ENGLISH Paper – 1  

Q.1 (Do not spend more than 30 minutes on this question.)  

Write a composition (300 – 350 words) on any one of the following: 

(a) Write an original short story in which two children and their Grandfather are  the main characters.  

(b) Closed Circuit Television (CCTV) must be installed in every class room. Give your views either for or against this statement. 

(c) Your class had to conduct a Morning Assembly. Write an account of how you  prepared for it, what your role was and what you gained from the experience. 

(d) Summers are becoming hotter with each passing year. Write a description of  one such very hot day. What did you see and hear as you walked outside?  How were birds and animals affected?  

(e) Study the picture given below. Write a story or a description or an account of  what it suggests to you. Your composition may be about the subject of the  picture or you may take suggestions from it; however, there must be a clear  connection between the picture and your composition.  

Answer :

(a) Ramesh and Sneha were the siblings aged twelve and nine. They had . been taught to defend themselves in any eventuality. One evening on a Saturday, they were alone at home doing their home work. Their grandfather had gone for his daily evening walk. All of a sudden there was a sudden and threatening knock on the gate. But as they were fully occupied with their studies, they did not entertain any fear. But when the door was rapped repeatedly, Ramesh felt that there was someone outside asking them to open the door.

But before the grandfather left, he had forewarned his grandchildren against such occurrence. Ramesh being quite smart and alert, rang up his grandfather quietly telling of the gate being knocked. Sneha was a bit scared, but Ramesh cheered her up saying that Grandfather had been informed of this and that he would come surely and take all the steps necessary for their welfare and safety.

Grandfather who had not gone very far off was still in the park. As soon as he received the phone call from his grandson Ramesh, he talked for a second with his friend! He lost no time to reach his residence. But the knockers or miscreants no sooner did they see the two men walking towards them than they began to take to their heels. Grandfather who had taken all the preemptive steps proved the better of the miscreants, as he had also informed the nearby police station of the regular nuisance being created in the surroundings.

The two constables seemed to come from nowhere and they pounced upon the feeling trouble makers who were taken to the police station for interrogation and follow-up action. Grandfather entered the house and found Sneha deeply disturbed. He consoled her and applauded Ramesh for his alertness and presence of mind in dealing with the tense situation. Ramesh’s parents who were away to attend some official function in another city on hearing this felt proud of their son who always showed fearlessness and courage in any trying situation.

(b) For the statement Installing closed circuit television in every classroom is going to be a ‘ powerful instrument to keep proper decorum and discipline in a school or college classroom. It is argued in favour of this that when the students and the teachers0are being closely watched through CCTV’s being monitored by the, head of the institution the desired results will be positive and concrete. No, doubt there is going to be a huge clamour against this move.

Some will, surely protest against installing CCTV’s on the ground that their liberties of expression and movement are going to be thwarted, others will oppose the move thinking that they are being pried upon unnecessarily. But it is not difficult to set aside their arguments taking into consideration the overall good results that will ensue by installing this device of closely watching the activities and atmosphere in the classroom.

The device will prove a big boon to the authorities. The head of the institution will feel surely less burdened with cases of indiscipline if he is in a position to monitor each classroom through this device. There is rampant indiscipline in our institutions. Schools and colleges witness widespread rowdyism and hooliganism on account of the restlessness among students and dissatisfaction of the teachers.

Students bunk classes and stray into nearby refreshment houses, canteens or cinema halls. Restlessness is writ large on many a face. If we wish to create proper study atmosphere in our classrooms and want to see our students and teachers do their primary job sincerely, we can hope to attain a great deal by installing the closed circuit televisions.

Not only will it give a healthy look to the classroom by keeping everything spick and span, it will also help find out the wrong doer and no innocent person will be ever punished since the footage will make out the things clearer. Thus installing closed circuit television in each classroom will have so many advantages that many disadvantage will weigh too light and look insignificant.

