his escape from the jail, she does not want that the two young boys should know about it. But after a prolonged talk, she confides in them and reveals her identity and that of her son.

She says that she is not Mrs. Parker, but she is Mrs. Felton and her son Roger is in jail. She says, “Oh, my dear boys, I’ am trusting you, as I have never trusted anyone”. She had only one object when she took the cottage and that is to help Roger to escape. She has kept the car ready for use ever since she came there. Moreover, there takes place a hot discussion between Joe and Mrs. Parker, When Joe says that he has seen a convict enter her house she pretends not to have seen anybody. When insisted she tells that it is her nephew from London who has arrived in the morning.

She performs a successful part in making the boy escape from jail. She is a courageous lady who makes all kinds of arrangements for escape. Her dialogue reveals the crux of the plot Joe has told the password “Regent” which would help his escape and baffle the people. It is Roger who had disguised himself as the warder. Actually, Mrs, Parker is the running thread in the play. She dominates the whole labyrinth of the plot.

The core sentence “Where women are concerned, the unexpected always happens” is appropriately justified by her activities in the play. Her involvement marks an anÿeye-catching fact in a beautiful way. Her importance in the play can not be ruled out. As a matter of fact, judging from all respects, Mrs. Parker is truly the central and pivotal character of the play. She is, in fact, – a courageous and intelligent lady. She is a superb and fantastic creation by the playwright. On the whole, her activities are inspiring, thought-provoking, elevating and heart-enduring

Question 2.
Can you suggest another title for the play? Justify your choice of the proposed alternative.
Answer:
The one-act play “The Unexpected” is, undoubtedly, the best masterpiece of Alia Adkins, a prominent and outstanding playwright of this era. The playwright has superb mystery in providing apt and suitable titles to the plays. Adkins’ plays are fascinating, interesting, alluring, and heart-enduring. The way Adkins deals with the women characters with the appropriate titles is really magnificent and fantastic.

In fact, the title is the crown piece of any work of art. The caption should be eye-catching and significant. It should be apt and suggestive. It is like a signboard that speaks out what is usually contained inside. It is rather suggestive and expressive. The file of this discussed play, “The Unexpected” is aptly justified in this real sense- of the term. This title is so named because, “where a woman is concerned, the unexpected, always happens”. However, an alternative title for the play may be subscribed to the play.

The alternative title may be “When women are involved” However, the involvement of women in different matters ultimately results in Here, Mrs. Parker being the representative of teeming millions of women who get themselves involved in. several things and mince matters like anything. Mrs. Parker is seen taking a house near the jail. Two young men named Alec and Tom get in. Mrs. Parker at the outset declines to let them know why she is insisting on living in that cottage, But very soon she takes them into confidence and tells everything she has in her mind. She is not Mrs. Parker.

She is actually Mrs. Felton who has taken the house near the jail to help her innocent son Roger escape from die jail, The two young men promise to help her and her son. But another young boy Joe appears at that very moment and makes the matter unexpected tilings. They make a fuss about things. very complicated. On the other hand, Joe wishes to bring to the limelight die intention and project of Mrs. Parker. He makes an analytical sketch of Mrs. Parker having a Bentley sports car. and why she lives near the jail.

The two convicts have escaped from the jail and the warder is after them. Mrs. Parker has made all possible preparations to make his son escape in the daylight. A young man enters Mrs. Parker’s house with the convict suit in the presence of Alec and Tom. Mrs. Parker remains silent. Joe comes in again and declares that he has seen the convict enter the house. In the meanwhile, the warder enters and Joe says,that there is a convict and his dress.

The warder seizes the prison clothes and arrests the young men who have been there. They leave the place in the Bentley car with the password “Regent” from Joe who has got it from his constable uncle. In the end, it is seen that the warder is none other than Mrs. Parker’s son. As a matter of fact, the title of die play is apt and suggestive. From the above description, it is very much clear that the central and pivotal. the character Mrs. Parker is very much concerned with the title of the play. The title becomes meaningless if we eliminate Mrs. Parker from the play. On the whole, the title is interesting, thought-provoking, and elevating.

Question 3.
Sketch the character of Mrs. Parker.
Answer:
Actually, the one-act play “The Unexpected” is, indeed the best typical masterpiece of Alia Adkins, a popular and outstanding playwright of the modern predicament. The playwright is undoubtedly a superb and excellent master in the art of characterization. Adkins’ dealing with lively women characters is really very fantastic. Adkins’ characters are courageous, clever, shrewd, and lively. Such a pivotal character is Mrs. Parker in this discussion play. However, a character is his or her own destiny. One can make or mar one’s character. Drama is a literary device that makes use of characters who speak their mind through dialogue.

The one-act play “The Unexpected” by Alia Adkins presents a volley of characters who cross and recross the stage. Among all the characters in the play, Mrs. Parker rules supreme. She is the principal and pivotal character around whom all the characters revolve cyclically. A close study of her character has become the necessity of the hour. Of course, MTS. Parker acts as a loving mother. She is not able, to stand the imprisonment of her innocent son. She makes all possible efforts to make her son escape from jail.

As the first step towards escape, she takes a house close to the jail. This intensifies the suspicion of the people like Joe. He enters Mrs. Parker’s house and cross-examines her from different angles. But this does not exasperate her. She makes a patient approach for achieving her greater interest. She supplicates to Alec and Tom in order to leave the place instantly. But they do not leave. Again, Mrs. Parker is a courageous lady. She handles the situation tactfully. She is compelled to tell Alec and Tom and begs them to help her in the mission. They extend helping hands. They are in the house. Joe comes back again and declares that he has seen a convict enter the house.

A young man who has just arrived and whom Joe has thought of being the convict has changed into some dress given by Mrs, Parker. In the meanwhile, the warder appears on the scene. Joe tells that the escaped convict is there. He finds the prison clothes and arrests the young man. Joe goes with them. Technically, the warded collects the password from Joe, because all the roads are strictly watched, They go away in the Bentley car.

The warder is none other than Roger, Mrs. Parker’s son who gets escaped safely with the password and the Bentley car. However, Mrs, Parker is shrewd and clever enough in tackling situations properly. She controls the two young boys Alec and Tom who play according to her tune. Joe is also carefully managed so that he can not get a little bit of an idea about the smooth escape. Alec and Tom get angry with Joe and rise up to thrash him like anything, but she tactfully forbids them. Joe is also technically managed when he comes proudly to make an investigatory approach in order to get a job.

Everybody is properly manipulated and has a presence of mind and unparalleled sly, wit. She administered by means of Mrs. Parker’s dominates over the play and the play without her falls into sheer nonsense. As a matter of fact, Mrs. Parker is actually the central and pivotal character in the play. She is a superb and fantastic representation of a courageous and cunning woman in general. She is, indeed, Adkins’ best manifestation of a typical character. On the whole, the play is elevating, attractive, alluring, and heart-touching due to her extraordinary power of handling and tackling a critical situation.

Question 4.
Imagine that you are a news reporter working for a national English daily. Make a report on the escape of a hard-core criminal from the local prison and his subsequent arrest.
Answer:
Cuttack, 20 January: A hard: core unconscious by means of a chemical obtained criminal who has been involved in myriad antisocial activities and convicted in a court of law and sentenced life long rigorous imprisonment escaped from the Central Jail, Choudwar at 2 a.m. last night. He intoxicated the sentry of the jail and made him from his supporters through some secret deals and made him unconscious. He administered the same chemical to his convicts who went asleep. Availing himself of the privilege, he sneaked out of the jail and disappeared within a moment. The jail authorities have not become successful to trace the criminal 50 far. AH, the police stations have been informed to remain alert to nab the escaped convict.

Vocabulary

abandon, logical, animate
abound, measurable, coherent
absurd, mobile, combustible
halt, moderate, communicable
happy, moral, competent
allergic, movable, complete
catholic, mutable, comprehensible
hero, partial, conclusive
Jacobian, patient, consequent
national, penetrable, rational
thesis, pertinent, able
act, perceptible, attach
attack, ability, ascend
balance, accurate, encourage
legal, active, forward
legible, adaptable, increase
legitimate, adequate, and impart.
liberal, advisable, persuade
literate, addable, careful
Answer:
abandon- upkeep
abound- lack
absurd- right
halt- vacillate
happy- unhappy
allergic- antiallergic
Catholic- anti-catholic
hero- antihero/villain
Jacobian- anti-Jacobian .
national- antinational
thesis- antithesis
act- rest/counteract
balance- imbalance
legal- illegal
legible- illegible
legitimate – illegitimate
liberal – illiberal
illiterate – illiterate
logical, – illogical
measurable – immeasurable
mobile – immobile
moderate – immoderate
moral – immoral
movable – immovable
mutable – immutable
partial – impartial
patient – impatient
penetrable – impenetrable
pertinent – impertinent
perceptible – imperceptible
ability – inability
accurate – inaccurate
active – inactive
adoptable -inadoptable
adequate – inadequate
advisable – inadvisable
aidable – inaidable
animate – inanimate
coherent – incoherent
combustible – incombustible
communicable – incommunicable
competent – incompetent
complete – incomplete
comprehensible – incomprehensible
conclusive – inconclusive
Consequent – inconsequent
rational – irrational
able – unable
attach- detach
ascend – descend
encourage – discourage
forward-backward
increase – decrease
impart – take
persuade – dissuade
careful – careless

The Unexpected Summary in English

Section-I
Pre-reading Activity :
Question 1.
What kind of movie/stage interests you most? Do you like viewing suspense movies/dramas? Can you name some of the elements that go with a suspense play?
Question 2.
Here is a gripping suspense play, “the unexpected by Alla Adkins? a British playwright what do you think this play going to be about?

Focussing Questions
As you read section 1 of the play, try to find answers to the following questions:
Question 1
What would you say about the setting of the play? Is it urban or rural? How about the weather? Is it pleasant or gloomy?

Question 2.
What makes Joe suspect the activities of Mrs. Parker? Characters in the Play
1. Mrs. Parker
2. Alec
3. Tom
41 Joe Badger
5. f Convict’
6. Warder

Setting
A room in a lonely cottage on Dartmoor, The room is simply furnished. Table (set for tea) down R, C. Armchair down L.C. Door up R. Door up L. At the rise of the curtain, Mrs. Parker is discovered at the table preparing tea. Knock at door L. Mrs. Parker answers it. Enter Alec and Tom

Gist
Paragraphs: 1-7
Mrs. Parker greets Alec and Tom and says that she had not expected them to see that afternoon. Alec replies that they had to cycle over to see her. He also says that they have brought her an exciting piece of news. She asked what the excitement was. It is that the two convicts have escaped from the prison that afternoon. Listening to this Mrs. Parker drops the tea cozy in her hand and remains motionless. Alec makes it clear that they have got away from working and going about it. half an hour before. They are believed to be somewhere on the moors. He asks if they have frightened her. Tom assures that there is nothing to be scared of because the convicts are not likely to come that way.

Paragraphs: 8-10
Recovering from her tension, Mrs. P&rker says that is right. She says that she has been thinking of me. She advises them to start back for the village as soon as they have tea because their mother will be worried about their life if they are not home before long. In the absence of Mrs. Parker, Alec says why she had been a bit nervous about a conflict. She has lived alone in this cottage for the last six months and has never shown the slightest fear of tramps or of anything else for that matter, but she has become as frightened as a rabbit. Tom recites his father’s statement, “Where women are concerned, the unexpected always happens.”

Paragraphs: 11-28
is Joe Badger. He says that he has come to see Mrs. Parker. He also asks what the two kids have been doing there. They object to the There is another knock at the door. It word ‘kids’. Joe tells them that a couple of convicts are prowling about in the vicinity. Mrs. Parker enters saying why, Joe! What are you doing here on such an evening, Joe has just come to ask a few questions to Mrs. Parker. It is because he has to help his constable uncle in the village. Mrs. Parker offers him tea which he declines politely. He starts that two desperate criminals ready to murder everybody if they get the chance. He has been taking correspondence lessons from a school of detectives. He asks why a lady should like to live alone in a place like that.

Paragraphs: 29-36
Mrs. Parker is obviously startled. Joe also continued why she should live as near to the prison as she possibly can. Mrs. Parker asks why he asks her such questions. Joe calmly replies that it is because she has been hearing things down in the village. He tells her that she should not think that he is not making any accusations against her. Mrs. Parker says that thanks need to be given to the police to mind their own business. Joe asks her why she is having with her a Bentley sports car hidden away in an old shed where no one is likely to notice it. Thoroughly alarmed asks him how dare he spy on her like that. As his uncle is the constable and I want to join the force myself. It is his business; to find out things. Mrs. Parker says that Joe must leave the house at once before any unpleasant situation takes place.

