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Punjab State Board PSEB 11th Class English Book Solutions English Letter Writing Exercise Questions and Answers, Notes.

PSEB 11th Class English Letter Writing

Some Important Letters

(1) How You Fared in Your English Paper

Suppose you are Rakesh. Do you remember that one Mr A.C. Gogoi became your friend when you were travelling with him from Delhi to Kanpur ? Do you also remember that you did not do well in English Paper – A, and your friend advised you to make up in English Paper – B?

Now at the end of your examination, write a letter to Mr Gogoi, A/255 Paan Bazaar, Guwahati (Assam), telling him about the examination, particularly how you did in the two English Papers.

2204-A Model Town
Patiala
24 April 20 ……

Dear Mr Gogoi
I still remember our sweet meeting in the Gomti Express while travelling from Delhi to Kanpur. We took each other’s address and I promised to write to you first. I could not write to you earlier because of the examination. Only yesterday I finished my last paper.

I have done quite well in the remaining papers. I hope to get very good marks in my Mathematics and Science Papers. In Social Studies and Punjabi too I hope to get at least second class marks. It is only in English that I have not done too well. In fact, at the end of English Paper – A I was completely disappointed. I was about to give up. But my friend Hardeep advised me to take heart and make up in Paper – B. I worked very hard for it. Now I hope to get at least 50 marks in Paper – B.

I am free for more than two months now. I shall go to college in July. I plan to spend my holidays with a friend at Shimla. It will be cool and pleasant there. Will you please join us there for a few days ?

With best wishes
Yours sincerely
Rakesh

(2) A Letter of Advice to A Friend

Suppose you are Parkash. You live at 125 Kucha Harnam Singh, Phagwara. Your friend Gurinder, who lives opposite Govt. Middle School Goraya, is thinking of running away to Mumbai to become a film actor. Write him a letter of advice, telling him that it is not wise to do so.

125 Kucha Harnam Singh
Phagwara
16 March 20 ………
Dear Gurinder

Last week, Subhash came here to buy seeds for his farm. He told me that you are planning to run away to Mumbai to become a film actor. I do not think this will be a wise step for you. Dreams of becoming film actors often lead young boys and girls into grief and difficulties. Very foolishly they leave their sweet homes and run away to Mumbai with stolen money. Very soon this money is spent and they have to starve. They have to sleep on pavements. No film company allows them to enter their gates even.

I think you should look after your father’s lands. You can really earn a lot of money this way. However, if you feel a strong urge to become a film actor, you should first practise acting on the college stage. You should complete your B.A. first. Then you can join the Film and Television Institute at Pune. If you have talent for acting, you will surely get good offers from film companies. I am sure you will consider my advice and act upon it.

With best wishes
Yours sincerely
Prakash

(3) To Brother Asking for Money

Imagine you are Robert William and you are studying in Class XI at the Mayo College, Ajmer. In a few months, you have to appear in the final examination. Your father sent you the examination fee last month, which you spent away in buying some clothes for yourself. You cannot write to your father again for the fee. Write to your brother, who lives at 23 / 2, South Extension III, New Delhi, explaining everything and asking him to lend you Rs 800/- only.

12 Partap Hostel
Mayo College
Ajmer
18 April 20 ……..
Dear Brother

I am writing you this letter with a sense of shame and guilt. My Annual Examination comes off in the month of April. The admission forms are being sent. Father sent me two thousand rupees to deposit my examination fees and other college dues. But last Monday I was going through the bazaar with one of my friends. I saw a pullover in the window of a shop. It caught my fancy. I bought it for ?1000/-. The fact that I was to deposit my fees quite slipped out of my mind.

Now I am ashamed of my thoughtlessness. I do not want to trouble dear father once again for money. He will feel bad about it. I request you to lend me Rs 800/- so that I may be able to pay my fees.I hope you won’t disappoint me. I shall save from my pocket-money to pay off the loan.

Yours affectionately
Robert William

(4) To Mother About How You Helped An Old Man

On Friday last week, while you were returning home from school, it suddenly started raining. The roads became slippery and cycling became dangerous. Right then, you ran into an old man and he had to be taken to hospital. Write a letter of not more than 100 words, to your mother, giving her an account of what happened. Your name is Seeta and you live in Amritsar. Your house is situated on Court Road; its number being 729.

729 Prem Niwas
Court Road
Amritsar
7 April 20 ……..
My dear Mother

On Friday last week, I was returning home from school. I was riding my cycle. Suddenly, it started raining. The roads became slippery. Cycling became dangerous. Just when I was taking a turn on the road, an old man came walking across it. My cycle ran into him. He was knocked down. He was badly wounded in his leg.

The old man was very noble. He did not get angry with me. He said that it was not my fault. However, I knew my duty. I at once took the old man to a nearby hospital. I got his wounds dressed. Then I took him to his house and left: him there. The old man blessed me again and again.
With regards

Your loving daughter
Seeta Puri

(5) Advising Friend Against Early Marriage

You are Harpreet Kaur. You live at 125—A, Railway Road, Jalandhar City. A classfellow of yours (Surinder) comes from Nakodar and tells you that Gurpreet’s parents are arranging Gurpreet’s marriage shortly. Gurpreet does not like to get married so soon. After all, like you, she has just passed the senior secondary examination and is barely 16. Write a letter to Gurpreet (House No. 233, Mohalla Kalyana, Nakodar), advising her how she can convince her parents that it is too early for her to get married. You can tell her that even law does not permit it.

125-A Railway Road
Jalandhar City
11 April 20 ……….
My dear Gurpreet

I was very unhappy to learn from Surinder that your parents are arranging your marriage shortly. She also told me that you don’t like to get married so soon. You are perfectly right. After all you are barely 16 as yet.

You should try to convince your parents. Tell them that it will spoil your life. You have just passed the senior secondary examination. They should let you do B.A. at least. Marriage at so early an age is very harmful. It spoils the health of a girl. Moreover, law does not permit it. Parents can’t marry off a girl less than 18 years of age. It can lead to imprisonment as well as fine.

I hope your parents will see reason and postpone the idea of arranging your marriage. With best wishes

Yours sincerely
Harpreet Kaur

(6) Inviting Friend to A Hill Station

Your name is Neelam and you live at House No. 576, Shastri Nagar in Mussoorie. Write a letter to your friend inviting him to spend the summer vacation with you.

House No. 576
Shastri Nagar
Mussoorie
27 May 20 ………
My dear Sushil

I am very glad to know that your school has broken up for the summer vacation. I invite you to spend your vacation with us at Mussoorie.

Mussoorie is called the Queen of Hill-stations. The air here is cool and bracing. The rains have set in. We have a shower of rain almost daily. After a shower, the weather becomes pleasant. Fruit is cheap and can be had in plenty.

I shall take you round the various beauty spots here. Hiking among the mountains has a joy of its own. It will certainly be a treat if you come. We shall have a jolly good time here. My parents will be very happy to have you in our midst. Kindly write me the time and date of your arrival. I am anxiously waiting for you.

Yours sincerely
Neelam

(7) Showing Inability to Accept An Invitation

Suppose you are Mohan living in 132, Friends’ Colony, Moga. Your friend Ramesh has invited you to visit Delhi and see the Historical buildings there. Write him a letter of thanks, showing your inability to accept his invitation.

132 Friends’ Colony
Moga
28 March 20 ……..
My dear Ramesh

I received your letter yesterday. It shows your deep love for me. You have invited me to visit Delhi and see the historical buildings there. I thank you for it.