(c) Conducting a morning assembly in a school is an enrichening experience in leadership and gaining administrative skills. It is an experience that must be gained to develop one’s all round personality. A morning assembly in an institution gives ample scope to a student to keep himself fully acquainted with the school activities and to have interaction with a number of fellow students and a galaxy of teachers.

Last Friday, the Dean of Students Council called me to his office and asked me to take the responsibility of holding the morning assembly of the school on the occasion of the Republic Day celebrations in the school. I was also instructed to seek help of the deputy dean and the head boy of the school. Though at first I did not feel thrilled at the idea, yet on second thought I felt that it was an opportunity given to me to show my acumen in organizing big functions.

At once I got set to work to make it really eventful and memorable. Surinder, my trusted close friend, on learning this volunteered himself to render me every possible help in this, connection. Seeking help from another artist friend. Mr Sunil I got prepared some posters showing importance of the Day. The deputy dean was duly consulted and on taking his nod I prepared the programme to be executed on the day.

The students and the teachers gathered in the open on the appointed day. I had prepared my speech to be made on the occasion. In my speech I welcomed all the students and spoke that we all should be indebted to the freedom fighters whose long and painful struggle won us our freedom. I also highlighted the importance of the Republic Day that we celebrate on 26th January every year. My speech was highly cheered with clappings.

The deputy dean also spoke, laying stress on preservering our freedom and discharging our duties sincerely and doing nothing which may bring a slur on the fair name of the country. All the gathered listened to him with rapt attention. Then a vow was taken by the gathered assembly that we would keep our heads high and spirits cheerful for the upliftment of the country.

This experience of holding the morning assembly was challenging but rewarding. This has stilled confidence in me and enhanced my organizational capabilities. The experience has taught me the value of interacting with fellow students. With open mind and the spirit of cooperation anything can be achieved.

(d) Summers are getting hotter with each passing year. The effect of the climate change is being felt all around. Inspite of so many facilities with which to fight the scorching heat during summer, the heat of the season continues to torment the people, the poor being hit the worst. This year, the 6th of June was regarded as the hottest day of the year. The vertical rays of the sun began to be felt soon after the morning. It was close. At noon, it was almost impossible to go out of doors. Lemonade and other cold drinks failed to quench thirst.

We had hardly finished our lunch when the power broke down. I had planned to have a nap after lunch. Even this was snatched due to the failure of our inverter. I was feeling agitated and upset when my uncle dropped in unexpectedly. Though we welcomed him yet the unbearable heat of the sun was oppressing our nerves so acutely that somehow our inner irritability at the power breakdown betrayed itself. My mother asked me to go to the market to bring some household items for the kitchen.

Willy nilly I had to go out. I took an umbrella to protect myself from sunstroke. As I was moving about, I found some poor rickshaw pullers carrying their load, sweating hard. As I looked towards the fields, the cows and buffaloes were equally disquiet due to extreme heat from which there appeared no respite. The birds in the trees were also quiet.

It took me half an hour to complete my errand. I had to take water twice on the way as my lips were getting dry. When I reached home at about 4 pm I felt a sigh of relief because the conditions outside were much worse than inside. I sat down to relax when all of a sudden the sky was overcast with the clouds of dust. Evidently the dust storm was making its appearance.

Soon it began to blow so hard that we had to close all doors and windows to keep the dust out. It was suffocating inside. The dust storm died down in about fifteen minutes, leaving the dust setling on everything and every being. But thank God, the power was restored and we could have the fans and coolers giving us much needed relief. Such hot days leave their indelible imprint on men, animals and birds.

(e) A school excursion to a nearby lake was arranged to acquaint the students with the flora and fauna of the area. It being an educational trip it was accompanied by the geography teacher who could explain to them the importance of preserving ecology and wildlife. The trip comprised ten boys and girls of 7th and 8th classes. Putting on their school uniforms, they reached their destination in about half an hour.