Paragraph: 37.
Joe warns her that he is leaving but he must go to the bottom of things. She replies that he will get to the bottom of the duck pond if he does not clear out quickly Joe leaves. She comes forward saying that he is going to make a great deal of trouble for her. Alec asks why she has never told them so far that she has a Bentley sports car kept hidden from view. It is because they might have worried her to drive it. She demanded them to leave immediately. She tells them if they promise her “that you will never repeat what I am going to tell”. They promised

Analytical Outlines :

• Mrs. Parker greets Alec and Tom.
• She has. not expecting them to see it that afternoon.
• Alec replies that they have to cycle over to see her.
• He also says her that they have brought her an exciting piece of news.
• She wanted to know what it was.
• The two convicts escaped from the prison that afternoon.
• Listening to this, Mrs. Parker drops the tea cozy from her hand.
• She also remains motionless,
• Alec makes it clear.
• They have got away from working about half an hour before.
• They are believed to be somewhere on the moors.
• He asks if they have frightened her.
• Tom assures that there is nothing to be worried about.
• Because the convicts do not come that
• Mrs. Parker recovers from tension.
• Mrs. Parker says it is the all right way.
• She says that she has been thinking of them.
• She advises them to go back to the
• They should go after taking the tea.
• Because their mother must be worried; about them.
• Again they are not home for a long time
• Alec says she has been a bit nervous:
• has lived alone in this cottage village.
• She has lived for the last six months.
• She has never shown the slightest fear of tramps.
• But now she has become as frightened as a rabbit.
• Tom recites his father’s statement.
• “Where women are concerned, the unexpected always happens.”
• There is. another knock at the door.
• It is Joe Badger.
• He has come to see Mrs. Parker.
• He asks what the two kids have been doing there.
• They object to the word ‘kids’.
• Joe tells that a couple of victims are prowling about in the vicinity.
• Mrs. Parker enters saying why.
• She says what they are doing there- on such an evening.
• Joe has just come to ask her a few questions.
• He has to help his constable uncle in the village.
• Mrs. Parker offers him tea.
• He declines politely.
• He tells about the two desperate criminals,
• They can murder everybody by getting a chance.
• He has been taking correspondence lessons from a school of detectives.
• He asks why a lady should like to live
• Mrs. Parker says why he is asking such questions.
• Joe calmly replies that she has been things down in the village.
• He says her that he is not making any accusations against her.
• Mrs. Parker says police will mind their own business. alone in a place like that.
• Mrs. Parker is obviously startled.
• Joe also says why she should live as near to the prison.
• Joe asks her about her car.
• She- is going with a Bentley sports car.
• It is hidden away in an old shed.
• No one is likely to notice it there.
• Thoroughly alarmed asks him how dare he spy on her like that.
• His uncle is a constable.
• He wants to join the force himself.
• It is his business to find out things.
• Mrs. Parker says that Joe must leave the house at once.
• He should leave before any unpleasant situation takes place.
• Joe warns her that- he is leaving.
• But he must go into the bottom of tilings.
• He should get to the bottom of the duck pond.
• Then Joe leaves,
• She says that he is going to make a lot of trouble for her.
• Alec asks why she has never told them about the car.
• He also wants to know about that hidden Bentley sports car.
• She says it because they might have worried her to drive it.
• She says him to leave immediately.
• She tells them to promise something.
• She says not to repeat telling those things.
• They promised.

Meaning Of Difficult Words :

tea cozy – an area of open uncultivated highland covered with grass.
moor – a soft cover of cloth or wool put over a teapot to keep the tea hot.
working gang – a group of prisoners working outside the prison to work as laborers on Some projects.
what’s up – what’s wrong
prowling – moving quietly and carefully to avoid being noticed, wandering like a hunting animal
goal-bird – (also spelled jailbird) a person who is in prison or has been in prison.
sauce – rude behavior.
afore – before
the gas – bag, empty talker.
knock your, block – hit your head.
blighter – (swear word) devil.
furnished – decorated, arranged with furniture.
indeed – in fact, really.
convicts, – proven criminals.
motionless – without movement,
scare about – ‘to get afraid about
slightest – the least, the minimum, a bit
frightened – fearful, terrified, afraid of.
rabbit- hare.
toasting – frying.
at large – at liberty
a couple of – two, a pair of.
melodramatic – sentimental
gesture – action, movement
desperate – full of despair, furious.
probably – possibly, likely.
scone – startle, frighten, make afraid.
correspondence lesson – lessons on journalism.
decent – nice, good, efficient.
obviously – clearly, naturally.
startled – surprised, amazed, astonished, etc
confounded – confused, puzzled.
accusations – to act of accusing.
thoroughly – completely
alarmed – frightened.
blighter – darker, gloomier

Section-II

Gist
Paragraphs: 53-56
When Tom and Alec promised to abide by what she said, Mrs. Parker continues and says that somewhere in the prison a boy is suffering for another’s crime. It was the Felton forgery case which tells about imprisonment. Roger Felton is innocent of that crime as either of the boys. But working in the same office with Roger was a scoundrel who pretended to be his friend. This man signed his employer’s name to a cheque, but he covered his tracks so cleverly that when the forgery was discovered suspicion fell up on Roger. Roger was known to be in money difficulties and so has had unusual opportunities for passing a forged cheque. Finally, he was convicted and sentenced to three years of penal servitude. This was quite unbearable. Alec said that she spoke about the matter as if she had known Roger before. She replied that he was her son and her real name is Mrs. Felton and her disguised name was Mrs. Parker.

Paragraphs: 57-61
Tom exclaimed whether it was a fact. It was her son who had been convicted. Mrs. Parker rose from her chain and said as she was trusting them as she never trusted anyone else in her life. She had only one object when she took that cottage and it was to help Roger to escape. She has kept the car ready for use ever since. She came there and she thought that her son was one of the escaped convicts. If he had at all escaped he had known where she had been staying. He would be there very soon. She had kept in reserve/ a suit of clothes, and she requested them to leave the place and not tell about it to anyone, But Alec said if they would be allowed to stay they could help her and her son. But Mrs. Parker told them emphatically to leave the place because she did not want them to be caught in the process

Paragraphs: 62-67
There is another knock at the door, Alec opens the door. The convict enters the room quickly. He looks in alarm at the boys, Mrs, Parker gasps, and clutches the table as though about to fire. Tom cries for water, and Mrs. Parker recovers and says she is alright, Alec declares it a forehand to the convict not to be afraid of the two- young strangers because his mother had already told them his story and they will show any kind of help in their capacity to help him escape from the jail.’ The convict requests his mother not to lose her nerve. He is followed by police and it is time to make a plan to get away. She took him to change clothes.

Paragraphs: 68-81
Alec, flinging himself in the armchair says that of all the extraordinary adventures who on earth thought they should be mixed up in a thrill- like that? Tom repeated what his father said, “Where women are concerned the unexpected always happens”. Alec said if the convict had to escape, he had to have a mighty lot of luck because all the roads were sure to be watched, and it would be difficult to escape. Tom said that it was a nerve-racking job to escape from prison. They would be
pounced upon at any moment to be caught.

There is another knock and the boy look at one another in alarm. Alec says that it sounds as though someone have pounced. Tom says to him to wait a bit because it may be. a warder from the prison. Someone has perhaps come to enquire. Alec declares to open the door because a delay will make things suspicious. He opens the door and Joe’ enters. Joe asks where is Mrs. Parker. Alec replies that she is quite busy at the moment. Joe advances to the room and says that he should look for Mrs. Parker personally.

Tom tells him that he will be getting a thick ear if he starts worrying Mrs. Parker again. Joe replies if it so happens the two young men will find themselves in the prison cell the next day. Joe says there is perhaps something suspicious going on around there. he has seen him come in. What do they have about that to say? Alec hides his alarm and replies that he has not the least idea what he has been talking about. Joe says that they should be arrested for helping a convict escape. He has seen the convict in the room. He lies low and watches. He says that.

Paragraph: 82
Mrs. Parker enters and asks Joe what he is doing there. But Joe replies that he has seen a convict enter the house. Whether she will hand. him over to him or should he go to ask for help? Mrs! Parker says that it is not any convict but her nephew who has arrived from London that morning. She calls the convict by the name Frank to appear before her. The convict appears in an ordinary suit. Mrs. Parker says to the convict that the young man Joe has an idea he has seen a convict enter the house. The convict pretendingly says Joe is making a mistake to say so. Joe says that he has seen this young man a short while ago in a convict’s suit. The convict says that Joe will get into serious trouble if he tells like that. Joe replies if there is no convict’s dress inside, he would be sure that he is not a convict.

Joe asks if he can have a look in the next room. There must be the convict’s dress. The convict stops the hint from telling nonsense and asks him to get out of the house Joe leaves saying “all right! I’m going, but mind-yon; I have, ray bil$e outside; 1 am going straight to my uncle”. Tom gets enraged and says that he can not go to the police; he will rather go to the doctor. Enraged Joe rushes savagely at tom who skilfully avoids his blows. Mrs, Parker requests Tom and Joe to stop fighting There is an at the door, and die boys stop fighting. Joe holds a handkerchief to his face as though hurt. Mrs. Parker advised the convict, to get out the back way.

Analytical Outlines :

• Tom and Alec promise to obey her advice.
• She says a boy is suffering for another’s crime in the prison.
• It is the Felton forgery case.
• It tells about imprisonment.
• That man is Roger Felton.
• He is actually innocent of the crime.
• A scoundrel was working in Roger’s office.
• He pretended to be Roger’s friend.
• That man signed his employer’s name on a cheque!
• He did it very tactfully and cleverly.
• The forgery was discovered.
• But Roger was suspected of that crime
• Roger was in money difficulties.
• He has had unusual opportunities for passing a forged cheque.
• Finally, he was convicted.
• He was sentenced to three years of penal servitude.
• This was quite unbearable.
• Alec said that she spoke about the matter as if she had known Roger before.
• She replied that he was her son:,.
• She said her real name is Mrs, Felton.
• Her disguised name is Mrs. Parker.
• Tom exclaimed whether it was a fact.
• He said that it was her son who had
• She was trusting them.
• But she never trusted anyone else in her life.
• She had only one objective to take that cottage.
• It was to help Roger to escape.
• She had kept the car ready for use ever being convicted.
• She came there for that purpose.
• She thought mat her son was one of the escaped convicts.
• If at all he had escaped.
• He had known where she had been since.
• She had kept in reserve a suit of staying.
• He would be there very soon clothes.
• She requested them to leave the place.
• She also requested them not to tell about this to anyone.
• But Alec said if they would be allowed to stay, they could help her and her son.
• But Mrs. Parker told them emphatically to leave the place.
• Because she did not want them to be caught in the process.
• There is another knock at the door.
• Alec opens the door.
• The convict enters the room quickly.
• He looks in alarm at the boys.
• Mrs. Parker gasps and clutches the table as though about to faint!
• Tom cries for water.
• Mrs. Parker recovers very soon.
• She says that she is alright.
• Alec says the convict not to be afraid of them.
• Because his mother had already told them his story.
• They will try to help him.
• So that he will escape from jail.
• The convict requests her mother not to be nervous.
• He is followed by the police.
• It is time to make a plan to get away,
• She took him to change clothes.
• Alec sits on die armchair.
• He .says that it is an extraordinary adventure.
• It is, really, more thrilling.
• Tom repeats what his father said, “where women are concerned, the unexpected always happens”
• Alec said that the convict had to escape.
• It entirely depends upon his luck.
• Because all roads were sure to be
• Hence, it would be difficult to escape.
• Tom said that it was a nerve-racking job to escape from prison.
• They would be caught at any moment.
• There is another knock at the door.
• The boys look at one another in alarm.
• Alec says “someone has pounced.
• Tom says to him to wait a bit watched.
• Because it may be a warder from the prison.
• Someone has perhaps comedo enquired.
• Because the delay will make the thing suspicious.
• He opens the door.
• Joe enters the room. ,
• Joe asks where Mrs. Parker is.
• Alec replies that she is quite busy at the moment.
• Joe advances to the room.
• He says he will look for Mrs. Parker personally.
• Tom tells him that he will be getting a thick ear.
• If he starts worrying about Mrs. Parker again.
• Joe says if it so happens, they will be in the prison cell the next. day
• Joe says something suspicious going around there.
• He lies low and watches. ‘
• He says that he has seen the convict come in.
• Alec hides his alarm.
• He replies that he has not the least idea about that.
• Joe says they should be arrested for helping a config to escape.
• Joe says that he has seen the convict in the room.
• Mrs. Parker enters,
• She asks Joe why he, is,.d$ng’ there.
• But Joe replied’s! that he has a convict entered the house.
• Otherwise, he will go to ask for help.’
• Mrs. Parker says that it is not any convict.
• But it is his nephew seen a
• He asks whether she will hand him over to him.
• He has arrived from London that
• She calls the convict by the name Frank.
• Then Frank appears before her.
• The convict appears in an ordinary suit.
• She tells the convict that the young man is Joe’s morning.
• He tells that he has seen a convict enter the house.
• The convict pretendingly says Joe is making a mistake to say so.
• Joe says he has seen him in a convict’s suit.
• He has seen in a short while ago.
• The convict says that Joe will get into serious trouble. tv;
• If he tells like that.
• Joe replies. check the house for convicts!s suits.
• If no convict’s suit is found, he will not be a convict.
• Joe asks if he can have a look in the next room.
• There must be the convict’s dress.
• The convict stops him from telling nonsense.
• The convict asks him to get out of the house.
• Joe leaves saying all right.
• Joe says that he is going, but his bike is outside.
• He says that he is going straight to his constable uncle.
• Tom gets enraged.
• Tom says that he can not go to the police.
• He says to Joe that he will rather go to a doctor.
• Enraged Joe sashes savagely at Tom.
• Tom skilfully avoids his blows.
• Mrs. Parker requests Tom and Joe to stop fighting.
• There is a loud knock- at the door.
• The boys stop fighting.
• Joe holds a handkerchief to his face as
• Mrs. Parker advised the convict to get though hurt out of the back way.