But I regret to inform you that I won’t be able to visit Delhi in the near future. I met with an accident last Sunday. I was coming home from college. A scooterist ran into me. I was knocked down. I broke my right leg. I was taken to the hospital. The doctor applied plaster to my leg. I have to use a crutch to move about. It gives me pain also. Due to this disability I am unable to travel. I promise to visit you as soon as I get well.
With sincerest regards

Yours sincerely
Mohan

(8) Congratulating on Winning A Scholarship

Imagine you are Harish. You live in Amritsar at Guru Nanak Wara (House No. 2577). Write a letter to a friend congratulating him on winning a scholarship.

House No. 2577
Guru Nanak Wara
Amritsar
12 April 20 ……..
My dear Mukesh

The result of the Plus 2 Examination was out today. I looked up your roll number on the Internet. My joy knew no bounds when I saw that you are getting 385 marks. You have got not only a very high first division, but your name appears in the list of scholarship- winners also. Please accept my heartiest congratulations on your brilliant success. Really, it is a splendid success. You have brought honour to your family and to us also. Your hard work has borne fruit after all.

Please convey my congratulations to your dear parents. They must be very glad at your success. When are you giving a party to celebrate your success ? Please don’t forget to keep my share. May you progress in life by leaps and bounds !
Congratulating you once again

Your loving friend
Harish

(9) Informing About Winning A Prize

Imagine you are Harish. You live in Amritsar at Guru Nanak Wara (House No. 2577). Write a letter to your father informing him about a prize which you have won by standing first in the house examinations.

House No. 2577
Guru Nanak Wara
Amritsar
12 April 20 ……..
My dear Father

The prize distribution function of our college was held last Monday. The Chief Minister presided over the function. You will be glad to know that I have won the first prize by standing first in the house examinations. There were many prize-winners, but I was the first to be called for getting the prize. I went to the stage and shook hands with the President. The students and teachers gave loud cheers. The President gave me the prize and took me in his embrace. There was a loud applause once again. After this, I came back to my seat. My friends, congratulated me again and again. I wish, Papa, you had been there on thit day.

After giving away the prizes, the President made a speech. Last of all our Principal thanked the President and the function came to a close. My friends gathered round me and asked for a party. I entertained them with sweets and cold drinks.
With regards

Your loving son
Harish

(10) Sympathising on Failure

Your name is Kamal and you reside in Ludhiana at 2511/3, Bharat Nagar. A friend of yours has failed in the Matriculation examination. Write a letter to him, encouraging him to try again.

2511 / 3,
Bharat Nagar
Ludhiana
17 April 20 ………
My dear Rohit

The result of the Matriculation Examination is out today. I am sorry not to find your name among the successful candidates.

To be quite honest about it, your failure in the examination does not surprise me much. You fell ill just before your examination. The doctor had advised you complete rest, but you insisted on appearing in the examination. You could hardly walk to the Examination Hall.

I advise you not to give way to despair. After all you are not to be blamed. Examinations are not a sure test of one’s ability. They are a mere chance. Please do not take your failure to heart. Keep up your spirits. Take your failure as a stepping-stone to success. Work hard for the next year. God will bless you with better luck next time.
With deep sympathies

Yours very sincerely
Kamal

(11) Permission to Continue Your Studies

Imagine that your name is Bhupinder and you live in a village named Bham which has a post office from where letters are distributed. This village is in Hoshiarpur district. Your father desires that you should discontinue your studies after 10+1 examination. Write him why he should let you continue your studies.

V. & P. O. Bham
District Hoshiarpur
13 April 20 ……….
My dear Father

I received your letter yesterday. I am very sad to know that you want me to discontinue my studies after my 10+1 Examination. It is true that you want me to lend you a hand in business. But, Father, you should realise the value of education. After doing my B.Com., I shall be able to help you in a better way. I shall then maintain all the accounts myself. If I discontinue my studies now, I will be handicapped for the whole of my life. Moreover, I am not a weak student. I have never failed in any examination. I shall do my B.Com. in the next four years. I request you to employ some young man for your help. I shall be ever at your beck and call after finishing my studies.
I hope you won’t compel me to discontinue my studies.

Yours lovingly
Bhupinder

(12) Explaining Cause of Your Failure

Suppose you are Naresh. You live in Basant Cottage, Railway Road, Jalandhar City. Write a letter to your father explaining the cause of your failure in the House Examination.

Basant Cottage
Railway Road
Jalandhar City
6 April 20 ……..
My dear Father

I am very sorry to inform you that I have failed in the December Test. I fail in English and Economics. In History and Pol. Science, too, I have not fared well. But believe me, Father, I am not to be blamed for it.

My failure is not due to any carelessness on my part. In the class, I was always attentive. I put in hard work. I never missed any period. Nor did I ever waste my time in idle talk. Unluckily, I fell ill before the examination. I caught a severe cold. The doctor advised me to take complete rest. I could not revise my courses of study. So, I could not do the papers well. Kindly excuse me this time. I hope to fare quite well in the Annual Examination.
With regards

Yours affectionately
Naresh

(13) A Cheerful Letter to A Sick Friend

Your name is Kamal and you reside in Jalandhar at 60, Jawahar Nagar. Write a bright and cheerful letter to a friend who is lying ill in a hospital.

60 Jawahar Nagar
Jalandhar
27 March 20 ……..
My dear Anil

Your elder brother met me yesterday. He told me that you have been operated for appendicitis. I hope you will bear it up and be well soon. You will be up and doing as soon as your wounds heal up. Avoid exertion for some time. Follow the advice of your doctor and be careful about your health.

Dear Anil, I have a very good news for you. My father has bought a car. He has promised to take us to Srinagar. We shall go by our car. You will also go with us. We shall go when you recover completely. We shall have a very happy time together. We shall enjoy the beauty of hills and waterfalls on the way.

Please keep me informed about your health.
With best wishes

Your loving
friend Kamal

(14) Suggestions for Improvement in Studies

Imagine you have a younger brother. You have received his progress report from his school. The report is unsatisfactory. Write a letter giving him some suggestions to improve his performance.

14 Railway Road
Malerkotla
12 April 20 ………
My dear Rakesh

I have just received your progress report for the December Test. It is very disappointing. I am pained to learn that you fail badly in English and Mathematics and get bare pass marks in the other subjects. Your tutor has complained that you are often late for school and do not do your homework regularly. He also writes that you keep bad company.

Dear Rakesh, it is never too late to mend. Turn over a new leaf and avoid bad company. Put your heart and soul into your studies.

You should try to be in the good books of your teachers. Do your homework regularly and never be late for school. You should try to make up your deficiency in English and Mathematics. Request your teacher to suggest you some good books on these subjects. You should read every subject daily. Frame a time-table and work according to it.

I hope you will take my suggestions seriously. Remember it will be no use crying over spilt milk.

Yours affectionately
Suresh Jindal

(15) Thanking for the Birthday Gift

Suppose you are Ankit Jain. You live at 554, Royal Enclave, Ludhiana. Write a letter to your uncle, thanking him for the birthday gift that he sent for you.

554, Royal Enclave
Ludhiana
II October 20 ……..
My dear Uncle

Thank you for the lovely gift you have sent me on my birthday. Your gift is truly after my heart. The wristwatch sent by you looks very beautiful. All my friends have liked it very much.

Dear uncle, I was badly in need of a watch. I was often late for school. I had to pay some fine every month. This watch will now prove useful for me. It will help me during the examinations. It will also help me to regulate my daily work. It is a token of your love for me. I shall keep it with great care. I once again thank you for this nice present.

Yours affectionately
Ankit Tain

(16) Advising Your Brother to Take Part in Games

You are Mohit Verma living at 405, Green Park, Ludhiana. Write a letter to your younger brother, Namit, who is a bookworm, persuading him to take part in games.