Their first halt was at a shop dealing in snacks, toys and stationery. Aerated drinks and confectionery fascinated them the most. Mr Sardana, the accompanying teacher, prevailed upon them to avoid any soft drinks or toffees as they are not good for health. The sound advice of the teacher was taken earnestly by the students. Taking a few eatables, they all proceeded to move towards an enclosure where were some birds of different species.

Birds of different hues and sizes uttering varying cries cast a spell on them. The teacher explained to them that man’s greed and cruelty has resulted in the depletion of birds population. Some of the birds were really on the verge of extinction. He stressed upon the need to be kind to all birds and animals and the real worth of life is realized when man learns to live in harmony with nature. All the students appreciated the views of the teacher and took a vow to follow his advice and treat all birds with love and kindness. Aakriti, the most sensitive of them all, resolved that she would feed the birds daily and persuade her parents to do the same too.

Abhinav, the youngest of the lot, was sobbing. When asked why he was sobbing, he told his teacher that he had left his eatables at the shop. The teacher Mr Sardana consoled him that he should not worry and that all of them would share their things with him and they would pick up the eatables as they go back.

Kalpana, the student of 7th class, was found, eating a burger stealthily. She had brought it with her as she took it daily at lunch. The teacher suggested her to avoid eating fast food too frequently. One might take it only occasionally. But one must avoid eating fast food. The excursion was over in about four hours and they returned home in the evening fully refreshed and enlightened about so many things.


Q. 2 (Do not spend more than 20 minutes on this question.)  

Select any one of the following:  

(a) You want to start a new club in your school. 

Write a letter to your Principal requesting permission to start the club, explain  your role in it and give reasons to prove that the club will be beneficial for  the school. 

(b) Your friend has not fared well in the recent examinations. Write a letter to  him / her expressing your concern. Give him / her some advice on how to score  better marks and offer to help him / her to improve his / her performance.


The Principal

St. Xaviers School


Subject: Request to start a new club in school


All the students of the school feel proud of the excellent functioning of the so many clubs in the school. These clubs are providing great opportunities to the students in their all round development of personality. At the same time it is commonly felt that there is no Health Club in our school. I approach you with an earnest request to start the Health Club in the school at the earliest for the benefit of all the students. The cost of opening this club will be much less in proportion to the overall benefits that will accrue to one and all.

The Health Club will cater to the physical and psychological needs of the students who love to lead tension free healthy life and pursue their studies more wholeheartedly and devotedly. The Health Club to be headed by a young science teacher will work under your patronage and guide the students what to do to keep themselves disease free. The students need guidance on essential food items to be included in their diet. A yoga instructor should be engaged to instruct the students on the benefits of , yoga and meditation. Some tips from him on taking home made-potions will keep them in proper physical shape and strength.

Sir, I am hopeful that you will consider my proposal and take the earliest steps to start the Health Club to ensure healthy mind in healthy body.

With regards

Yours sincerely

Sundar (Class XII A, Roll No 15)



45, Nirmal Colony

Tilak Road


5 January 20….

Dear Mukesh

I have just received your letter expressing your great dissatisfaction with your performance in the Second Terminal Examination held in December. Your disappointment though quite genuine, is misplaced as I am aware you had not been keeping good health for the last few months. You were also burdened with the responsibility of looking after your ailing mother. Naturally, you did not have sufficient time and energy to attend to your studies. Under the circumstance you need not underestimate your capabilities and intelligence.

Mukesh dear, you must recall how brilliant your career had been throughout. In your class-X examination you had a creditable score. Even now you need not feel worried about the final examination. I am confident of your stamina for work with which to make up for the loss in studies. With your improved health and your mother in a position to attend to herself you will be able to put your heart and soul in your studies and do much better in the final examination.