Meaning Of Difficult Words :

personal servitude – the punishment of being sent to prison and forced to do hard physical labor.
stagger – walk very unsteadily, to confound.
impudence – unblushing, disrespectful manner take leave of.
your senses – gone mad.
Sock him beauty – formal) hit him hard
crime – offense, misdoing, an evil act
innocent – simple and honest, blameless, sinless
details – in elaborate, vivid.
pretended – feigned, aspired
suspicion – doubtful state of mind.
circumstantial – proof obtained from circumstances.
evidence – changes, conveniences.
opportunities –
disgrace – disrespect.
servitude – slavish attitude.
trusting – believing, having faith
object – aim, goal, target.
thrill – a sharp sensation
clutches – groups, holds.
faint – to become senseless.
don’t lose your nerve – don’t get irritated.
extraordinary adventures – risk-taking step.
a mighty lot of luck -a powerful luck
all the roads are sure to be watched – police patrolling be made
pounce on, – jump over
delay will only make things suspicious – people will start doubting due to delay.
I saw him come in – I saw the convict enter the house of Mrs. Parker
have you taken leave of your senses – gone mad?
If you saw ……this morning ’ – If at all you have Seen anybody he is my nephew who has arrived from London this morning.
Oh, him I suppose – a satirical statement
sarees – You have then kept in reserve the sports ear for this purpose
ridiculous – absurd, grotesque, unnatural.

Section-III

Joe opens the door. The warder enters, and Tom and Alec look alarmed. Mrs. Parker clings to the convict’s arm as though the strain is almost too much, for her. The warder looks about the room suspiciously and begs pardon for entering, and looking about. He does not feel concerned with the excitement. What he is interested in is searching for the escaped convict Two convicts have escaped- one is already caught and the other is being searched for.

He asks if anybody of them has seen a stranger entering the house, Joe replied that the warder should look no further because the convict is already in his front. Then he points to the convict. The wader went closer to him and said that he thought he recognized him. Mrs. Parker says that it is a mistake. Joe replies that he has seen him sneak in here about ten minutes ago.

If he needs Proof his prison clothes are in the next room. He says he was going to fetch his uncle, the constable of the village. When those boys stopped him for which they have been fighting The warder warned Mrs. Parker that something serious is going to happen to her. it Is obvious that she is helping the convict to escape and he has to report the matter to the authority.

The warder leaves and Mrs. Parker says when her son is taken back to the prison anything may happen to her. He is ready to face any situation come that may. The warder says to the convict that he doesn’t think it will be a bad idea if takes him back in that sports car the lady has outside. The car is an important piece of evidence and he doesn’t want anyone to tamper with it. Joe says that he has his bike outside and he will ride up to the prison after the warder. He also wishes to meet the Governor and appraise the situation so that he would get a channel to get into the force. It might help him.

The warder says he had a better ride tonight as all the roads are guarded and; he might have trouble passing. However, of course, he will give him the password which is against the regulations. But Joe says that he already knows the password i.e. “Regent”. The Warder is astonished to know that Joe has known it: joe says that it is his uncle who has told him the password, although it is against the regulations. Alec and Tom came forward to give a good thrashing down to Joe. But Mrs. Parker forbids it.

She says that the convict taken back to the prison is riot Roger, her son, It Was a boy whom she hadn’t seen before. Alec asked them if her son did not escape. But, she said he did. It is the warder himself who arrested the boy. Roger has said that he has managed to overcome the warder in wrestling and changed himself into the warder. They all laugh and enjoy. They ask why Mrs. Parker is weeping. She says it is due to excess happiness tear drops come out of her eyes.

Analytical Outlines:

• Joe opens the door.
• The warder enters.
• Tori! and Alec look alarmed.
• Mrs. Parker clings to the convict’s arm.
• As though the strain is almost too much for her.
• The warder looks about the room suspiciously.
• He begs pardon for entering and looking about.
• He is riot concerned with the excitement.
• He is also interested in the escaped convict.
• Two convicts have escaped.
• One is already caught.
• The other is being searched for.
• He asks if anybody of them has seen a stranger entering the house.
• Joe replies that the wader should look
• Because the convict is already in his front,
• Then Joe points to the convict.
• The warder goes closer to him.
• He says that he thinks he recognizes him.
• Mrs. Parker says that it is a mistake.
• Joe replies that he has seen him sneaking here about ten minutes ago.
• If he needs proof his prison clothes are
• He says he wa$ going to fetch his constable uncle from the village.
• But those boys stopped him.
• Because, they have been fighting, for him.
• The warder produces handcuffs.
• He goes towards the convict. no further in the next room.
• Mrs. Parker is in tears.
• She requests not to take him.
• The warder asks him whether she has known about the entry of the convict into her house.
• Joe says that she has.
• she has a sports car hidden in her shed.
• It is ready to get him away.
• The warder goes to see the prison.
• He is followed by Mrs. Parker.
• The warder returns with the convict’s clothes.
• He also comes with a parcel followed by Mrs. Parker.
• The parcel contains some provisions.
• It prepares for a long journey.
• The warder warned Mrs. Parker.
• Something serious is going to happen to her.
• It is clear that she is helping the convict escape.
• He has to report the matter to the authority.
• The warder leaves.
• Mrs. Parker says when her son is taken back to prison things may happen to her.
• He is ready to face any situation.
• The warder says to the convict that it will riot be a bad idea.
• If he is taking him with the sports car the lady has outside.
• The car is an important piece of evidence.
• He does not want anyone to tamper with it.
• Joe says that he has his bike outside.
• He will ride up to the prison after the warder.
• He also wishes to meet the Governor.
• He will apprejaMb the situation with him.
• So that he would get a channel to get into the force.
• It might help him.
• Does the warder say he had to better ride tonight. ?
• As all the roads are guarded.
• He might have trouble passing.
• Of course, he will give him the password.
• It is against the regulation.
• But Joe says that he already knows the password.
• The password is “Regent”.
• The warder is astonished by this.
• Because Joe knows the password.
• Joe says that he knows it from his constable uncle.
• Actually, it is against the regulation.
• Alec and Tom came forward to give a good thrashing down to Joe.
• But Mrs. Parker forbids to do so. ‘
• She says that the convict was” taken back to
• It was a strange boy.
• She had not him before the prison, not Roger, her son.
• Alec asked then her son did not escape.
• But she said he did.
• It is the warder himself who arrested the boy.
• Roger has overcome the warder in wrestling.
• So, he changed himself into a warder.
• They all laugh and enjoy.
• They ask why Mrs. Parker is weeping.
• She says it is due to excess happiness.
• So tear drops automatically come out of her eyes

Meaning Of Difficult Words:

blew – (informal) an expression of great surprised
suspicious – doubtful, expressing doubt
fetch – go and bring something or somebody
exits – in fact, truly speaking.
howled – clearly, tersely
indeed – leaves the stage.
obviously – shouted.

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 10 Sequences and Series will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 10 Sequences and Series

Sequence:
A sequence is a function whose domain is N (The set of natural numbers).
Note: We can use the set of whole numbers as a domain.

Real Sequence:
If the range of a sequence is a subset of ‘R’, then it is a real sequence.
⇒ If: N → R is a sequence then f(n) for n = 1, 2, 3, ….. are the terms of the sequence.

Finite and infinite sequence:
A sequence with a finite number of terms is a finite sequence otherwise it is infinite.
Note: We denote a sequence by (t_n) or {t_n} where f(n) = t_n

Series:
An expression of the type t₁ + t₂ + t₃ + ….. (or ∑t_n) where t_n is the nth term of a sequence is a series.

Partial sums:
If \(\sum_{n=1}^{\infty} t_n\) is a series then a sum \(\mathrm{S}_n=\sum_{k=1}^n t_k\) is called the nth partial sum of the series for n = 1, 2, 3 …..
∴ s₁ = t₁, s₂ = t₁ + t₂, s₃ = t₁ + t₂ + t₃ and so on.

Progression:
Progression is a sequence whose terms follow as pattern.
Arithmetic progression (A.P):
A sequence  (t_n) is an A.P. If t_n+1 – t_n = d (constant) for n = 1, 2, 3, …..

(a) General form: a, a + d, a + 2d, a + 3d …..
(b) n^th term: t_n = a + (n – 1)d, where t₁ = a, and the common difference = d
(c) Sum of first n terms (Sn):
S_n = \(\frac{n}{2}\)[2a + (n – 1)d]
= \(\frac{n}{2}\)[a + l]
where a = first term
d = common difference
l = last term (or nth term)

Note:

1. If a, b, c are in A.P. then 2b = a + c.
2. If 3 numbers are in A.P. then we take them as a – d, a, a + d.
3. If 4 numbers are in A.P. then we take rhem as a – 3d, a – d, a + d, a + 3d.

(d) Insertion of arithmetic means between two given number:
Let m₁, m₂, m₃ …. m_n are ‘n’ arithmetic means between ‘a’ and ‘b’ then m_k = a + \(\frac{k(b-a)}{n+1}\) for k = 1, 2, ….. n.

Geometric progression (G.P):
If \(\frac{t_{n+1}}{t_n}\) = r (constant), for n = 1, 2, 3, ….. then the sequence (t_n) is a geometrical progression.

(a) General form: a, ar, ar², ar³ …..
(b) nth term of GP: nth term of G.P. = t_n = ar^n-1.
(c) sum of first n terms of a G.P.: S_n = \(\frac{a\left(1-r^n\right)}{1-r}(\text { for } r \neq 1)\)
(d) sum of an infinite G.P.: If |r| < 1 then the sum of the infinite G.P. a, ar, ar² ….. is S_∞ = \(\frac{a}{1-r}\)

Note:

1. If a, b, c are in G.P. then b² = ac
2. If 3 numbers are in G.P. we take them as \(\frac{a}{r}\), a, ar.
3. If 4 numbers are in G.P. then we take them as \(\frac{a}{r^3}, \frac{a}{r}, a r, a r^3\)

(e) Insertion of  geometric means between  two numbers:
If g₁, g₂ ……g_n are n geometric means between a and b then g_k = a \(\left(\frac{b}{a}\right)^{\frac{k}{n+1}}\), k = 1, 2, 3, …. n

Harmonic Progression (H.P):
A sequence a₁, a₂, a₃ ….. of non zero numbers is called a Harmonic progression if the sequence \(\frac{1}{a_1}, \frac{1}{a_2}, \frac{1}{a_3}\) ….. is an A.P.

(a) Harmonic mean:
Harmonic mean(H) between two numbers a and b is \(\frac{1}{\mathrm{H}}=\frac{\left(\frac{1}{a}+\frac{1}{b}\right)}{2}\)
= \(\frac{a+b}{2 a b}\)
⇒ H = \(\frac{2 a b}{a+b}\)

(b) Insertion of n harmonic means between two numbers:
Let H₁, H₂ ….. H_n are n harmonic means between a and b then \(\frac{1}{\mathrm{H}_K}=\frac{1}{a}\) + k_D, where D = \(\frac{a-b}{(n+1) a b}\).

Relation among A.M., G.M. and H.M.
AM ≥ GM ≥ HM

Arithmetic co-geometric sequence(AGP):
If (a_n) is an A.P. and (b_n) is an G.P. then the series (a_nb_n) is called an arithmetic co-geometric sequence.

(a) General form: a, (a + d) r, (a + 2d) r², (a + 3d)r³,…..
(b) nth term of A.G.P.: t_n = {a + (n – 1)d} r^n-1.
(c) sum of first terms of A.G.P.:
The sum of first n terms of A.G.P. a, (a + d) r, (a + 2d) r², …..  is
S_n = \(\frac{a}{1-r}+d r\left(\frac{1-r^{n-1}}{(1-r)^2}\right)-\frac{[a+(n-1) d] r^n}{1-r}\) for r ≠ 1
(d) sum of infinite A.G.P.: If |r| < 1 then we have \(S_{\infty}=\frac{a}{1-r}+\frac{d r}{(1-r)^2}\)

Sum of special sequences.:

Binomial Series:
(a) Binomial theorem for any real index:

• (1 + x) ⁿ = 1 + nx + \(\frac{n(n-1)}{2} x^2+\frac{n(n-1)(n-2)}{3 !} x^3+\ldots\) for |x| < 1
• (1 – x)^-1 = 1 + x + x² …..
• (1 + x)^-1 = 1 – x + x² – x³ …..
• (1 + x)^-2 = 1 – 2x + 3x² – 4x³ …..
• (1 – x)^-2 = 1 + 2x + 3x² + …..