405, Green Park
Ludhiana
6 January 20 ……..
My dear Namit

I have just received a letter from Sushma. I am sorry to learn that you are gone very weak in health. You often fall ill. No doubt, you are doing quite well in studies. But you are doing so at the cost of your health. Dear Ajitabh, this is not good. Overwork will tell upon your health. If you go on studying without rest, you will certainly ruin your health.

You must know that games are as useful as studies. They are part and parcel of education. They make us active and smart. They keep us healthy. They widen our circle of friendship. They teach us many good things. Above all, they keep us physically fit. So you must take part in games. I trust you will act upon my advice.

With love
Yours affectionately
Mohit Verma

(17) A Letter of Condolence

Imagine you are Aman Verma. You live at 503, Surya Enclave, Phagwara. Write a letter of condolence to your friend who has lost his father.

503, Surya Enclave
Phagwara
20 August 20 ……..
Dear Sumit

I was shocked to learn about the untimely death of your father. He was quite healthy. I met him the other day. I never thought that his end was so near. He was a very noble man. He was kind to all. He was a lovable father. He took keen interest in your studies. He looked upon me as his own son. I feel your father’s death as a personal loss to me.

Dear Sanjeev, do not give way to grief. Death spares nobody. Your loss is great, but tears cannot bring your dear father back. It is useless to shed tears. Such was God’s will and we must bow to it. Try to console your younger brothers and sisters. May God grant peace to the departed soul !

With deep sympathies
Yours sincerely
Aman Verma

(18) About the Life in Hostel

You are Mohini Sharma living at Kamla Devi, Girls’ Hostel, DAV College, Ludhiana. Write a letter to your mother, telling her about the life in your hostel.

Room No. 53
Kamla Devi Girls’ Hostel
DAV College
Ludhiana
30 August 20 ……..
My dear Mother

I have been living in the college hostel for the last two months. It is a new experience for me. I have liked this life very much.

Our hostel has lovely surroundings. All around it, there are tall, green trees. The rooms are very airy. They are well-lit. Each room is shared by four students. My room-mates are luckily very good girls. I have made friends with them. The food served in our hostel is very tasty and nourishing. We get fruit and milk daily. You have nothing to worry about me.

With regards
Yours loving daughter
Mohini Sharma

(19) About Increasing Thefts

Suppose you are Anuj Gupta. You live at 15, Upkar Nagar, Ludhiana. Write a letter to the Police Commissioner complaining about the increasing number of thefts in your area.

15 Upkar Nagar Ludhiana
7th April 20 ………
The Police Commissioner
Ludhiana
Respected Sir

Recently there has been an alarming increase in the number of thefts in the Upkar Nagar area of this city. Hardly a day passes when there is no theft or burglary. Cases are regularly reported to the nearest Police Station but no headway has so far been made in apprehending the culprits. To be quite frank, people have started doubting that some policemen have a hand in these thefts and burglaries. Though it is a wild charge, the fact remains that the culprits always go scot-free. There is a danger to the life of the residents also since the burglars come armed with weapons.

It is requested that night patrolling in this area should be intensified and all-out efforts should be made to nab the culprits.

Yours faithfully
Anuj Gupta

(20) About Poor Pouce Patrolling

Write a letter to the Superintendent of Police of your district complaining about poor patrolling by the police in your area resulting in petty crimes. Sign yourself as ABC.

16 Railway Road
Amritsar
30 March 20 ……..
The Superintendent of Police
Amritsar
Subject : Crimes Due to Poor Police Patrolling Sir

It pains me to bring to your kind notice the poor patrolling by police in this area. I think there is nobody to check whether the policemen on duty are doing their job honestly. Two or three policemen are often seen in the early hours of the night. They move about here and there with long sticks in their hands. They harass the villagers going back home after their day’s work. They extort money from them on one pretext or the other.

This so-called patrolling party disappears after about 10 p.m. There is no night watchman also in this area. The thieves and burglars have a free time to enter any house they choose. Hardly a day passes when there is no case of theft.

Sir, I request you to put some honest policemen on patrol duty in this area. All the residents shall feel obliged to you.

Yours faithfully
ABC

(21) About Poor Condition of Roads and Street Lights

Write a letter to the Municipal Commissioner, informing him about the poor condition of the roads and street lights in your locality explaining the difficulties faced by the people of the area. You are Rajeev / Ragini.

350 Model Town
Ludhiana
15 July 20 ……….
The Municipal Commissioner
Amritsar

Subject : Complaint about Poor Condition of Roads and Street Lights Sir

I beg to draw your kind attention to the poor condition of the roads and street lights in our locality. The bad roads and the dark streets cause a lot of difficulty for the people of this area. The roads are dotted with pits and have become bumpy. There always remains a fear of accidents. And at night the situation becomes worse when there are no street lights. People have to grope their way in the dark. It becomes very easy for antisocial elements to play mischief anywhere they like.

It is, therefore, requested that urgent steps should be taken to improve the condition of roads and also to make the street lights functional.

Yours faithfully
Rajeev

(22) Requesting for Opening A Dispensary

You are Vinay Jain, living at 23, Rampur, Kathua. Write a letter to the Deputy Commissioner of your district, making out a case for the opening of a dispensary in your area.

H.No. 23
Rampur, Kathua
5 January 20 ……..
The Deputy Commissioner
Kathua
Subject : Opening of a Dispensary in Our Area Sir

Our village Rampur is at a distance of about fifteen kilometres from Kathua. It is quite a big village. It has a population of about 2000 people. But it is a pity that there is no dispensary here. People have to depend upon quacks who befool and fleece the poor villagers. It is almost impossible to walk all the way to Kathua for getting medical treatment.

There is much talk about rural developnent on the part of the government. It is claimed that electricity, pure drinking water and medical facilities are being provided in each village. But sadly, our village has not so far won the attention of the health department. It is requested that keeping in view the great need of the villagers, a good dispensary should be opened here. A whole-time doctor should also be appointed so that the villagers have not to run to the city for sound medical advice. It is hoped that a sympathetic consideration shall be given to our request.
Thanking you

Yours faithfully
Vinay Jain

(23) About the Delay in the Delivery of Your Mail

You are Ishqpreet Singh Nanda. Write a letter to the Post Master General, complaining about the delay in the delivery of your mail by the postman and asking him to make enquiries.

53 Vijay Nagar
Amritsar
17 May 20 ………
The Post Master General
Amritsar
Subject : Delay in the Delivery of Mail Sir

I beg to draw your kind attention to the irregular delivery of letters in our locality. This problem has become a big grievance for all the residents of our locality.

Ram Lai, the postman of our beat, is very careless and irregular. He does not do his duty honestly. He seldom visits our locality. Whenever he comes, he does not deliver the mail properly. Almost every resident has put a letter box on the outer wall of his house. But the postman does not care to put letters into the boxes. He throws them at the doors of the houses. Sometimes, he hands them over to the children playing in the street. Many important letters are thus lost or delayed. Every resident has suffered because of his negligence. We have warned the postman many a time, but to no effect.

Kindly look into the matter and take necessary steps for the regular delivery of our letters.

Yours faithfully
Ishqpreet Singh

(24) Misuse and Poor Maintenance of the Public Park

You are Shaan of 32, Kailash Colony, Ram Nagar. Write a letter to the editor of a newspaper about the misuse and poor maintenance of the public park in your colony.