Dear Mukesh, all is not lost. Look forward to your bright future awaiting you. You may seek help of your close meritorious friends and seek guidance and certain important topics. Prepare your subjects intelligently without resorting to cramming. Go out for a morning walk daily to keep yourself physically fit and mentally sound. I am always ready to render any help you may need. I would like to visit you shortly and help you make plans for intensive preparations for the final examination. Till then stay tension free and in high spirits. Looking forward to seeing you soon.

Yours sincerely


Q.3 (a) Your school is hosting an Inter-School Quiz Competition.  

Write out a notice to be displayed in your school giving all details for the  event. 

(b) Write an e-mail to the Principal of a neighbouring school requesting him / her.

To send a team of three members to participate in the Quiz Competition. 

Answer: (a)

St. Jude’s Convent School, Saharanpur


10 October 20 …

Inter-School Quiz Competition

Our school is hosting an Inter-school Quiz Competition on 15 October, 20… at 11 a.m in the school auditorium. As many as nine schools are sending their students to participate in the competition. The Deputy Commissioner has kindly acceeded to our request to preside over the function and give away the prizes to the winners. All are requested to attend the function and make it a success.

Dear Sir/Madam


(Cultural Secretary)

(b) From : prstjcss@gmail.com

Date : 12 : 11 : 19, 14 : 04 : 20

To : prss@gmail.com


Subject : Inter-School Quiz Competition

You will be glad to know that our school in holding an inter-school Quiz Competition on 15 October 20… at 11 am in the school auditorium. It will be a great favour to me if you kindly send three students to participate in the Quiz Competition. I would apppreciate if some staff member of your school accompanies these participants. I may assure you that the participants will be looked after well.

Looking forward to your cooperation.

C.J. Avasthi


St. Jude’s Convent School, Saharanpur

Q.4 Read the following passage carefully and answer the questions that follow: 

Billy Weaver had travelled down from London and by the time he arrived it  was nine o’clock in the night and the moon was coming up. 

“Excuse me,” he asked a porter. “but is there a cheap hotel nearby?” 

“Try The Bell Hotel,” the porter answered, pointing down the road.  

Billy thanked him, picked up his suitcase and set out to walk the distance to  The Bell Hotel. He had never been to Richmond before. But the man at the  Office had told him it was a splendid city.  

Billy was seventeen years old. He was wearing a new navy-blue overcoat, a  new brown hat, and a new brown suit, and he was feeling fine. He walked  10

briskly down the street. He was trying to do everything briskly these days. The  big shots up at the Head Office were fantastically brisk all the time. They were  amazing. 

The road was lonely and dark with a few scattered houses.  

Suddenly, in a downstairs window Billy saw a printed notice propped up  against the window glass. It said Bed and Breakfast.  

He moved a bit closer and peered through the window into the room, and the  first thing he saw was a bright fire burning in the hearth. On the carpet in front  of the fire, a little dog was curled up asleep with its nose tucked into its belly.  The room in half-darkness was filled with pleasant furniture. There was a  piano and a big sofa and several plump armchairs; and in one corner he spotted 20 a large parrot in a cage. Animals were usually a good sign in a place like this,  Billy told himself and it looked to him as though it would be a pretty decent  house to stay in.  

Then a queer thing happened to him. He was in the act of stepping back and  going away from the window when he felt a strange urge to ring the bell! 

He pressed the bell. He heard it ringing, and then at once the door swung open  and a woman was standing there. 

She gave him a warm welcoming smile. 

“Please come in,” she said pleasantly. Billy found himself automatically 30 

moving forward into the house.  

“I saw the notice in the window,” he said, holding himself back. 

“Yes, I know.” 

“I was wondering about a room.” 

“It’s all ready for you, my dear,” she said. She had a round pink face and very  gentle blue eyes. 

“How much do your charge?” 

“Five dollars a night, including breakfast.” 

It was fantastically cheap. He could easily afford it. 


(a) Give the meaning of the following words as used in the passage: 

One-word answers or short phrases will be accepted. 