Exponential series:

Logarithmic Series:

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 15 Statistics will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 15 Statistics

Measures Of Central Tendency:
A measure of central tendency or average is a value, that is the representative of whole data and signifies its characteristics.
Different measures of central tendency are: (a) Mean (b) Median (c) Mode.

(a) Mean (Arithmetic Mean):
Mean of ungrouped data: The mean of ‘n‘ observations x₁, x₂ …..x_n = \(\bar{x} \frac{\sum_{i=1}^n x_i}{N}\)

Mean of grouped data:
(i) Direct Method
If x_i are the mid values of the intervals with frequency f_i then the mean \(\bar{x}=\frac{1}{N} \sum_{i=1}^n f_i x_i\)

(ii) Shortcut Methods:
(1) Assumed mean method
Mean = \(\overline{\mathrm{x}}=\mathrm{A}+\frac{1}{\mathrm{~N}} \sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{f}_{\mathrm{i}} \mathrm{d}_{\mathrm{i}}\)
where A = the assumed mean ⇒ d_i = x_i – A

(iii) Step Deviation Method:
Mean = \(\overline{\mathrm{x}}=\mathrm{A}+\frac{\mathrm{C}}{\mathrm{N}} \sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{f}_{\mathrm{i}} \mathrm{u}_{\mathrm{i}}\)
where A = The assumed mean, C = Class width
u_i = \(\frac{d_i}{C}=\frac{x_i-A}{C}\)

(b) Median
(i) Median of ungrouped data:
Let n is the number of observation.
Arrange the observations in ascending or descending order.
⇒ If n is odd, Median = \(\left(\frac{\mathrm{n}+1}{2}\right)^{\mathrm{th}}\) observation.
⇒ If n is even, Median = \(\frac{\left(\frac{\mathrm{n}+1}{2}\right)^{\mathrm{th}} \text { observation }+\left(\frac{\mathrm{n}}{2}+1\right)^{\mathrm{th}} \text { observation }}{2}\)

(ii) Median of grouped data

• Get \(\frac{\mathrm{N}}{2}\) and cummulative frequencies of all classes.
• Get the Median class.
  Median class = The class whose cumulative frequency is just greater than (or near to) \(\frac{\mathrm{N}}{2}\).
  Median = l + \(\frac{\mathrm{m}-\mathrm{c}}{\mathrm{fm}}\) × h,
  where l = lower limit of median class .
  h = Class width of median class M = \(\frac{\mathrm{N}}{2}\).
  c = Cummulative frequency of the class preceeding the median class.
  f_m = Frequency of the median class.

(c) Mode
Mode is the most frequent value.
⇒ We can find mode using the empirical formula:
Mode = 3 Median – 2 Mean.
(i) Mode for Grouped data
⇒ Get the Modal class: It is the class with maximum frequency.
Mode = \(l+\frac{\mathrm{f}_{\mathrm{m}}-\mathrm{f}_1}{2 \mathrm{f}_{\mathrm{m}}-\mathrm{f}_1-\mathrm{f}_2} \times \mathrm{c}\)
where l = lower limit of modal class.
f_m = Frequency of modal class.
f₁ = Frequency of the class just preceeding modal class.
f₂ = Frequency of the class just suceeding modal class.

Measure Of Dispersion:
The variability or scatter or spreading of data is known as dispersion.

Some of the measures of dispersion are:

(a) Range
(b) Mean deviation
(c) Variance
(d) Standard deviation

(a) Mean deviation: Mean deviation is the mean of absolute deviations of all observations from a central value (Mean or Median).

For Group – B
A = 35, C = 10


As C. V of Group – A is more, the data for group – A is more dispersed

For Group – A

Analysis Of Frequency Distribution:
Coefficient of variation (C. V) = \(\frac{\sigma}{x}\) × 100

Note:

• The distribution with greater C. V is more variable or dispersed and lesser C. V is less variable or more consistent.
• If two distributions have same mean then they can be compared on the basis of their standard deviation.

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 14 Limit and Differentiation will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 14 Limit and Differentiation

Limit Of A Function:

A real number ‘l’ is called the limit of the function f(x) as x tends to ‘a’ if for every ∈ > 0, there exist δ > 0 such that |f(x) – l| < ∈ whenever |x – a| < δ
We write \(\lim _{x \rightarrow a}\) f(x) = l
Left and right hand limit:

Left hand limit of f(x) as x → a is:
\(\lim _{x \rightarrow a-}\) f(x) = \(\lim _{x \rightarrow 0}\) f(a – h)

Right hand limit of f(x) as x → a is:
\(\lim _{x \rightarrow a+}\) f(x) = \(\lim _{h \rightarrow 0}\) f(a + h)

Existance of limit:
\(\lim _{x \rightarrow a}\) f(x) exists if it is unique, irrespective of any type of approach i.e if LHL = RHL. i.e if \(\lim _{x \rightarrow a-}\) f(x) = \(\lim _{x \rightarrow a+}\) f(x)

Indeterminate forms:
The forms : \(\frac{0}{0}, \frac{\infty}{\infty}\), ∞ – ∞, 0 × ∞, 0°, ∞° and 1^∞ are called indeterminate forms in mathematics.

Properties of limit:

Some standard limits:

Limit At Infinite And Infinite Limits:

(a) We write \(\lim _{x \rightarrow a}\) f(x) = ∞ if for a given m > 0, there exists δ > 0 such that |x – a| < δ ⇒ f(x) > m for large m.

(b) We write \(\lim _{x \rightarrow a}\) f(x) = -∞ if for a given m < 0, there exists δ > 0 such that |x – a| < δ ⇒ f(x) < m for large |m|.

(c) \(\lim _{x \rightarrow ∞}\) f(x) = l if for given ∈ > 0 there exists k > 0 such that x > k ⇒ |f(x) – l| < ∈ for large x.

(d) \(\lim _{x \rightarrow -∞}\) f(x) = l if for given ∈ > 0, there exists k < 0 such that x < k ⇒ |f(x) – l| < ∈ for large |k|.

(e) We write \(\lim _{x \rightarrow ∞}\) f(x) = ∞ if for m > 0 there exists k > 0 such that x > x ⇒ f(x) > m for large m.

(f) \(\lim _{x \rightarrow ∞}\) xⁿ = \(\left\{\begin{array}{lll}
\infty & \text { if } & n>0 \\
1 & \text { if } & n=0 \\
0 & \text { if } & n<0
\end{array}\right.\)

(g) \(\lim _{n \rightarrow ∞}\) xⁿ = \(\left\{\begin{array}{ccc}
0 & \text { if } & |x|<1 \\
1 & \text { if } & x=1 \\
\infty & \text { for } & x>1
\end{array}\right.\) does not exist for x ≤ -1.

Some useful expansions:

Techniques to find limit:
If \(\lim _{x \rightarrow a}\) f(x), does not take any indeterminate form then get the limit just by putting x = a(provided that the limit is finite).
If \(\lim _{x \rightarrow a}\) f(x) takes any indeterminate form then either use formula or simplify to remove the indeterminate form before finding limit.
The indeterminate form can be removed by using.

• Factorisation
• Rationalisation
• Expand  formula or any other techniques.

Differentiation:

(a) Let y = f(x) is a function.
The derivative (differential coefficient) of y or f(x) with respect to x is \(\frac{d y}{d x}\) = f'(x) = \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\)

(b) The differentiation of y = f(x) at x = a is \(\left.\frac{\mathrm{dy}}{\mathrm{dx}}\right]_{\mathrm{x}=\mathrm{a}}\) = f'(a) = \(\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}\)

(c) Differentiability of y = f(x) at x = a:

(d) Geometrical meaning of differentiation:
Geometrically f'(x) or \(\frac{d y}{d x}\) represents the slope of tangent to y = f(x) at any point P(x, y)
⇒ Slope of tangent to y = f(x) at A(x₁, y₁) = \(\left.\frac{d y}{d x}\right]_{\left(x_1, y_1\right)}\)

(e) Some rules of differentiation:

(f) Differentiation of some standard functions:

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 7 Linear Inequalities will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 7 Linear Inequalities

Inequality:
A statement with symbols like >, ≥, <, ≤ is an inequality.

Different types of inequality:

(a) Numerical inequality: It is an inequality involving numbers not variables.
(b) Literal inequality: It is the inequality involving literal numbers(variable).
(c) Strict inequality: An inequality with only > or < symbols is a strict inequality.
(d) Slack inequality: An inequality with only ≥ or ≤ symbols is a slack inequality.

Linear inequality:
An inequality involving variables in the first degree is called linear inequalities.
(a) General form of inequalities:
(i) In one variable: ax + b > or ≥ or < or ≤ 0
(ii) In two variables: ax + by + c > or ≥ or < or ≤ 0.

Intervals:

• Closed Interval: [a, b] = {x ∈ R: a ≤ x ≤ b}
• Open Interval: (a, b) = {x ∈ R: a < x < b}
• Semi-open or semi-closed interval:
  ⇒ [a, b) = {x ∈ R: a ≤ x < b}
  ⇒ (a, b] = {x ∈ R: a < x ≤ b}

Basic properties of inequalities:
(1) a > b, b > c ⇒ a > c
(2) a > b ⇒ a ± c > b ± c
(3) a > b

• m > 0 ⇒ am > bm, \(\frac{a}{m}>\frac{b}{m}\)
• m < 0 ⇒ am < bm, \(\frac{a}{m}<\frac{b}{m}\)

(4) If a > b > 0, then
a² > b², |a| > |b| and \(\frac{1}{a}>\frac{1}{b}\)
If a < b < 0, then
|a| > |b| and \(\frac{1}{a}>\frac{1}{b}\)

Graphical solution of linear inequalities in two variables:
Working rule:

Let the inequality is ax + by + c < or ≤ or > or ≥ 0

Step – 1: Consider the equation ax + by + c = 0 in place of the inequality and draw its graph (Draw a dotted line for > or < and a bold line for ≥ or ≤).
Step – 2: Take any point that does not lie on the graph, and put the coordinate in the inequality.
If you get true then the inequality is satisfied. Shade the half-plane containing that point otherwise the inequality is not satisfied. In this case shade the half plane region that does not contain the point.
Step – 3: The shaded region is the required solution.

Solution of a system of linear inequalities in two variables:

Step – 1: Draw the graph of all lines.
Step – 2: Shade the appropriate region for each inequality.
Step – 3: The common region is the required solution.

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 11 Straight Lines will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 11 Straight Lines

Distance formula:
Distance between two points A (x₁, y₁) and A (x₂, y₂) = \(\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)

Section Formula:
If C(x, y) divides the join of A (x₁, y₁) and A (x₂, y₂) in the ratio m: n internally then, x = \(\frac{m x_2+n x_1}{m+n}\), y = \(\frac{m y_2+n y_1}{m+n}\)

Note:

• If the division is external then, x = \(\frac{m x_2-n x_1}{m-n}\), y = \(\frac{m y_2-n y_1}{m-n}\)
• If C(x, y) is the midpoint then x = \(\frac{x_1+x_2}{2}\), y = \(\frac{y_1+y_2}{2}\)

Area of triangle formula:
The area of triangle with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) is given by  = \(\frac{1}{2}\)[x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

Different points related to a triangle:
(a) Centroid of the triangle with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) is = G \(\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)\)

(b) In centre of a triangle with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) is = I \(\left(\frac{a x_1+b x_2+c x_3}{3}, \frac{a y_1+b y_2+c y_3}{3}\right)\)

Slope Of A Line:
(a) Angle of inclination: the angle θ made by a line with positive x-axis is the angle of inclination.
(b) Slope of a line: Slope of a line is the tangent of angle of inclination. i,.e m = tan θ.
(c) Slope of a line joining A(x₁, y₁), and B(x₂, y₂) = \(\frac{y_2-y_1}{x_2-x_1}\)

Note:

(i) Slope of x-axis = 0
Slope of any line parallel to x-axis = 0

(ii) Slope of y-axis  = ∞
Slope of any line parallel to y-axis = ∞

Angle Between two Lines:
Angle Φ between two lines with slope m₁ and m₂ is given by tan Φ = \(\pm \frac{\left(m_1-m_2\right)}{1+m_1 m_2}\)

Note:

• To find the acute angle between two lines use the formula. tan Φ = \(\left|\frac{m_1-m_2}{1+m_1 m_2}\right|\)
• Two lines are parallel if m₁ = m₂
• Two lines are perpendicular if m₁m₂ = (-1).