32 Kailash Colony
Ram Nagar
17 April 20 …….
The Editor
The Daily Reporter
Chandigarh
Subject : About the Misuse and Poor Maintenance of the Public Park Sir

We have a big public park in our locality. But sadly it has fallen into miserable state due to the total neglect of the concerned officials. The plants in the park have withered because they are hardly ever watered. All the park has overgrown with prickly weeds which make it impossible for the children to play there. Heaps of garbage have come up at all the corners of the park. Thus the park has become the most ugly spot of the colony. It has also become a den for antisocial elements who starts collecting there as soon as the night begins to fall. It is hoped that the publication of these lines in your esteemed paper will help to draw the attention of the corporation officials to take proper steps for the upkeep of this park. A well-kept park will certainly prove a boon for the residents.

Yours truly
Shaan

(25) About the Evil of Begging

You are Rohit Verma living at 53-B, Model Town, Jalandhar. Write a letter to the Editor of a newspaper, highlighting the evils of begging on the streets in your city.

53-B Model Town
Jalandhar
2 October 20 ……….
The Editor
The Tribune
Chandigarh
Subject : The Evil of Begging Sir

Beggars have become a great nuisance these days. They pester people for alms in trains, buses, bazaars and streets. They shout curses if one refuses to listen to them.

No doubt, some beggars deserve our sympathy. They are handicapped. They are unable to earn their living. But the pity is that most of the beggars are able-bodied. Begging has become a profession for them. They find it the easiest way to earn their living. Some of them are criminals. They beg only to hide their crimes. This evil is a slur on the fair name of our country.

Begging should be abolished by law. It should be made a punishable offence. The govern¬ment should open asylums for those beggars who are really helpless. Able-bodied beggars should be forced to work. If they go without work, they must also go without food. We should have no sympathy for such impostors. We should not encourage them by giving alms. People can thus play a big role in eradicating this evil.

Yours truly
Rohit Verma

(26) For Change of Your Name

You are Jagmeet Dua living at 59, Rama Avenue, Jalandhar. You want to change your name. Write a letter to the Editor of a newspaper for change of name.

59 Rama Avenue
Jalandhar
24 Feburary 20 …….
The Editor
Jalandhar Times
Jalandhar
Sir

I have changed my name recently and I wish to announce it through the concerned column of your reputed weekly newspaper. I have enclosed the copy of the affidavit which I have for this purpose. I have also enclosed with this letter the required demand draff of Rs 500/- as the charges for publishing such intimations. The matter to be published reads : “Everybody should note that I, Jagmeet Dua S/o S. Harmeet Singh Dua, the resident of 59, Rama Avenue Jalandhar, have changed my name from Jagmeet Dua to Jagmeet Singh Dua. In future, I should be known by this name.”

Yours truly
Jagmeet Dua

(27) Requesting to Condone the Shortage of Lectures

Write an application to the Principal of your school, requesting him to condone the shortage of lectures in your case.

The Principal
B. C. M. School
Jalandhar
7 April 20 ……
Subject : Condoning the Shortage of Lectures Sir

With due respect, I wish to state that I am a student of class XI in your reputed school. My class teacher has told me that I am short of lectures. I do not have the habit of bunking my classes. As a matter of fact, my younger brother was seriously sick in the month of February. He was in hospital for two weeks. My father is posted far away in Nagaland as a B.S.F. jawan. He couldn’t get leave to reach home. There were only my mother and I left to look after him. Therefore, I had to miss classes for two weeks.

I have always been a bright student. I always top my class. I have participated in many cricket matches as a team member of the school cricket eleven and brought laurels to the school. I will study day and night to top the class again. You are very humbly requested to condone the shortage of lectures. I will be very obliged to you.

Thanking you
Yours obediently
Rohit Pahwa
XI-B

(28) For Some Changes in the School Library

Write an application to the Principal of your school, requesting him to make some effective changes in the school library.

The Principal
DAV Senior Secondary School
Phagwara
20 May 20 …….
Subject : Changes in the School Library Sir

I study in class XI-A of this school. I visit the library of the school very often. A good library is a part and parcel of a good school. But the condition of our school library puts me off. Books are not properly catalogued. Students have to face a lot of difficulty in finding the books of their choice. Magazines and journals are not subscribed to. Even there is no reading room.

The books should be properly catalogued The arrangement of books should be in the alphabetical manner Good magazines and journals should be subscribed to. The placement of books should be section-wise.

The suggestions given above will go a long way in making the visit to library a meaningful and pleasant experience.

Yours obediently
Deepak Sbarma

(29) Full Fee Concession

Write an application to the Principal of your school, requesting him to grant you full fee concession and also some help out of the Students’ Aid Fund.

The Principal
Govt. Senior Secondary School Ludhiana
20 August 20……..
Sir

I am a student of class XI of your school. My father is a poor man. He works as a peon in a local factory. He gets only Rs 7850 per month. He has a large family to support. We have no other source of income. It is very difficult for my father to meet the expenses of my education. He is too poor to pay my fees.

Sir, I am one of the good students of my class. I have always fared well in my examinations. I am in the good books of my professors. I take part in games also. I am a member of the college cricket eleven. Kindly grant me full fee concession as well as some help from the Students’ Aid Fund. I shall be highly thankful to you for this kindness.

Yours obediently
Raman Jeet
XI-A

(30) Requesting for Incorporation of Change of Name

Write an application to the Principal of your school for incorporation of change of name in the school records.

The Principal
Alpine International School
Civil City
Jalandhar
16 August 20 ……..
Subject : Incorporation of Change of Name in the School Records Sir

I want to state that I have changed my name. Earlier it was Harpreet Kaur. Now it is Harpreet Kaur Randhawa. This change of name has been published in all the leading newspapers including my Aadhaar Card. It is, hence, requested that this change be incorporated in the school records as well. I will be highly obliged.
Thanking in anticipation

Yours obediently
Harpreet Kaur
XI-A

Exercise From Grammar Book (Fully Solved)

(1) Complaining About The Use of Loudspeakers

Write a letter to the Deputy Commissioner of your district, complaining about the use of loudspeakers in your town.

15 Nehru Park
Patiala
18 March 20 ……..
The Deputy Commissioner
Patiala
Subject : Nuisance of Loudspeakers in the City Sir

The nuisance of loudspeakers in the city is increasing day by day. They are used indiscriminately during day as well as night. They are used in temples and gurdwaras. They are used on marriages, jagrans, meetings, rallies and all sorts of social, religious and other functions. Sometimes even shopkeepers put up loudspeakers to attract the customers and to boost their sales. And then there are street-criers who don’t let you have a moments rest. The poor students are the worst sufferers.

They find it difficult to concentrate on their studies with so much noise around. For the common man, too, the noise of loudspeakers is very jarring and harmful. The pollution due to noise is as harmful as the pollution of air and water. So, it is requested that some check must be put on the use of loudspeakers in the city so that the residents can get a calm and peaceful atmosphere to live in. It will be an act of philanthropy towards the city dwellers.

Yours respectfully
Rajiv

(2) Need of A Park for Children

Write a letter to the Deputy Commissioner of your district, requesting for a park for children in your city.

124 Model Town
Karnal
17 July 20 ………
The Deputy Commissioner
Karnal
Sir

It is a matter of regret that there is no park for children in our area Children have no proper place to play in. They play either in the streets or on the roadside. There always remains a danger of their being run over by some speeding vehicle. It is the duty of the civic authorities to look to this need of their tiny citizens.

Children have an inborn love of beauty and nature. They love flowers, trees, parks and gardens. This love of beautiful objects changes into a love of beautiful thoughts when they grow up. So we must provide our children with beautiful surroundings if we want them to grow into men and women of refined tastes. Parks are necessary from another point of view also. They add to the beauty of a town. Children can play there while the elders can refresh their weary minds. So, it is requested that at least one big park should be provided for children in our locality.

Thanking you
Yours faithfully
Vinay Chaudhry

(3) About the Loss of Your Bicycle

Write a letter to the S.H.O. of your area, reporting the loss of your bicycle.