(i) splendid (line 7)  

(ii) spotted (line 20)  

(iii) automatically (line 29)  


(b) Answer the following questions briefly in your own words. 

(i) How did the porter assist Billy? [2] 

(ii) Why did Billy want to do everything briskly?

(iii) Why did Billy think animals were a good sign in a place like this?

(iv) Which sentence tells you that something strange happened to Billy?

(v) How much did the room cost?  


(c) In not more than 50 words, give a brief account of what Billy saw as he looked  through the window of the room. 


(a) (i) great

(ii) noticed

(iii) instinctively

(b) (i) The porter assisted Billy by pointing out the name of the hotel that he should try.

(ii) As the big shots at the Head office were also doing things briskly all the time, Billy too wanted to do everything briskly.

(iii) Billy thought animals were a good sign in such a place because they gave an atmosphere of homeliness and warmth.

(iv) He was in the act of stepping back and going away from the window when he felt a strange urge to ring the bell.

(v) The room cost five dollars a night, including breakfast.

(c) As Billy looked through the window of the room, he saw a bright fire burning in the hearth. A little dog was curled up asleep on the carpet in front of the fire. There was a piano and a big sofa and several plump chairs. He also noticed a parrot in a cage there. It appeared a pretty place to stay in.


Q.5 (a) Fill in each of the numbered blanks with the correct form of the word given in brackets. Do not copy the passage, but write in correct serial order the word  or phrase appropriate to the blank space. 


(0) roamed 

Once upon a time, in the days when genies and giants (0)___________ (roam)  the land, there (1) ____________ (live) a farmer (2)____________ (name)  Baba Ayub. He lived with his family in a little village by the name of Maidan  Sabz. Because he had a large family to feed, Baba Ayub (3) ____________ 

(see) his days (4) ____________ (consume) by hard work. Every day, he  (5)___________ (labour) from dawn to sundown, (6)____________ (plow)  his field and (7) ____________ (turn) the soil and (8)___________ (tend) to  his meagre pistachio trees. 

(b) Fill in each blank with an appropriate word: 

(i) The puppy was hiding __________ the sofa. 

(ii) Stop worrying __________ your future. 

(iii) When I stepped __________ the lift, I found it had stopped working. (iv) We had to use a bridge to go __________ the river. 

(v) I have lived in this town __________ ten years. 

(vi) Please switch __________ all lights and fans when you leave the room.

(vii) Ronnie is married __________ my cousin. 

(viii) The gift came __________ a birthday card. 


(c) Join the following sentences to make one complete sentence without using  and, but or so

(i) He was very ill. He did not take any medicine. 

(ii) You come back from your holiday. We will discuss the problem. 

(iii) He remained absent on Friday. It was foolish of him. 

(iv) Rahul ran all the way to the bus stop. He missed the bus. 


(d) Re-write the following sentences according to the instructions given after each. Make other changes that may be necessary, but do not change the  meaning of each sentence. 

(i) The old woman said to Arun, “Can you help me to cross the street?” (Begin: The old woman asked Arun …………………) 

(ii) As soon as the sun rose over the hills, the fog disappeared. 

(Begin: No sooner…………………) 

(iii) It rained so heavily that they could not go for the picnic. 

(Rewrite: Using ‘too …………………to’) 

(iv) If your friends get here before 7 o’clock we can take them out for dinner. (Rewrite: Using ‘unless’.) 

(v) The school captain was elected by the students of classes XI and XII.  (Begin: The students…………………) 

(vi) Greenland is the largest island in the world. 

(Rewrite: Using ‘larger’.) 

(vii)How cruel Shylock was to demand his pound of flesh! 

(Begin: It was cruel…………………) 

(viii) Arun was asked by his mother to explain the missing buttons on his shirt. (Rewrite: Using ‘explanation’)

Answer :

(a) (1) lived

(2) named

(3) saw

(4) consumed

(5) laboured

(6) plowed

(7) turned

(8) tended

(b) (i) under

(ii) about

(iii) into

(iv) across

(v) for

(vi) off

(vii) to

(viii) with

(c) (1) Though he was very ill, he did not take any medicine.