Collinearity Of Three Points:
Three points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are collinear if
(i) Sum of distances between two pairs of points = Distance between the 3rd pair.
Or, (ii) Area of Δ ABC = 0
Or, (iii) Let B(x₂, y₂) divides the join of AC in ratio k: 1
∴ \(x_2=\frac{k x_3+x_1}{k+1}, y_2=\frac{k y_3+y_1}{k+1}\)
The value of k obtained from two cases are equal.
Or, (iv) Slope of AB = Slope of AC.

Equation of a straight line:
Lines parallel to co-ordinate axes:
(i) Equation of any line parallel to x-axis is, y = k
⇒ Equation of x-axis is, y = 0

(ii) Equation of any line parallel to y-axis is, x = k
⇒ Equation of y-axis is, x = 0

Lines Not Parallel To Any Axes:
(i) Slope intercept form:
Equation of a line with slope ‘m’ and y-intercepts ‘c’ is: y = mx + c

(ii) Point slope form:
Equation of a line with slope ‘m’ and passing through a point A(x₁, y₁) is: y – y₁ = m(x – x₁)

(iii) Two point form:
Equation of the line passing through A(x₁, y₁) and B(x₂, y₂) is : \(\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}\)

(iv) Intercept form:
Equation of a line with x-intercept ‘a’ and y-intercept ‘b’ is \(\frac{x}{a}+\frac{y}{b}=1\)

(v) Normal form:
Equation of a line whose distance form origin is P and the perpendicular drawn form origin to the line makes an angle α with positive direction of x-axis is: x cos α + y sin α = P

(vi) Parameteric form or symmetric form:
Equation of the line passing through A(x₁, y₁) and making an angle θ with positive direction of x-axis is: \(\frac{x-x_1}{\cos \theta}=\frac{y-y_1}{\sin \theta}\) = r
Or, x = x₁ + r cos θ, y = y₁ + r sin θ
where r = The directed distance between points P(x, y) and A(x₁, y₁)

(vii) General form:
General equation of a straight line is Ax + By + C = 0

Note:

• Slope of this line = –\(\frac{\mathrm{A}}{\mathrm{B}}\)
• x-intercept = –\(\frac{\mathrm{C}}{\mathrm{A}}\)
• y-intercept = – \(\frac{\mathrm{C}}{\mathrm{B}}\)
• Two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are parallel if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\) perpendicular if a₁a₂ + b₁b₂ = 0 and coincident if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

Condition of concurrency of three lines:
Three lines a₁x + b₁y + c₁ = 0 a₂x + b₂y + c₂ = 0 and a₃x + b₃y + c₃ = 0 are concurrent if \(\left|\begin{array}{lll}
a_1 & b_1 & c_1 \\
a_2 & b_2 & c_2 \\
a_3 & b_3 & c_3
\end{array}\right|\) = 0

Family Of Lines:

(i) Equation of lines parallel to the line ax + by + c = 0 is given by: ax + by + λ = 0
(ii) Equation of lines perpendicular to the line ax + by + c = 0 is given by bx – ay + λ = 0
(iii) Equation of lines passing through the point of intersection of two lines.
a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is given by: (a₁x + b₁y + c₁) + λ(a₂x + b₂y + c₂)

Distance of a point from a line:
The perpendicular distance of A(x₁, y₁) from the line ax + by + c  = 0 is: d = \(\left|\frac{a x_1+b y_1+c}{\sqrt{a^2+b^2}}\right|\)

Distance between two parallel lines:
ax + by + c₁ = 0 and  ax + by + c₂ = 0 is d = \(\left|\frac{c_1-c_2}{\sqrt{a^2+b^2}}\right|\)

Position of a point with respect to a line:
A point A(x₁, y₁) lies
(i) above the line ax + by + c = 0 if \(\frac{a x_1+b y_1+c}{b}\) > 0
(ii) below the line ax + by + c = 0 if \(\frac{a x_1+b y_1+c}{b}\) < 0

Equation of bisectors of angle between two intersecting lines:
(i) Equation of angle bisector of two lines. a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is given by \(\frac{a_1 x+b_1 y+c_1}{\sqrt{a_1^2+b_1^2}}=\pm \frac{a_2 x+b_2 y+c_2}{\sqrt{a_2^2+b_2^2}}\)

Note:

Out of two bisector take one and find the angle between that bisector and one line. If the angle is less than 45° then that bisector is the bisector of acute angle, otherwise, the other bisector is the bisector of acute angle.

(ii) Bisector of angle containing a given point (h, k):

Step – 1: Check the sign of a₁h + b₁k + c₁  and a₂h + b₂k + c₂

• If they have same sign then the bisector of angle containing (h, k) is: \(\frac{a_1 x+b_1 y+c_1}{\sqrt{a_1^2+b_1^2}}=\frac{a_2 x+b_2 y+c_2}{\sqrt{a_2^2+b_2^2}}\)
• If they have opposite sign then the bisector of angle containing (h, k) is: \(\frac{a_1 x+b_1 y+c_1}{\sqrt{a_1^2+b_1^2}}=-\frac{a_2 x+b_2 y+c_2}{\sqrt{a_2^2+b_2^2}}\)

Change Of Axes (Shifting Of Origin):

(i) Translation of coordinate axes.
Let O'(h, k) is the origin of system S’ with respect to origin O(0, 0) of the system S. S’ is the translation of S. If (x, y) and (x’, y’) are the coordinate of a point P in the system S and S’ respectively then
x’ = x – h and y’ = y – k Or, x = x’ + h, y = y’ + k

(ii) Rotation of axes:
Let S’ is a rotation of S, α is the measure of rotation
If (x, y) and (x’, y’) are the coordinate of a point P with respect to S and S’ then x = x’ cos α – y’ sin α and y = x’ sin α + y’ cos α

(iii) Translation as well as a rotation:
If S’ is a combination of translation followed by a rotation then x = h + x’ cos α – y’ sin α, y = k + x’ sin α + y’ cos α

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 6 Complex Numbers and Quadratic Equations will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 6 Complex Numbers and Quadratic Equations

Unit imaginary number ‘i’.
The unit imaginary number i = √-1
i² = -1
i³ = -i
i⁴ = 1
In general (i)⁴ⁿ = 1, (i)⁴ⁿ⁺¹ = i, (i)⁴ⁿ⁺² = -1, and (i)⁴ⁿ⁺³ = -i.
⇒ If a and b are positive real numbers then
√-a × √-b = -√ab
√a × √b = √ab

Complex Number
General form: = z = a +ib

• a = Real part of (z)  = Re (z)
• b = Imaginary part of (z) = I_m(z)
• a + i0 is purely real and 0 + ib is purely imaginary .
• a + ib = c + id iff a = c and b = d

Complex Algebra
(a) Addition of complex numbers
If z₁ = a + ib and z₂ = c + id then z₁ + z₂ = (a + c) + i(b + d)

Properties:

• Addition is commutative: z₁ + z₂ = z₂ + z₁
• Addition is associative: (z₁ + z₂) + z₃ = z₁ + (z₂ + z₃)
• 0 + i0 is the additive identity.
• -z is the additive inverse of z.

(b) Subtraction of complex numbers:
z₁ = a + ib and z₂ = c + id then z₁ – z₂ = (a – c) + i(b – d)

(c) Multiplication of complex numbers:
z₁ = a + ib and z₂ = c + id then z₁z₂ = (ac – bd) + i(bc + ad)

Properties:

• Multiplication is commutative: z₁z₂ = z₂z₁
• Multiplication is associative: z₁(z₂z₃) = z₁z₂(z₃)
• 1 = 1 + i0 is the multiplicative identity.
• If z = a + ib then the inverse of z.
  z^-1 = \(\frac{1}{a+i b}=\frac{a-i b}{(a+i b)(a-i b)}\)
  = \(\frac{a-i b}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{i b}{a^2+b^2}\)
• Multiplication is distributive over addition. z₁(z₂ + z₃) = z₁z₂ + z₁z₃

Conjugate and modulus of a complex number:
If  z = a + ib the conjugate of z is \(\bar{Z}\) = a – ib.
⇒ We get conjugate by replacing i by (-i) Modulus of z = a + ib is denoted by |z| and |z| = \(\sqrt{a^2+b^2}\)

Properties Of Conjugate:
(i) \((\overline{\bar{z}})\) = z
(ii) z + \(\bar{z}\) = 2 Re (z)
(iii) z – \(\bar{z}\) = 2i m̂ (z)
(iv) z – \(\bar{z}\) ⇔ z is purely real
(v) Conjugate of real number is itself.
(vi) z + \(\bar{z}\) = 0 ⇒ z is purely imaginary.
(vii) z. \(\bar{z}\) = [Re(z)]² + [m̂(z)]²
= a² + b²
= |z|²
(viii) \(\overline{z_1+z_2}=\overline{z_1}+\overline{z_2}\)
(ix) \(\overline{z_1-z_2}=\overline{z_1}-\overline{z_2}\)
(x) \(\overline{z_1z_2}=\overline{z_1}\overline{z_2}\)
(xi) \(\left(\overline{\frac{z_1}{z_2}}\right)=\frac{\overline{z_1}}{\overline{z_2}}\)

Properties of modulus:
(1) Order relations are not defined for complex numbers. i,e,. z₁ > z₂ or z₁ < z₂ has no meaning but |z₁| < |z₂| or |z₁| > |z₂| is meaningful because |z₁| and |z₂| are real numbers.
(2) |z|  = 0 ⇔ z = 0
(3) |z| = |\(\bar{z}\)| = |-z|
(4) |z| ≤ Re (z) ≤ |z| and -|z| ≤ m̂ (z) ≤ |z|
(5) |z₁z₂| = |z₁| |z₂|
(6) \(\left|\frac{z_1}{z_2}\right|=\frac{\left|z_1\right|}{\left|z_2\right|}\)
(7) |z₁ ± z₂|² = |z₁|² + |z₂|² ± 2 Re (z₁\(\bar{z}_2\))
(8) |z₁ + z₂|² = |z₁ – z₂|² = 2(|z₁|² + |z₂|²)
(9) |z₁ + z₂|² ≤ |z₁| + |z₂|

Square Root Of Complex Number:
Let z = a + ib
Let √z = x + iy

If b > 0 then x and y are taken as same sign.
If b < 0 then x and y are of opposite sign.

Representation of a complex number:
We represent a complex number in different forms like
(i) Geometrical form
(ii) Vector form
(iii) Polar form
(iv) Eulerian form or Exponential form

(i) Geometrical form:
Geometrically z = x + iy = (x, y) represents a point in a coordinate plane known as Argand plane or Gaussian plane.

(ii) Vector form:
In vector form a complex number z = x + iy is the vector \(\overrightarrow{\mathrm{OP}}\) where p(x, y) is the point in the cartesian plane.

(iii) Polar form:
A complex number z = x + iy  in polar form can be written as z = r(cos θ + i sin θ) where r = \(\sqrt{x^2+y^2}\) = |z| and θ is called the argument and -π < θ ≤ π. Technique to write z = x + iy in polar form.
Step – 1: Find r = |z| = \(\sqrt{x^2+y^2}\)
Step – 2: Find α = tan^-1 \(\left|\frac{y}{x}\right|\)
Step – 3:
θ = α for x > 0, y > 0
θ = π – α for x > 0, y > 0
θ = -π + α for x > 0, y > 0
θ = -α for x > 0, y > 0
Step – 4: Write z = r(cos θ + i sin θ)

(iv) Eulerian form or Exponential form z = r e^iθ, because e^iθ = cos θ + i sin θ where θ is the argument and r is the modulus if z.

Note:
(1) |z₁ z₂ z₃ ….. z_n| = |z₁||z₂| …. |z_n|
(2) arg (z₁z₂ …. Z_n) = arg (z₁) + arg (z₂) + ….. + arg (z_n)
(3) arg \(\left(\frac{z_1}{z_2}\right)\) = arg (z₁) – arg (z₂)
(4) arg \((\bar{z})\) = -arg (z)

Cube Roots Of Unity:
Cube roots of unity are 1, ω, ω² where ω = \(\frac{-1 \pm i \sqrt{3}}{2}\)

Properties of Cube roots of unity:
(i) Cube roots of unity lie on unit circle |z| = 1
(ii) 1 + ω + ω² = 0
(iii) Cube roots of -1 are -1, -ω, -ω²
(iv) 1 + ωⁿ + ω²ⁿ \(=\left\{\begin{array}{l}
0 \text { if } n \text { is not a multiple of } 3 \\
3 \text { if } n \text { is a multiple of } 3
\end{array}\right.\)
(v) z³ + 1 = (z + 1) (z + ω) (z + ω²)
(vi) -ω and -ω² are roots of z² – z + 1  = 0.