16 Chander Nagar
Ludhiana
5 June 20 ……..
The Station House Officer
Police Station Civil Lines
Ludhiana
Sir

I beg to report the loss of my cycle in Kamla Market. I went into Khan Cloth House to make some purchases this afternoon. I locked my cycle. I placed it outside the shop. When I came out after about thirty minutes, I found my cycle missing. I enquired from several persons, but none could give me any clue.

Sir, mine is a Hero Cycle. It bears the number AKL 4125. It is black in colour. It is quite a new one. I bought it only last month.

I hope you will do your best to trace out my lost cycle. I shall feel highly obliged if you let me know as soon as you get any clue.
Thanking you in anticipation,

Yours faithfully
ABC

(4) About the Bad Condition of Buses

You are Meena. You live at 209, Sector 69, Mohali. Write a letter to the Editor of a newspaper, complaining about the bad condition of buses in Punjab.

H.No. 209
Sector 69
Mohali
15 February 20 …….
The Editor The Tribune Chandigarh
Subject : Bad Condition of Buses in Punjab Sir

I shifted my residence from Ambala, Haryana, about two years ago to the industrial hub of Punjab, Ludhiana. I am pained to see the pitiable state of buses run by the Punjab Roadways. I wish to voice by concern through the columns of your esteemed paper.

As was natural in my case, I was forced to compare the buses of Punjab with those of Haryana Roadways. The buses here are in a very bad shape. They make too much noise while creeping on the road. In just too many cases, the passengers are told to get off at some desolate place because of breakdown. The behaviour of running staff towards public calls for a complete overhaul. The bus shelters are in a very bad state, if at all they exist somewhere. A friend of mine was informed through his RTI petition that there were 450 buses grounded in Ludhiana workshop alone as on 20 January, 20 ……..

I do fondly hope that these few lines will wake the concerned authorities from their deep slumber. A sense of duty and strong willpower on their part can do wonders.

Yours truly
Meena

(5) About Reckless Driving

You are Suman. You live at 119, Sector-70, Mohali. Write a letter to the Editor of a newspa-per, expressing your views on the reckless driving.

119 Sector-70
Mohali
2 May 20 …….
The Editor
The Hindustan Times
New Delhi
Sir

Rash driving has become very common these days, especially among the youth. As a result, accidents have become almost a matter of daily occurrence. We often see young guys zooming through the streets on their motorbikes. They drive at a reckless speed with no regard to their own safety or that of others. This dangerous practice has already claimed the lives of several innocent children of the town. There are traffic rules, no doubt, but they are hardly ever followed. People are not educated about these rules and they break them unknowingly. But even those who know the rules, more often break them than follow them. We often see motorists jumping the red lights. Heavy and deterrent fines should be imposed on such people.

It is also important that people should be educated about the need of safe driving. They should be told that speed no doubt thrills, but it kills also. The best course would be to raise the penalty for overspeeding. The driving licences of persistent offenders should be impounded.

Yours truly
Suman

(6) For A Testimonial

Suppose you are Mandeep Randhawa. You live at 1802, Main Bazar Abohar. Write a letter to your Principal, requesting him to issue your testimonial / character certificate.

1802 Main Bazar
Abohar
15 July 20 …….
The Principal
Govt. Girls Senior Secondary School
Main Bazar
Abohar
Subject : Request for a Testimonial / Character Certificate.
Sir

I was a student of your school for five years, from 20 …… to 20 ……, and cleared the Senior Secondary Examination held in March 20 …….., under roll no. 56372, securing first division.

During my days in your school, I participated in various curricular and co-curricular activities. Many a time, I won prizes also for my meritorious performance. I was a member of school’s N.C.C. unit and attended two annual camps also. As a member of the school cricket team, I participated in the inter-school district tournament and fared well as a batsman.

I now intend to join PEC University of Technology, Chandigarh, and for that I need a testimonial / character certificate. Kindly issue me the same and oblige.
Thanking you

Yours obediently
Mandeep Randhawa

(7) Complaining About the Insanitary Conditions

Imagine you are Mohan. You live at 83, Doon Valley Dehradun. Write a letter to the Commissioner of your Municipal Corporation, complaining about the insanitary conditions in your locality.

83 Doon Valley
Dehradun
10 April 20 ……..
The Commissioner
Municipal Corporation .
Dehradun
Subject : Insanitary Conditions in Our Locality
Sir

I beg to draw your attention to the insanitary conditions of our locality, Model Town. It has been my unhappy lot to live in this area for the last few months.

Mainly poor people live in this area. Perhaps that is why no Sanitary Inspector has ever visited it. There are very few proper drains here. These drains are not cleaned regularly. They are never flushed with water. No dustbins have been provided. People throw all their refuse here and there. Flies and mosquitoes buzz about. All this gives this area a very dirty look.

I hope you will realize our difficulty. You are requested to take suitable measures to improve the sanitary conditions of this area.
Thanking you in anticipation

Yours faithfully
Mohan

(8) About The Evil of Eve-Teasing and Chain-Snatching

You are Amab. You live at House No. 92, Model Town, Moga. Write a letter to the Editor of a newspaper, highlighting the evil of eve-teasing and chain-snatching.

92 Model Town
Moga
26 June 20……
The Editor
The Tribune
Chandigarh
Sir

There has been an alarming rise in the incidents of chain-snatching and eve-teasing in our area during the past few days. There is hardly any day when one such incident doesn’t take place. The press, too, has reported about it. All cases are duly brought to the notice of the police officials of the area. But sadly, no suitable steps have been taken to nab the culprits. Now people have begun to point an accusing finger at the police also. Through the columns of your newspaper, I request the authorities concerned that some effective steps be taken immediately so that the residents, and especially the girls, can move about without any sense of fear.

Yours truly
Arnab

(9) Need of Opening A Library

Imagine you are Manjit. You live at 101, New Town, Mohali. Write a letter to the Mayor of your town, stressing the need for a public library in your town.

House No. 101
New Town
Mohali
15 April 20 ………
The Mayor
Municipal Corporation Mohali
Subject : Opening a Public Library in Our Town
Sir

Our town was designed to be a replica of Chandigarh many years ago. Today, it has blossomed into a developed city in its own right. Being in close proximity with Chandigarh, it is now inhabited by people who are not only educated, but they also wish to increase their knowledge.
It is, indeed, a pity that there is no library for the use of public. Everybody cannot afford to buy magazines and newspapers for themselves. Moreover, there is no good bookshop in this small town. So, the people remain out of touch with current affairs. Their knowledge cannot be kept up to date.

The Municipal Corporation has not so far given any attention to this need. The absence of a public library does not do justice to the fair name of this town.

The population of Mohali will ever remain grateful to you if their long-standing desire is fulfilled.

I hope that you will graciously use your good offices to persuade authorities to open a public library in our town.

Yours faithfully
Manjit

(10) Indiscipline Among the Students

Imagine you are Aman. Write a letter to the Editor of a newspaper, highlighting the causes of indiscipline among the students.

15 Adarsh Nagar
Karnal
18 May 20 ………..
The Editor
The Hindustan Times
New Delhi
Sir

Colleges and universities were once thought to be the temples of learning. Students used to go there for higher studies. They pursued their studies seriously and wholeheartedly. But mod¬ern students have profaned the sanctity of these temples. They have defiled their atmosphere. Students indulge in acts of violence and indiscipline. Politics has become a plaything for them. They take part in politics without knowing what they are driving at.

Corrupt and unscrupulous politicians are the root cause of indiscipline in our colleges and universities. They lead the innocent students astray in order to gain their selfish ends. They instigate the students to create problems of law ana order. Most of the strikes in our colleges and universities are the acts of hired politicians. It is the duty of teachers and parents to keep the students on the right path. They should caution the students about the evil designs of politicians.

Yours truly
Aman

(11) About the Loss of Your Motorcycle

You are Rimpy. You live at House No. 65, Model Gram, Ludhiana. Write a letter to the S.H.O. of your area, reporting the loss of your motorcycle.

65 Model Gram
Ludhiana
5 June 20 ……
The Station House Officer
Model Gram Police Station
Ludhiana
Sir

I am writing this letter to lodge an FIR about my motorcycle that has been stolen. Last night after coming home from my office, I parked my motorcycle outside the house. When I got up this morning, I found my motorcycle missing. I asked all my neighbours, but no one could give me any clue about it.

It is Hero Honda Passion Plus of the 2009 model. It is of red colour and the registration po. is PB10-AB0320. I hope on the basis of the given information, you could help me trace my motorcycle at your earliest.

Thanking you in anticipation
Yours faithfully
Rimpy

(12) Asking For The Replacement Of Defective Goods

You are Bhiwani. You live at House No. 29, Teachers’ Enclave, Kapurthala. Write a letter to a firm, complaining that the goods sent by it were defective and ask for a free replacement.

29 Teachers’ Enclave
Kapurthala
13 April 20……
Messrs Ram Nath & Sons
Daryaganj
New Delhi
Subject : Replacement of Defective Printers Dear
Sirs

The two HP printers that I had ordered for on 5th March were delivered yesterday, but I regret to inform you that one of them has been found badly damaged. The carton containing the printer appeared to be in a perfect condition. Therefore, I accepted the delivery and signed for it. I unpacked the printers myself with great care. I can only say that the damage must have been caused due to careless handling prior to packing. It is requested that the damaged printer should be replaced at your cost.

Yours faithfully
Bhiwani

(13) Applying for the Job of Sales Manager

Suppose you are Pari. You live at House No. 101, Subhash Colony, Jalandhar. Write a letter to the General Manager of a firm to appoint you as Sales Manager.

101 Subhash Colony
Jalandhar
27 July 20 ……..
The General Manager
New World Publication Ludhiana
Subject : Appointment as Sales Manager
Dear Sir

I am writing to you to apply for the post of Sales Manager in your establishment. It is in response to your advertisement in The Pioneer dated 22 July, 20…… . After doing my MBA from Punjabi University, Patiala, I worked for two years with K.K. and Sons, Jalandhar, a well-known company for the publication of school and college books. Presently, I am working with UBS Publishers, Delhi, as their Sales Manager. I am well-acquainted with the market and am personally known to many bigwigs in this field.

I would welcome the chance of being a part of your establishment and I am confident I shall be able to boost your sales backed by my abilities and vast experience. I shall be available for an interview any day next week. I am looking forward to hearing from you.

Yours faithfully
Pari

(14) About the Flood Situation in Your Area

Suppose you are Babita. Write a letter to the Deputy Commissioner of your district, about the flood situation in your area.

H.No. 235
Preet Vihar
Ludhiana
The Deputy Commissioner
Ludhiana
Subject : Flood Situation in Our Area
Sir

The recent floods have made the life of the people in our area miserable. Our area is a low-lying area, so the water from the adjoining localities also collects here in every rainy season. The elderly people can’t go for a walk in the morning and evening. Little children find it nightmarish to go to their schools. The buses meant for conveying them don’t come to our area due to waterlogging. Housewives cannot go for shopping for their day-to-day needs. Thus people of all ages and spheres have to suffer.

Every year, the same thing happens with a clockwork regularity. Some show of action is shown when rains set in, and people are assured of some permanent measures to be taken. But noth¬ing is done and with the end of the rainy season, all assurances are thrown to the winds.We request you, sir, to do the needful for the present calamity which has gripped the residents.
Thanking you in anticipation

Yours faithfully
Babita

(15) For The Remission of Fine

You are Sarita. Your address is 156, Kaarvan Apartments, Sector 11, Panipat. Write an application to the Principal of your school, requesting him for the remission of fine.

The Principal
Rama Senior Secondary School
Panipat
18 March 20 ……
Sir

Our English teacher gave us a test on Monday. That day, I was suffering from high fever. So I could not take the test. The teacher fined me fifty rupees.

I am a good student. I wanted to take the test. I had also done full preparation for the test. But I was helpless. Kindly remit my fine. I shall be thankful to you for this kindness.6

Yours obediently
Sarita
Class – XI – C

(16) Complaing About the Frequent Breakdown of Electricity

You are Himalaya. You live at 118, Motia Apartments, Khanna. Write a letter to the S.D.O. (Electricity), against frequent breakdown of electricity in your locality.

118 Motia Apartments
Khanna
6 June 20 ……..
The S.D.O. (Electricity)
P.S.P.C.L.
Khanna
Subject : Frequent Breakdown of Electricity in Our Area
Sir

I regret to inform your honour about the frequent breakdown of electricity for the last about three months in this part of the town. In these hot months, it becomes unbearable to do without electric power for even a few minutes. But you can imagine the lot of people when they have to go without it for the whole day and night. When enquiries are made from the nearest station, no satisfactory answer is given. Residents are put off with vague replies.

The officials concerned are also very rude and indifferent to the difficulty of the residents. Poor students are the worst sufferers. The examinations are drawing near. Without proper power supply, it becomes almost impossible for them to study. It is requested that continuous power supply should be ensured so that the residents have not to suffer.

Yours faithfully
Himalaya

(17) Wishing Good Health to Your Friend on His Recovery From Illness

Suppose you are Hannan. Write a letter to your friend who has recovered from dengue and wish him good health.

88/4 Model Town
Jalandhar
29 March 20 ……..
My dear Manjit

I am very glad to learn that you have recovered from dengue. I heartily congratulate you on your recovery. I was much distressed when I heard that you were down with dengue. Thank God that you have got well. The happy news of your recovery has given me immense joy.

Please take complete rest for some days more. Be very careful about cleanliness around you. Follow the advice of your doctor. I will come to see you soon.
With best wishes

Yours sincerely
Harman

(18) About An Educational Tour

\bu are Prem. You live at 11, Kamla Nagar, New Delhi. Write a letter to your friend, Mahipal, sharing your experiences of an educational tour you have recently made to places in south India.

11 Kamla Nagar
New Delhi
15 May 20 ……..
My dear Mahipal

You may probably know about one tradition of our school. Our school arranges educational trips to different parts of the country about every six months. They prove very useful to us. We come to know about our country and its people in a better light.

Last month, our class was taken to places in south India. We travelled by train. A compart¬ment had been reserved for us. Our first stop was at Hyderabad. It is the capital ofTelangana and its history is very rich. The trips to Nizams palace and Charminar were very informative and enjoyable. We also visited some other monuments of historical importance.

From there, we went to Bengaluru. There we saw the famous Vidhana Saudha (Vidhan Sabha), whose architecture is superb. We were also taken on the guided tour of Bharat Electronics, Hindustan Aeronautics Limited and Hindustan Machine Tools. We were filled with pride to see that we were steadily but surely marching forward to become a really developed nation.

Our last destination was Chennai. We visited the famous temples of Dravida culture there. We were also taken around some big modern factories there.

On coming back to Delhi, we were asked to give short lectures on what we had learned from our educational tour. Such tours are a veritable blessing for the student community. Now I am looking forward to our next trip.

Yours affectionately
Prem

(19) About Joining Indian Army as A Commissioned Officer

Suppose you are Harneet. You live at 110, Sector 72, Mohali. Write a letter to your uncle, who is an Ex-Army Officer, asking for details about the various options about joining Indian Army as a Commissioned Officer.