De-moivre’s theorem:
(a) (De-moivre’s theorem for integral index)
(cos θ + i sin θ)ⁿ = cos (nθ) + i sin (nθ)

(b) (De-moivre’s theorem for rational index)
cos (nθ) + i sin (nθ) is one of the values of (cos θ + i sin θ)ⁿ

(c) nth roots of unity
nth roots of unity are 1, α, α², α³ …..α^n-1. where α = e^{i\(\frac{2 \pi}{n}\)} = cos \(\frac{2 \pi}{n}\) + i sin \(\frac{2 \pi}{n}\)

Properties:

• 1 + α + α² ….. + α^n-1 = 0
• 1 + α^p + α^2p + ….. + α^(n-1)p \(= \begin{cases}0 & \text { if } p \text { is not a multiple of } n \\ n & \text { if } p \text { is a multiple of } n\end{cases}\)
• 1. α. α² ….. α^n-1 = (-1)^n-1
• zⁿ – 1 = (z – 1) (z – α) (z – α²) …..(z – α^n-1)

Quadratic Equations:
The general form: ax² + bx + c = 0  …(i)
Solutions of quadratic equation(1) are
x = \(\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\)
D = b² – 4ac is called the discrimination of a quadratic equation.
D > 0 ⇒ The equation has real and distinct roots.
D = 0 ⇒ The equation has real and equal roots.
D < 0 ⇒ The equation has complex roots.

Note:
In a quadratic equation with real coefficients, the complex roots occur in conjugate pairs.

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 9 Binomial Theorem will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 9 Binomial Theorem

Binomial Theorem For Positive Integral Index:
For any a,b ∈ R, and n ∈ N
(a + b)ⁿ = ⁿC₀ aⁿ + ⁿC₁ a^n-1b + ….. ⁿC_n bⁿ

Note:

(a) (a + b)ⁿ = aⁿ + na^n-1 b + \(\frac{n(n-1)}{2 !}\) a^n-2b² ….. + bⁿ
(b) (1 + x)ⁿ = ⁿC₀ + ⁿC₁ x + ⁿC₂ x² + ….. + ⁿC_n xⁿ
(c) (a – b)ⁿ = ⁿC₀ aⁿ – ⁿC₁ a^n-1 b + ⁿC₂ a^n-2b² ….. + (-1)ⁿ bⁿ
(d) (1 – x)ⁿ = ⁿC₀ – ⁿC₁ x + ⁿC₂ x² ….. + (-1)ⁿ xⁿ

Some conclusions from the Binomial theorem:

• There are (n + 1) terms in the expansion of (a + b)ⁿ
• We can write (a + b)ⁿ = \(\sum_{r=0}^n{ }^n \mathrm{C}_r a^{n-r} b^r\) and (a – b)ⁿ = \(\sum_{r=0}^n(-1)^r{ }^n \mathrm{C}_r a^{n-r} b^r\)
• The sum of powers of a and b in each term = n
• As ⁿC_r = ⁿC_n-r (The coefficient of terms equidistant from the beginning and the end are equal).
• (r + 1)^th term (General term)
  = t_r+1 = ⁿC_r a^n-rb^r
• (a + b)ⁿ + (a – b)ⁿ = 2[ⁿC₀aⁿ + ⁿC₂ a^n-2b² + ….]
• (a + b)ⁿ – (a – b)ⁿ = 2[ⁿC₁ a^n-1b + ⁿC₃ a^n-3b³ + ….]
• (middle terms):
  ⇒ If n is even then the middle term = \(t_{\left(\frac{n+2}{2}\right)}=t_{\left(\frac{n}{2}+1\right)}\)
  ⇒ If n is odd there are two middle terms. They are = \(t_{\left(\frac{n+1}{2}\right)} \text { and } t_{\left(\frac{n+3}{2}\right)}\)
• t_r+1 from the end in the expansion of (a + b)ⁿ = t_r+1 from the beginning in the expansion of (b + a)ⁿ.

Binomial Theorem For Any Rational Index:
If n ∈ Q and x ∈ R such that |x| < 1 then (1 + x)ⁿ = 1 + nx + \(\frac{n(n-1)}{2 !} x^2\) + \(\frac{n(n-1)(n-2)}{3 !} x^3+\ldots .\)

Note:

(1) (1 + x)^-1 = 1 – x + x² – x³ + …..
(2) (1 – x)^-1 = 1 + x + x² + …..
(3) (1 + x)^-2 = 1 – 2x + 3x² – 4x³ + …..
(4) (1 – x)^-2 = 1 + 2x + 3x² + 4x³ + …..

Odisha State Board CHSE Odisha Class 11 Math Notes Chapter 8 Permutations And Combinations will enable students to study smartly.

CHSE Odisha 11th Class Math Notes Chapter 8 Permutations And Combinations

Fundamental Principle Of Counting:
(a) Fundamental principle of Multiplication:
If we choose an element from set A with m element and then one element from set B  with n elements, then are total number of ways we can make a choice is exactly mn.

OR

If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of ways in which both the events can occur in succession in mn ways.

(b) Fundamental Principle of addition: If there are two events such that they can be performed independently in m and n different ways respectively, then either of two events can be performed in (m + n) ways.

Note:
(a) Use the multiplication principle if by doing one part of the job, the job remains incomplete.
(b) Use the addition principle if by doing one part of the job, the job is completed.

Factorial Notation:
If n ∈ N then the factorial of n, denoted by n! or ∠n is defined as
n! = n (n – 1). (n – 2) … 3.2.1.

Note:
0! = 1

Properties of Factorial:
(1) Factorial of negative integers is not defined
(2) n! = n(n – 1)!
= n(n – 1) (n – 2)!
= n(n – 1) (n – 2) (n – 3)!
(3) \(\frac{n !}{r !}\) = n(n – 1) (n – 2) ….. (r + 1)
(4) Exponent of a prime number p in n! denoted by
\(\mathrm{E}_p(n !)=\left[\frac{n}{p}\right]+\left[\frac{n}{p^2}\right]+\ldots \ldots\)

Permutation:
Each of the arrangements which can be made by taking some or all objects or things at a time is called a permutation.

(a) Permutation of n different objects:

• Number of permutations of n different objects have taken all at a time = \({ }^n \mathrm{P}_n\) = n!.
• Number of permutations of n different objects taken none at a time = \({ }^n \mathrm{P}_0\) = 1
• Number of permutations of n different objects taken r at a time = \({ }^n \mathrm{P}_r\) = P(n, r) = \(\frac{n !}{(n-r) !}\)

(b) Permutation ofnon-distinct objects:
(1) Number of permutations of n objects taken all at a time of which p objects are of same kind and others are distinct = \(\frac{n !}{p !}\)
(2) Number of permutations of n objects taken all at a time of which p objects are of one kind, q objects are of a second kind and other are distinct = \(\frac{n !}{p ! q !}\)
(3) Number of permutations of n objects taken all at a time in which p₁ objects are of one kind, p₂ are of second kind, p₃ are 3rd kind ….. and
p_n are of nth kind and other are distinct. = \(\frac{n !}{p_{1} ! p_{2} ! \cdots p_{n} !}\)

(c) Restricted permutations:

• Permutation of distinct objects with repetition: The number of permutations of n different things taken r at a time when each thing may be repeated any number of times = n^r
• Number of permutations of n different things taken r at a time when a particular thing is to be always included in each arrangement = r. ^n-1P_r-1.
• Number of permutations of n different things, taken r at the time when p particular are to be always included in each arrangement = P(r – (p – 1) ^n-pP_r-p.
• Number of permutations of n different things taken r at a time, when a particular thing is never taken in each arrangement = ^n-1P_r.
• Number of permutations of n different things taken r at a time, when p particular things never taken in each arrangement = ^n-pP_r.

(d) Circular permutation:
(1) When we do an arrangement of objects along a closed curve we call it the circular permutation.
(2) Number of circular permutations of n distinct objects taken all at a time = (n – 1)!, where clockwise and anti-clockwise orders are taken as different, as arrangements round a table.
(3) Number of circular permutations of n distinct objects taken all at a time, where clockwise and anti-clockwise orders make no difference as beads or flowers in a necklace or garland.
= \(\frac{(n-1) !}{2}\)
(4) Number of circular permutations of n different things taken r at a time where clockwise and anti-clockwise orders are different = \(\frac{\left({ }^n \mathrm{P}_r\right)}{r}\)
(5) Number of circular permutations of n different things taken r at a time where clockwise and anti-clockwise orders make no difference = \(\frac{\left({ }^n \mathrm{P}_r\right)}{2 r}\)

(e) Some more restricted permutations:

• Number of permutations of n different things taken all at a time, when m specified things come together = m!(n – m + 1)!.
• Number of permutations of n different things taken all at a time when m specified things never come together = n!  – m!(n – m + 1)!.

Combinations:
Each of the different selections made by taking some or all objects at a time irrespective of any order is called a combination.

(a) Difference between permutation and combination:

• A combination is a selection but a permutation is not a selection but an arrangement.
• In combination the order of appearance of objects is immaterial, whereas in a permutation the ordering is essential.
• Practically to find permutations of n different objects taken r at a time, we first select objects then we arrange them.
• One combination corresponds to many permutations.

(b) Combinations of n different things taken r at a time:
The number of combinations of n different things have taken r at a time ⁿc_r = C(n, r) = \(\left(\begin{array}{l}
n \\
r
\end{array}\right)=\frac{n !}{r !(n-r) !}\)

(c) Properties of ⁿc_r :
(1) ⁿc_r = ⁿC₀ = 1, ⁿC₁ = n
(2) ⁿC_r = ⁿC_n-r
(3) ⁿC_r + ⁿC_r-1 = ⁿ⁺¹C_r (Euler’s formula)
(4) ⁿC_x = ⁿC_y ⇒ x = y or x + y = n
(5) n. ^n-1C_r-1 = (n – r + 1) ⁿC_r-1
(6) ⁿC_r = \(\frac{n}{r}{ }^{n-1} \mathrm{C}_{r-1}\)
(7) \(\frac{{ }^n \mathrm{C}_r}{{ }^n \mathrm{C}_{r-1}}=\frac{n-r+1}{r}\)
(8) If n is even then the greatest value of ⁿC_r is ⁿC_n/2.
⇒ If n is odd then the greatest value of ⁿC_r is \({ }^n \mathrm{C}_{\left(\frac{n+1}{2}\right)} \text { or }{ }^n \mathrm{C}_{\left(\frac{n-1}{2}\right)}\)

(d) Number of combinations of n different things taken r at a time, when k particular things always occur = ^n-kC_r-k

(e) The number of combinations of n different things, taken r at a time where k particular things never occur = ^n-kC_r

(f) The total number of combinations of n different things taken one or more at a time (or the number of ways of n different things selecting at least one of them) = ⁿC₁ + ⁿC₂ + ⁿC₃ + ….. + ⁿC_n = 2ⁿ -1

(g) The number of combinations of n identical things taken r at a time = 1.

(h) Number of ways of selecting r things out of n alike things where r = 0, 1, 2, 3 ….. n is (n+ 1).

(i) Division into groups:

• The number of ways in which (m + n) different things can be divided into two groups which contain m and n things respectively = \(\frac{(m+n) !}{m ! n !}\) for m ≠ n.
• If m-n then the groups are of equal size. Thus, division can be done in two ways as:
  ⇒ If order of groups is not important: In this case the number of ways = \(\frac{(2 n) !}{2 !(n !)^2}\)
  ⇒ If order of groups is important: In this case the number of ways = \(\frac{(2 n) !}{(n !)^2}\)

(j) Arrangement in groups:

1. The number of ways in which n different things can be arranged into r different groups = ^n+r-1P_n or n! ^n-1C_r-1
2. The number of ways in which n different things can be distributed into r different groups = rⁿ – ^rC₁(r – 1)ⁿ + ^rC₂(r – 2)ⁿ ….. + (-1)^r-1 . ^rC_r-1. (Blank groups are not allowed)
3. The number of ways in which n identical things can be distributed into r different groups where blank groups are allowed
   = ^(n+r-1)C_(r-1)
   = ^(n+r-1)C_n
4. Number of ways in which n identical things can be distributed into r different groups where blank groups are not allowed (each group receives at least one item) = ^n-1C_r-1

(k) Number of divisors:

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

CHSE Odisha 11th Class English Grammar Additional Questions

A. Rewrite the passages after correcting all grammatical errors in it.

(1) There is great excitement in the planet of Venus this week. For the first time, Venusia scientists manage to land an unmanned spacecraft in the planet Venus, and it is sending back signals, as well as photographs, ever since. The craft directed into an area known as Gonebay.
Answer:
There was great excitement on the planet of Venus this week. For the first time, Venusian scientists managed to land an unmanned spacecraft on the planet Venus, and it has been sending back signals, as well as photographs ever since. The craft was directed into an area known as Gonebay.
(2) How did birds know when to flew south for winter? How long do a bear sleep in winter? Do a porcupine really shoot its quills at an enemy? How do squirrels know where he buries nuts?
Answer:
How do birds know when to fly south for the winter? How long does a bear sleep in winter? Does a porcupine really shoot his quills at an enemy? How does a squirrel know where he buried a nut?

B. Correct the errors.

(a) He is an European.
(b) I met the concerned clerk.
(c) It is high time you get up early.
(d) It has been five years since I last met you.
(e) I congratulate you for winning the prize.
Answer:
(a) He is a European.
(b) I met the clerk concerned.
(c) It is high time you got up early.
(d) It is five years since I last met you.
(e) I congratulate you on winning the prize.