H.No. 110
Sector 72
Mohali
10 June 20 …….
Dear Uncle

I was born in a businessman’s family and since then, I have been enjoying a rather comfortable life. My father naturally wanted me to join him in his venture. He also gave me the option of starting a new venture of my liking, if I so desired.

But for some reason, I have never desired to become a businessman. I have always dreamt of becoming a Commissioned Officer like you. I have always looked upon you as my role model. I strongly yearn for an adventurous life. For this reason, I wish to join our country’s glorious army. While serving in the army, I will have many avenues to serve my motherland also.

Dear uncle, I implore you to guide me how I can satisfy my desire to become a Commis¬sioned Officer. I am soon to appear for the final of 10+2. I seek your guidance in deciding what course I must join after my 10+2. I will be equally interested in the infantry, admin¬istrative or technical branch of the army. As you know me quite well, you can guide me about which branch will suit my lifestyle and temperament. You can also decide then which branch of studies I should opt to fulfil my ambition.
I hope to hear from you soon.

Yours affectionately
Harneet

(20) About The Non-Payment Of Interest On The Deposited Amount

Write a letter to your bank manager regarding the non-payment of interest on an amount you have deposited in your account.

112 New Colony
Civil Lines
Dreamland
17 March 20 ……..
The Manager
The Progressive Bank
Model Town
Dreamland
Subject : Non-payment of Interest on the Deposited Amount
Dear Sir

I have a Savings Bank account No. 1234524567 with your branch. I opened the said account about 9 years back and since then, I have been largely satisfied with the services offered by you.

About a year ago, my grandfather, a big businessman of our city, passed away. After his property and cash were devided among the legal heirs, I recieved Rs 5 lakh as my share. I deposited the entire amount in my above savings account.

On going through the passbook, made up-to-date last week, 1 find that there is no entry showing the interest accrued on the said amount of deposit. On phoning up the accoun¬tant, I could not get any satisfactory reply from him.

I request you to kindly look into the case and take suitable action to credit the due interest into my account.
Thanking you in anticipation, I am

Yours faithfully
PQR

Letter-Writing Tasks for Practice

1. You are Rohit Bajaj, living at A-10, MIG Flats, Manali. Many telephones of your area have been dead for the last three months in spite of several complaints. Write a lettel to the Area Manager, Telephone Nigam Ltd., requesting him to get this serious fault rectified.
2. You are Rajan Mishra, living at D-203, College Road, Mandi. The footpaths of this place are being occupied by cycle dealers and transporters. Write a letter to the Municipal Commissioner, Mandi, requesting him to get the footpaths cleared.
3. Write a letter to the editor of a newspaper, expressing your concern about the ‘Problem of Unemployment in India’. Suggest some remedial measures.
4.. Write a letter to the Postmaster, General Post Office, Shimla, complaining about the late delivery of letters. You are Megh Hans of 29, Hans Niwas, New Shimla.
5. Write a letter to the President, Municipal Corporation of your city, informing him about the poor condition of roads and street in your locality. Sign yourself as Raman / Radha.
6 Write a letter to your friend, requesting him / her to spend summer vacation with you in Shimla. Sign yourself as Anita / Amit from Bilaspur, H.P.

Punjab State Board PSEB 10th Class Maths Book Solutions Chapter 12 Areas Related to Circles Ex 12.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2

Question 1.
Find the area of sector of a circle with radius 6 cm, if angle of the sector is 60°.
Solution:
Radius of sector of circle (R) = 6 cm

Central angle (θ) = 60°
Area of sector = \(\frac{\pi \mathrm{R}^{2} \theta}{360}\)

= \(\frac{22}{7} \times \frac{6 \times 6 \times 60}{360}\)

= \(\frac{132}{7}\) cm²
∴ Area of sector = 18.86 cm².

Question 2.
Find the area of a quadrant of a circle whose circumference is 22 cm.
Solution:
Circumference of circle = 22 cm
2πR = 22
R = \(\frac{22 \times 7}{2 \times 22}=\frac{7}{2}\) cm
R = \([latex]\frac{7}{2}\)[/latex] cm
Central angle [quadrant] (θ) = 90°
∴ Area of a quadrant = \(\frac{\pi \mathrm{R}^{2} \theta}{360}=\frac{\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 90}{360}\)

= \(\frac{77}{8}\)

Area of quadrant = 9.625 cm².

Question 3.
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Solution:
Length of minute hand of clock = Radius of circle (R) = 14 cm

We know that
60’ = 360°
1’ = \(\frac{360^{\circ}}{60}\) = 6°
5′ = 60 × 5 = 30°
Angle of sector (θ) = 30°
∴ Area swept by minute hand in 5 minutes = \(\frac{\pi R^{2} \theta}{360}\)

= \(\frac{22}{7} \times 14 \times 14 \times \frac{30}{360}\)

= \(\frac{1}{12}\) × 22 × 28 = \(\frac{154}{3}\) cm².

Hence, area swept by minute hand in 5 minutes is 5133 cm².

Question 4.
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:
(i) minor segment
(ii) major sector.
Solution:
Radius of circle (R) = 10 cm
Central angle (θ) = 90°

(i) Area of minor sector = \(\frac{\pi R^{2} \theta}{360}\)

= 3.14 × 10 × 10 × \(\frac{90}{360}\)

Area of minor sector = \(\frac{314}{4}\) = 78.5 cm²
Area of minor segment = Area of minor sector – Area of MOB
= 78.5 – \(\frac{1}{2}\) Base × Altitude
= 78.5 – \(\frac{1}{2}\) × 10 × 10
= 78.5 – 50 = 28.5
∴ Area of minor segment = 28.5 cm²

(ii) Area of major sector = \(\frac{(360-\theta)}{360}\)
= \(\frac{(360-90)}{360}\) × 3.14 × 10 × 10
= \(\frac{270}{360}\) × 3.14 × 100
= \(\frac{3 \times 314}{4}=\frac{3 \times 157}{2}\)
∴ Area of major sector 235.5 cm².

Question 5.
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
(j) the length of the arc
(ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
Solution:
(i) Radius of circle (R) 21 cm

Central angle(θ) = 60°
Length of arc = \(\frac{\theta}{360}\) × 2πR
= \(\frac{60}{360} \times 2 \times \frac{22}{7} \times 21\) = 22 cm
Hence, length of arc = 22 cm.

(ii) Area of sector formed by arc = \(\)
= \(\frac{22}{7} \times \frac{21 \times 21 \times 60}{360}\)
Area of sector = 231 cm²
∴ Since ∆OAB is equilateral triangle, θ = 60°.

(iii) Area of segment = Area of sector – Area of ∆AOB
= \(\frac{\pi R^{2} \theta}{360}-\frac{\sqrt{3}}{4}(\text { side })^{2}\)
= 231 – \(\frac{1.73}{4}\) × 21 × 21
= 231 – 0.4325 × 441
= 231 – 190.7325
Area of segment = 40.26 cm².

Question 6.
A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
Solution:
Radius of circle = (R) = 15 cm
Central angle (θ) = 60°

In ∆OAB, central angle θ = 60°
OA = OB = 15 cm
∴ ∠A = ∠B
Now, ∠A + ∠B + ∠O = 180°
2∠A ÷ 600 = 180°
∠A = 60°
∴ ∠A = ∠B = 60
∴ ∠OAB is equilateral.
[ Area of minor segment] = [Area of minor sector] – [Area of equilateral triangle]

= \(\frac{\pi R^{2} \theta}{360}-\frac{\sqrt{3}}{4}(\text { side })^{2}\)

= 3.14 × \(\frac{15 \times 15 \times 60}{360}-\frac{1.73}{4} \times(15)^{2}\)

= 15 × 15 \(\left[\frac{3.14 \times 60}{360}-\frac{1.73}{4}\right]\)

= \(\frac{225}{100}\left[\frac{314}{6}-\frac{173}{4}\right]\)

= \(\frac{225}{100}\) [52.33 – 43.25]

= \(\frac{225}{100}\) × 9.08

= \(\frac{2043}{100}\) = 20.43 cm²

Area of minor segment = 20.43 cm².
Area of major segment = Area of circle – Area of major segment.
= πR² – 20.43
= 3.14 × 15 × 15 – 20.43
= 706.5 – 20.43
= 686.07 cm²
Area of major segment = 686.07 cm².