C. Supply the correct tense of the verbs given in brackets.

1. Water always (freeze) at 0 degrees centigrade.
2. Students frequently (make) mistakes of tense usage when they do this exercise.
3. I (have) my hair cut whenever it gets too long.
4. I (take) my dog for a walk every evening before it died.
5. He (come) to my office whenever he needed money.
6. Last year she (wear) the same dress at every party.
7. Whenever I climb a hill, my ear (boil).
8. She (sing) very beautifully before she was married, but nowadays she (not sing) anymore.
9. I seldom (see) him at concerts these days. He (go) to them regularly before the war.
10. She cooks very well but her sister (cook) much better when I knew her.
11. Every time he opens his mouth, he (say) something foolish.
12. He occasionally makes a big effort, but usually he (not bother).
13. Whenever I (go) to see him, he was out.
14. In the past men frequently (fight) duels. Nowadays they seldom (do).
15. How often you (go) to the theatre when you were in London?
16. You (play) with dolls when you were a little girl?
17. The ancient Egyptians (build) pyramids as tombs for their kings.
18. When I was young, my father always (give) me some money on Saturdays.
19. If he is wise, a pianist (practise) four hours a day.
20. His parents don’t know what to do with their child. He (lie) habitually.
21. My aunt Jane (hate) girls who made up.
22. We all (study) Latin when we were at school.
23. Wood always (float).

Answer:
1. Water always freezes at 0 degrees centigrade.
2. Students frequently make mistakes of tense usage when they do this exercise.
3. I have my hair cut whenever it gets too long.
4. I took my dog for a walk every evening before it died.
5. He came to my office whenever he needed money.
6. Last year she wore the same dress at every party.
7. Whenever I climb a hill, my ear boils.
8. She sang very beautifully before she was married, but nowadays she does not sing anymore.
9. I seldom see him at concerts these days. He went to them regularly before the war.
10. She cooks very well but her sister cooked much better when I knew her.
11. Every time he opens his mouth, he says something foolish.
12. He occasionally makes a big effort, but usually, he does not bother.
13. Whenever I went to see him, he was out.
14. In the past men frequently fought duels. Nowadays they seldom do.
15. How often you go to. the theatre when you were in London?
16. Did you play with dolls when you were a little girl?
17. The ancient Egyptians built pyramids as tombs for their kings.
18. When I was young, my father always gave me some money on Saturdays.
19. If he is wise, a pianist practices four hours a day.
20. His parents don’t know what to do with their child. He lies habitually.
21. My aunt Jane hated girls who made up.
22. We all studied Latin when we were at school.
23. Wood always floats.

D. Put the verbs in brackets into the correct Present Tense, Continuous, or Simple.

1. Buses usually (run) along this street. but today they (not run) because it is under repair.
2. John (pass) the post office on his way to work every day.
3. She usually (sit) at the back of the class, but today she (sit) in the front row.
4. I rarely (carry) an umbrella, but I (carry) one now because it is raining.
5. What you generally (do) for a living?
6. You (enjoy) your English class today?
7. You (enjoy) washing dishes as a rule?
8. We nearly always (spend) our holidays at the seaside, but this year we are going to France.
9. Mr. Jones usually (sell) only newspapers, but this week he (sell) magazines as well.
10. You (wash) your hands before every meals.
11. Mary generally (begin) cooking at 11, but today she came home early and (cook) now, although il is only 10.30.
12. I’m sorry you can’t see her. She (sleep) still. She usually (wake) much earlier.
13. Why you (wear) a coat this morning? I never (wear) one till October.
14. Joan still (do) her homework. Her sister, who always (work) quicker, (play) already in the garden.
15. These builders generally (build) very rapidly. They (work) at present on two separate contracts.
16. What (do) you at this moment? If you (not do) anything, please help me.
17. John, who (study) medicine at present, hopes to go abroad after graduation.
18. He generally (come) to my office every clay, but today he (visit) his parents in the country.
19. You (watch) television often? The electrician (install) ours at this moment.
20. Mary usually (wear) a hat to go shopping. but today, as the sun (shine) she (not wear) one.

Answer:
1. Buses usually run along this Street, but today they are not running because it is under repair.
2. John passes the post office on his way to work every day.
3. She usually sits at the back of the class, but today she is sitting in the front row.
4. I rarely carry an umbrella, but I am carrying one now because it is raining.
5. What do you generally do for a living?
6. Are you enjoying your English class today?
7. Do you enjoy washing dishes as a rule?
8. We nearly always spend our holidays at the seaside, but this year we are going to France.
9. Mr. Jones usually sells only newspapers, but this week he is selling magazines as well.
10. Do you wash your hands before every meal?
11. Mary generally begins cooking at 11, but today she came home early and is cooking now, although it is only 10.30.
12. I’m sorry you can’t see her. She is still sleeping. She usually wakes much earlier.
13. Why are you wearing a coat this morning? I never wear one till October.
14. Joan is still doing her homework. Her sister, who always works quicker, is already playing already in the garden.
15. These builders generally build very rapidly. They are working at present on two separate contracts.
16. What are you doing at this moment? If you are not doing anything, please help me.
17. John, who is studying medicine at present, hopes to go abroad after graduation.
18. He generally comes to my office every day, but today he (is visiting) his parents in the country.
19. Do you often watch television? The electrician is installing ours at this moment.
20. Mary usually wears a hat to go shopping, but today, as the sun is shining she is not wearing one.

E. Put the verbs in brackets into the correct tense, Continuous or Simple.

1. You (see) the house on the corner? That is where I was born.
2. You (listen) to what I am saying You (understand) me?
3. I (notice) Mary (wear) a new hat today.
4. She (not understand) what you (mean).
5. I (need) a new suit. They (offer) special prices at the tailor this week.
6. You (smell) gas? I (think) the new stove is leaking.
7. Look at Mary! She (drink) up her medicine, but I can say that she (hate) it.
8. John (seem) rather tired today.
9. it still (rain), but it (look) as if it will soon stop.
10. You (mind) helping me a moment? I (try) to mend this table.
11. Ask him what he (want).
12. You (remember) the name of that girl who (walk) on the other side of the street?
13. ‘Will you have some tea?’ ‘I (prefer) coffee, please.’
14. I (suppose) I must go now. My wife (wait) for me at home.
15. You (see) this box? It (contain) matches.
16. These twins, who (resemble) one another so strongly, (study) art at present.
17. After what has happened, you really (mean) to say that you still (believe) him?
18. You (suppose) the children still (sleep)?
19. ‘The train still (stand) in the station. You (think) we can just catch it?
20. I (notice) you (possess) a copy of Waugh’s latest book. Will you lend it me?

Answer:
1. Do you see the house on the corner? That is where I was born.
2. Are you listening to what I am saying? Do you understand me?
3. I notice Mary is wearing a new hat today.
4. She does no: understand what you mean.
5. I need a new suit. They are offering special prices at the tailor this week.
6. Do you smell gás? I think the new stove is leaking.
7. Look at Mary! She is drinking up her medicine, but I can say that she hates it.
8. John seems rather tired today.
9. It is still raining, but it looks as if it will soon stop.
10. Do you mind helping me a moment? I urn Irving to mend this table.
11. Ask him what he wants.
12. Do you remember the name of that girl who is walking on the other side of the street?
13. ‘Will you have some tea?’ ‘I prefer coffee, please.’
14. 1 suppose I must go now. My wife is waiting for me at home.
15. Do you see this box? It contains matches.
16. These twins, who resemble one another so strongly, are studying art at present.
17. After what has happened, do you really mean to say that you still believe him?
18. Do you suppose the children still sleeping?
19. ‘The train is still standing in the station. Do you think we can just catch it
20. I notice you possess a copy of Waugh’s latest book. Will you lend it me?

F. Supply the correct form of the Present Perfect tense, Continuous or Simple in the place of the verbs in brackets.

1. They just (arrive) from New York.
2. They still (not succeed) in reaching the summit.
3. I this very minutes (receive) a telegram from my brother in India.
4. We already (have) breakfast.
5. I now (study) your proposals and regret I cannot accept them.
6. They (live) here since January.
7. We (wait) on the platform since three o’ clock.
8. She already (ring) the bell twice.
9. I see you just (have) your hair cut.
10. She (write) letters all morning, but I (not start) to write any yet.
11. The children (sleep) all this afternoon.
12. How long you (stay) in that old hotel?
13. They (work) in the same factory for twenty years now.
14. Since when you (have) that new car?
15. I (knock) on the door for ten minutes now without an answer.
16. They (build) that bridge for over a year and still it isn’t finished.
17. I (try) three times and (be) successful only once.
18. How many times you (be) to the cinema this week?
19. He (go) to the dentist off and on for six months.
20. He (take) the exam. three times and (fail) every time.
21. William (marry) the eldest Jones girl at last.
22. I (try) to get in touch with you for several days now.
23. She just (spend) three weeks at her grandmother’s.
24. He (work) hard on his book for some time and (finish) it at last.
25. You ever (read) ‘War and Peace’?

Answer:
1. They have just arrived from New York.
2. They have still not succeeded in reaching the summit.
3. I have this very minutes received a telegram from my brother in India.
4. We have already had breakfast.
5. I have now studied your proposals and regret I cannot accept them.
6. They have been living here since January.
7. We have been waiting on the platform since three o’ clock.
8. She has already rung the bell twice.
9. I see you have just had your hair cut.
10. She has been writing letters all morning, but I have no: starred to write any yet.
11. The children have been sleeping all this afternoon.
12. How long have you been staying in that old hotel?
13. They have been working in the same factory for twenty years now.
14. Since when have you had that new car?
15. I have been knocking on the door for ten minutes now without an answer.
16. They have been building that bridge for over a year and still it isn’t finished.
17. I have tried three times and have been successful only once.
18. How many times have you been to the cinema this week?
19. He has been going to the dentist off and on for six months.
20. He has taken the exam. three times and has failed every time.
21. William has married the eldest Jones girl at last.
22. I have been trying to get in touch with you for several days now.
23. She has just spent three weeks at her grandmother’s.
24. He has been working hard on his book for some time and has just finished it at last.
25. Have you ever read ‘War and Peace’?

G. Supply the missing prepositions using only to or at.

1. He is quite blind _____ her faults.
Answer:
to

2. He is extraordinarily clever _____ mimicking others.
Answer:
at

3. She, on the other hand, is very efficient _____ her work.
Answer:
at

4. He is an expert making himself understood in foreign languages.
Answer:
at

5. Contrary my expectations, I quite enjoyed myself at the party.
Answer:
to

6. She was standing too close _____ the fire and got burned.
Answer:
to

7. That fellow’s no good games at all.
Answer:
at

8. He carried out the project which had always been dear _____ his heart.
Answer:
to

9. We are all very indignant _____ the injustice done to him.
Answer:
at

10. I’m sorry! I’m very bad _____ explaining myself.
Answer:
at

11. He’s the one who’s so very lucky _____ cards.
Answer:
at

12. That device is entirely new _____ me.
Answer:
to

13 He’s not equal _____ the job they’ve given him.
Answer:
to

14. He remained faithful _____ his principles in spite of great pressure.
Answer:
to

15. The delay proved fatal _____ our plans.
Answer:
to

16. She was overjoyed _____ the prospect of meeting him again.
Answer:
at

17. His activities are very harmful _____ my interests.
Answer:
to

18. The government showed itself hostile _____ any progress.
Answer:
to

19. She’s no terribly cruel _____ her dog.
Answer:
to

20. I engaged him because he was so prompt in understanding my instructions.
Answer:
at

21. He was heartbroken _____ her indifference to him.
Answer:
at

22. He doesn’t like me although I’ve always been kind _____ him.
Answer:
to

23. Yes, he’s the kind of person who is always quick figures.
Answer:
at

24. This is much inferior _____ the one I bought last week.
Answer:
to

25. You will be liable _____ a heavy fine if you do that.
Answer:
to

26. This flower is not native _____ England.
Answer:
to

27. Naturally she was sad _____ the death of her parrot.
Answer:
at

28. He does his work carefully but he’s terribly slow ______ it.
Answer:
at

29. Who wouldn’t be triumphant _____ their success in the examination?
Answer:
at

30. A dutiful daughter and obedient _____ her parents.
Answer:
to

31. You shouldn’t be surprised _____ a thing like that.
Answer:
at

32. It should be obvious _____ the meanest intelligence.
Answer:
to

33. The seeds are peculiar ______ this genus of plant.
Answer:
to

34. Can’t you manage to be a little more polite your aunt?
Answer:
to

35. He works in a factory. Previous _____ that he was in a laundry.
Answer:
to

36. I have been truly astonished _____ the number of people who believe it.
Answer:
at

37. This is quite irrelevant ______ the matter we are discussing.
Answer:
to

38. They were shocked _____ his apparent lack of appreciation.
Answer:
at

39. He was so rude _____ her that she never spoke to him again.
Answer:
to

40. Sacred _____ the memory of Mary Jones.
Answer:
to

41. They are very sensitive _____ people’s opinion of them.
Answer:
to

42. I’ve got one similar _____ yours.
Answer:
to

43. Subject _____ the exigencies of the service.
Answer:
to

44. The people of this country are very skilful ______ making dolls.
Answer:
at

45. It’s useful _____ me to have him about the house.
Answer:
to

46. It’s vital _____ a proper understanding of the problem.
Answer:
to

H. Supply the missing preposition using with, for or of.

1. Don’t be afraid _____ the dog! It won’t bite you.
Answer:
of

2. I can’t be angry _____ him now that he’s apologized _____ what he has done.
Answer:
with, for

3. He’s far ahead _____ the others in arithmetic.
Answer:
of

4. You ought to be ashamed _____ yourself.
Answer:
of

5. Are you aware _____ the fact that it is half past ten.
Answer:
of

6. I’m sorry. They are simply not capable doing it.
Answer:
of

7. Don’t disturb him! He’s busy _____ his accounts.
Answer:
with

8. He’s ambitious and eager _____ honours.
Answer:
for

9. For goodness sake! Do be careful _____ that vase. You could easily drop it.
Answer:
with

10. Children must be taught to be careful _____ traffic.
Answer:
of

11. I am not at all certain _____ the date of his arrival.
Answer:
of

12. His explanation was not consistent _____ the facts.
Answer:
with

13. Monsieur X was famous _____ his collection of pictures.
Answer:
for

14. I was conscious _____ a feeling of uneasiness.
Answer:
of

15. Kingston lies due west _____ London.
Answer:
of

16. I’m sorry. I’m not content _____ your explanations.
Answer:
with

17. The soldier was pronounced fit _____ service.
Answer:
for

18. Mary was terribly envious _____ Joan’s new hat.
Answer:
of

19. We are all very fond _____ going to the theatre.
Answer:
of

20. John is very discontented _____ his salary.
Answer:
with

21. I shall be grateful any advice you can give me.
Answer:
for

22. This exercise is full ______ the most terrible mistakes.
Answer:
of

23. Are you familiar _____ the works of Milton?
Answer:
with

24. The manager is well qualified _____ his position.
Answer:
for

25. That is something I am profoundly glad.
Answer:
of

26. This chair is not identical _____ the one I bought last year.
Answer:
with

27. He’s a sporting fellow, and always ready for anything.
Answer:
for

28. That student is ignorant _____ the first rules of grammar.
Answer:
of

29. Your explanation is incompatible _____ the story I heard.
Answer:
with

30. John, you will be responsible for providing the drinks.
Answer:
for

31. Judges must be independent of

political pressure.
Answer:
of

32. I know he’s a difficult child, but you must be patient _____ him.
Answer:
with

33. I am extremely sorry _____ the delay, but I was held up.
Answer:
for

34. He was jealous _____ his brother’s good fortune.
Answer:
of

35. Comedians are always popular holiday crowds.
Answer:
with

36. I can’t bake a cake as we are short _____ eggs this week.
Answer:
of

37. His income is sufficient _____ his needs.
Answer:
for

38. He’s always very shy approaching his chief.
Answer:
of

39. Let us be thankful _____ small mercies.
Answer:
for

40. It is wise to be sure _____ your facts before you speak.
Answer:
of

41. One is generally tolerant _____ small faults.
Answer:
of

42. She is, unfortunately, devoid _____ a sense of humor.
Answer:
of

43. They gave him a visa valid _____ all countries in Europe.
Answer:
for

44. I’m tired _____ arguing with you.
Answer:
of

45. They proved themselves unworthy _____ the trust which was placed in them.
Answer:
of

K. Supply the missing prepositions, from, about, on or in.

1. Keep away _____ the machine while it is running.
Answer:
from

2. He wsa singularly fortunate _____ his choice of wallpaper.
Answer:
in

3. He is intent _____ attending the football match on Saturday.
Answer:
on

4. I am very dubious _____ your chances of passing the examination.
Answer:
about

5. They are proficient _____ the use of their fists.
Answer:
in

6. This is quite different _____ what I expected.
Answer:
from

7. The diet here is deficient _____ vitamins.
Answer:
in

8. That young man is very keen _____ cycling.
Answer:
on

9. We are all very enthusiastic ________ our next holiday.
Answer:
about

10. It was far ______ my intention to suggest that he was unintelligent.
Answer:
from

11. He was perfectly honest _____ his intentions to win the prize at all costs.
Answer:
about

12. The secretary was not well qualified _____ shorthand.
Answer:
in

13. Some people appear completely immune _____ this disease.
Answer:
from

14. I am very reluctant _____ asking him to do this.
Answer:
about

15. Our plans must remain dependent _____ the weather.
Answer:
on

16. Everybody was very uneasy _____ the outcome of the negotiations.
Answer:
about

17. Of course, you are quite right _____ that.
Answer:
about

18. He was involved in an accident, resulting _____ the slippery condition of the road.
Answer:
from

19. The enemy is weak _____ artillery.
Answer:
in

20. Entomologists are still curious _____ the life-cycle of that month.
Answer:
about

21. I am not very interested _____ the story of your life.
Answer:
in

22. Put that cake back in the cupboard. where it will be safe _____ the cat.
Answer:
from

23. I’m afraid he is quite wrong _____ the date of the invasion.
Answer:
about

24. His father was very sad _____ his son’s failure in his final exams.
Answer:
about

25. I am extremely doubtful _____ the wisdom of pursuing that course of action.
Answer:
about

L. Supply the prepositions at or to as appropriate.

1. What time did you arrive _____ your home?
Answer:
at

2. He finds it difficult to accustom himself _____ the climate.
Answer:
to

3. AIl the visitors exclaimed _____ the beauty of the place.
Answer:
at

4. Just glance _____ this for me, would you?
Answer:
at

5. His debts amount _____ a considerable sum.
Answer:
to

6 I can only guess _____ the extent of the damage.
Answer:
at

7. It is useless to appeal _____ his better nature.
Answer:
to

8. She hinted darkly _____ all sorts of wild actions in his youth.
Answer:
at

9. If you want permission. you must apply _____ the caretaker.
Answer:
to

10. He was attached _____ the French Army during the war.
Answer:
to

11. He is too sick to attend _____ his duties.
Answer:
to

12. _____ what do you attribute your success in life?
Answer:
to

13. I’m sure this one doesn’t belong _____ me.
Answer:
to

14. He challenged him _____ a game of chess.
Answer:
to

15. It is very unkind to joke _____ the expense of the disabled.
Answer:
at

16. Shall I compare thee _____ a summer’s day?
Answer:
to

17. If you want them to hear, you’ll have to knock a good deal harder _____ the door.
Answer:
at

18. The prisoner was condemned _____ penal servitude for life.
Answer:
to

19. The fire was confined _____ the kitchen regions.
Answer:
to

20. I will never consent _____ her marrying that man.
Answer:
to

21. Just have a look _____ this for me, would you?
Answer:
at

22. I have been entirely converted _____ the use of an electric razor.
Answer:
to

23. Employees who have twenty-five years’ service become entitled _____ a pension.
Answer:
to

24. You can safely entrust your little son _____ her care.
Answer:
to

25. People who heard her voice marvelled _____ it.
Answer:
at

26. Let’s invite them all _____ dinner.
Answer:
to

27. Listen _____ me!
Answer:
to

28. Do you object my smoking?
Answer:
to

29. He peered _____ the exhibit on account of his short-sightedness.
Answer:
at

30. Such an idea would never occur _____ me!
Answer:
to

31. The patient is reacting very unsatisfactorily _____ the drug.
Answer:
to

32. The children peeped _____ the guests as they were arriving.
Answer:
at

33. I have been reduced ______ using oil for lack of fat.
Answer:
to

34. The children are playing _____ Red Indians again.
Answer:
at

35. She has been forced to resort _____ all sorts of devices to avoid him.
Answer:
to

36. The patient has not responded _____ treatment.
Answer:
to

37. It is very rude to point people in the street.
Answer:
at

38. If you’ll bring the drinks, I’ll see _____ the food.
Answer:
to

39. They have been subjected _____ all sorts of indignities.
Answer:
to

40. I refuse to submit ______ that sort of treatment.
Answer:
to

41. Can you wonder _____ it, if they are reduced _____ begging.
Answer:
at, to

42. I’m sorry he finally succumbed _____ the temptation of stealing.
Answer:
to

43. If you want to pass your examination, you il have to work very hard _____ your Latin.
Answer:
at

44. We shall never surrender _____ that enemy.
Answer:
to

45. I don’t know him, but he has been starting _____ me for ten minutes.
Answer:
at

46. I have never subscribed _____ the general opinion of him.
Answer:
to

47. Turn _____ page 22 and start reading!
Answer:
to

48. The government has again yielded _____ the pressure from outside.
Answer:
to

49. She always trusts _____ her neighbors to help her.
Answer:
to

50. Would you please reply my question?
Answer:
to

M. Turn the following into passive.

1. The government has called out troops.
Answer:
Troops have been called out.

2. Fog held up the trains. (agent required)
Answer:
Trains were held up by fog.

3. You are to leave this here. Someone will call for it later on.
Answer:
This is to be left here. k will be called for.

4. We called in the police.
Answer:
Police were called in.

5. They didn’t look after the children properly.
Answer:
Children were not properly looked after.

6. They are flying in reinforcements.
Answer:
Reinforcements are being flown in.

7. Then they called up men of 28.
Answer:
Men of 28 were called up.

8. Everyone looked up to him. (agent required)
Answer:
He was looked up to by everyone.

9. All the ministers will see him off at the airport. (agent required)
Answer:
He will be seen off at the airport by all the ministers.

10. He hasn’t slept in his bed.
Answer:
Bed hasn’t been slept in.

11. We can build on more rooms.
Answer:
More rooms can be built on.

12. They threw him out.
Answer:
He was thrown out.

13. They will have to adopt a different attitude.
Answer:
Different attitude will have to be adopted.

14. He’s a dangerous maniac. They ought to lock him up.
Answer:
He ought to be locked up.

15. Her story didn’t take them in. (agent required)
Answer:
They weren’t taken in by her story.

16. Burglars broke into the house.
Answer:
House was broken into.

17. The manufacturers are giving away small plastic toys with each packet of cereal.
Answer:
Small plastic toys are being given away.

18. They took down the notice.
Answer:
Notice was taken down.

19. They frown on smoking here.
Answer:
Smoking is frown on.

20. After the government had spent a million pounds on the scheme they decided that it was impracticable and gave it up. (Make only the first and last verbs passive)
Answer:
After a million pounds had been spent, the scheme was given up.

21. When I returned I found that they had towed my car away. I asked why they had done this and they told me that it was because I had parked it under a No Parking sign. (four passives)
Answer:
My car had been towed away. I asked why this had been done and was told that it had been parked.

22. People must hand in their weapons.
Answer:
Weapons must be handed in.

23. The crowd shouted him down.
Answer:
He was shouted down.

24. People often take him for his brother.
Answer:
He is often taken for his brother.

25. No one has taken cut the cork.
Answer:
The cork hasn’t been taken out.

26. The film company were to have used the pool for aquatic displays, but now they have changed their minds about it and are filling it in. (Make the first and last verbs passive)
Answer:
Pool was to have been used it is being filled in.

27. This college is already full. We ne turning away students the whole time.
Answer:
Students are being turned away.

28. You will have to pull down this skyscraper as you have not complied with the town planning regulations.
Answer:
Skyscraper will have to be pulled down as the town planning regulations have not been complied with.

N. Put the following sentences into passive, using infinitive construction where possible.

1. We added up the money and found that it was correct.
Answer:
Money was added up and found to be correct.

2. I’m employing a man to tile the bathroom.
Answer:
I am having the bathroom tiled.

3. Someone seems to have made a terrible mistake.
Answer:
A terrible mistake seem to have been made.

4. It is your duty to make tea at eleven o’ clock. (Use suppose.)
Answer:
You are supposed to make tea.

5. People know that he is armed.
Answer:
He is known to be armed.

6. Someone saw him pick up the gun.
Answer:
He was seen to pick up?

7. We know that you were in town on the night of the crime.
Answer:
You are known to have been.

8. We believe that he has special knowledge which may be useful to the police. (one passive)
Answer:
He is believed to have special knowledge.

9. You needn’t have done this.
Answer:
This needn’t have been done.

10. It’s a little too loose: you had better ask your tailor to take it in. (one passive)
Answer:
You had better have it taken in.

11. He likes people to call him — ‘sir’.
Answer:
He likes to be called sir’.

12. Don’t touch this switch.
Answer:
This switch isn’t to be/mustn’t be touched.

13. You will have to get someone to see to it.
Answer:
You will have to have/get it seen to.
(Or) It will have to be seen to.

14. It is impossible to do this. (Use can’t)
Answer:
This can’t be done.

15. Someone is following us.
Answer:
We are being followed.