Question 7.
A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use it π = 3.14 and √3 = 1.73).
Solution:
Radius of circle (R) = 12 cm
Central angle (θ) = 120°

In ∆OAM, from O draw, angle bisector of ∠AOB as well as perpendicular bisector OM of AB.
∴ AM = MB = \(\frac{1}{2}\) AB
In ∆OMA,
∠AOM + ∠OMA + ∠OAM = 180°
LOAM = 30°
Similarly, ∠OAM = 30° = ∠OBM

AB = 2AM
= 2 \(\left(\frac{\mathrm{AM}}{\mathrm{OA}}\right)\) OA
= 2 (sin 60°) 12
AB = 2 × \(\frac{\sqrt{3}}{2}\) × 12 = 12√3 cm
OM = OA \(\left(\frac{O M}{O A}\right)\) = 12 (cos 60°)
= 12 × \(\frac{1}{2}\) = 6 cm
Area of the segment = Area of sector – Area of ∆OAB.
Area of segment = \(\frac{\pi R^{2} \theta}{360^{\circ}}-\frac{1}{2} A B \times O M\)

= \(\frac{3.14 \times 12 \times 12 \times 120}{360}\) – \(\frac{1}{2}\) × 12√3 × 6

= \(\frac{314}{100} \times \frac{144 \times 120}{360}\) – 36√3
= 150.72 – 36 × 1.73
= (150.72 – 62.28) cm²
= 88.44 cm²
∴ Area of the segment = 88.44 cm².

Question 8.
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see fig.). Find:
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m (Use π = 3.14).

Solution:
Side of square = 15 m
(i) Length of Peg = Radius of rope (R) = 5 m
Centrral angle (θ) = 90° [Each angle of square]

Area of sector = \(\frac{\pi R^{2} \theta}{360}\)

= \(\frac{3.14 \times 5 \times 5 \times 90}{360}\)

Area of sector = \(\frac{3.14 \times 25}{4}=\frac{78.5}{4}\) m².
= 19.625 m²

(ii) When radius of sector increased to 10 m
Radius of sector OCD (R₁) = 10 m
Central angle (θ) = 90°
∴ Area of sector OCD = \(\frac{\pi R_{1}^{2} \theta}{360^{\circ}}\)

= \(\frac{3.14 \times 10 \times 10 \times 90}{360^{\circ}}\)

= \(\frac{314}{100} \times \frac{100 \times 90}{360^{\circ}}\)

= \(\frac{314}{4}\) = 78.5 m

∴ Increase in grazing area = Area of sector OCD – Area of sector OAB
= 78.5 – 19.625 = 58.875 m²
Increase of grazing area = 58.875 m²

Question 9.
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown In fig. Find:
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.

Solution:
Diameter of circle (D) = 35 mm
Radius of circle (R) = \(\frac{35}{2}\) mm
Number of diameter = 5
Number of equal sector = 10

(i) Wire used = Length of 5 diameters + circumference of circle (brooch) = 5(35) + 2πR
= 175 + 2 × \(\frac{22}{7}\) × \(\frac{35}{2}\)
= 175 + 110 = 285 mm

(ii) Sector angle of brooch = \(\frac{360^{\circ}}{\text { Number of sector }}\)
= \(\frac{360^{\circ}}{10}\) = 36°
Area of each brooch (Area of sector) = \(\frac{\pi R^{2} \theta}{360^{\circ}}\)

= \(\frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} \times \frac{36}{360}\)

= \(\frac{11 \times 35}{4}=\frac{385}{4}\) mm² = 96.25 mm²

∴ Area of each brooch = 96.25 m².

Question 10.
An umbrella has 8 ribs which are equally spaced (see fig). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Solution:
Radius of circle = 45 cm
Number of ribs = 8
Central angle (sector angle) = \(\frac{360^{\circ}}{8}\) = 45°
Area of sector = \(\frac{\pi R^{2} \theta}{360^{\circ}}\)

= \(\frac{45}{360^{\circ}} \times \frac{22}{7} \times 45 \times 45\)

= \(\frac{1}{8} \times \frac{22}{7} \times 45 \times 45\)

= \(\frac{22275}{28}\) cm²

Area of sector = 795.53 cm²
∴ Area between two consecutive ribs of the umbrella = 795.53 cm².

Question 11.
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
Solution:
Length of blade (R) = 25 cm
Sector angle (θ) = 115°
Wiper moves in form of sector.

Area of sector = Area çovered by one blade
= \(\frac{\pi \mathrm{R}^{2} \theta}{360^{\circ}}\)

= \(\frac{22}{7} \times \frac{115}{360} \times 25 \times 25=\frac{316250}{504}\)

= 627.48 cm²
Area covered by two blades of wiper = 2 Area of sector
= 2 × 627.48 = 1254.96 cm².

Question 12.
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 800 to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use x = 3.14)
Solution:
Sector angle (θ) = 80°
Radius of sector (R) = 16.5 km

Area of sea over which the ships are warned
Area of sector = \(\frac{\pi R^{2} \theta}{360^{\circ}}\)

= \(\frac{3.14 \times 16.5 \times 16.5 \times 80}{360}\)
= 189.97 km²
Area of sea over which the ships are warned = 189.97 km².

Question 13.
A round table cover has six equal designs as shown in fig. 1f the radius of the cover is 28 cm, find the cost of making the designs at the rate of 0.35 per cm². (Use √3 = 1.7)
Solution:
Number of equal designs = 6
Radius of designs (R) = 28 cm
Each design is in the shape of sector central angle (θ) = 6 = 60°

Since central angle is 60° and OA = OB
∴ ∆OAB is equilateral triangle having side 28 cm.

Area of one shaded designed portion = area of segment = Area of the sector OAB – area of ∆OAB
= \(\frac{\pi R^{2} \theta}{360^{\circ}}-\frac{\sqrt{3}}{4}(\text { side })^{2}\)

= \(\frac{22}{7} \times \frac{28 \times 28}{360^{\circ}} \times 60^{\circ}-\frac{1.7}{4} \times 28 \times 28\)
= 410.66 – 333.2 = 77.46.

Area of one shaded designed portion = 77.46
Area of six designed portions = 6 [Area of one designed]
= 6 [77.46] = 464.76 cm²
Cost of making 1 cm² = ₹ 0.35
Cost of making of 464.76 cm² = 464.76 × 0.35 = ₹ 162.68.

Question 14.
Tick the correct answer in the following:
Area of a sector of angle p° of a circle with radius R is
(A) \(\frac{p}{180}\) × 2πR
(B) \(\frac{p}{180}\) × πR²
(C) \(\frac{p}{360}\) × 2πR
(D) \(\frac{p}{720}\) × 2πR²
Solution:
Angle of sector (θ) = p°
Radius of circle = R
Area of sector = \(\frac{\pi \mathrm{R}^{2} \theta}{360}\)

= \(\frac{\pi \mathrm{R}^{2} \times p^{\circ}}{360}\)

= \(\frac{p^{\circ}}{720}\) × 2πR²
∴ Correct option is (D).