(ii) We will discuss the problem when you come back from your holidays.

(iii) It was foolish of him to remain absent on Friday.

(iv) In spite of running all the way to the bus stop Rahul missed the bus.

(d) (i) The old woman asked Arun if he could help her to cross the street.

(ii) No sooner did the sun rise over the hills than the fog disappeared.

(iii) It rained too heavily to go for the picnic.

(iv) Unless your friends get here before 7 o’clock we cannot take them out for dinner.

(v) The students of classes XI and XII elected the school captain.

(vi) Greenland is larger than any other island in the world.

(vii) It was very cruel of Shylock to demand his pound of flesh.

(viii) Arun was asked by his mother to give explanation about the missing buttons on his shirt into the hall.




Q.1 (a) Solve the following inequation and write down the solution set: 

11x − 4 < 15x+ 4 ≤ 13x + 14, xєW

Represent the solution on a real number line. 

(b) A man invests ₹4500 in shares of a company which is paying 7.5% dividend.  If ₹100 shares are available at a discount of 10%.


     (i) Number of shares he purchases. 

     (ii) His annual income. 

(c) In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below:

Marks 1 2 3 4 5 5 7 8 9 10
Number of Students 1 2 3 3 6 10 5 4 3 3

Calculate the following for the given distribution: 

      (i) Median 

      (ii) Mode 

Q.2 (a) Using the factor theorem, show that (x – 2) is a factor of x3 + x2 − 4x− 4. Hence factorise the polynomial completely. 

(b) Prove that:

(cosec θ − sin θ)(sec θ − cos θ)(tan θ + cot θ) = 1 

(c) In an Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find then 

     (i) first term 

     (ii) common difference 

     (iii) sum of the first 20 terms. 

Q.3  (a) Simplify 

(b) M and N are two points on the X axis and Y axis respectively. 

P (3, 2) divides the line segment MN in the ratio 2 : 3.


(i) the coordinates of M and N 

(ii) slope of the line MN. 

(c) A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the: 


      (i) radius of the cylinder 

      (ii) curved surface area of the cylinder ( Take π = 3.14) 


Q.4 (a) The following numbers, K + 3, K + 2, 3K – 7 and 2K – 3 are in proportion. Find K.

(b) Solve for x the quadratic equation x2 − 4x − 8 = 0. Give your answer correct to three significant figures. 

(c) Use ruler and compass only for answering this question. Draw a circle of radius 4 cm. Mark the center as O. Mark a point P outside the circle  at a distance of 7 cm from the center. Construct two tangents to the circle from the  external point P.Measure and write down the length of any one tangent. 


Q.5 (a) There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box. Find the probability that the number on the disc is: 

      (i) an odd number 

      (ii) divisible by 2 and 3 both. 

      (iii) a number less than 16. 

(b) Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% per annum and Rekha receives  Rs. 441 as interest at the time of maturity.  

Find the amount Rekha deposited each month. 

(c) Use a graph sheet for this question.  Take 1 cm = 1 unit along both x and y axis. 

     (i) Plot the following points: A(0,5), B(3,0), C(1,0) and D(1,–5) 

    (ii) Reflect the points B, C and D on the y axis and name them as B’, C’ and D’ respectively. 

   (iii) Write down the coordinates of B’, C’ and D’. 

   (iv) Join the points A, B, C, D, D’, C’, B’, A in order and give a name to the closed figure ABCDD’C’B’. 

Q.6 (a) In the given figure, ∠PQR = ∠PST = 90o, PQ = 5 cm and PS = 2 cm. 

     (i) Prove that ΔPQR ~ ΔPST. 

      (ii) Find Area of ΔPQR : Area of quadrilateral SRQT. 

(b) The first and last term of a Geometrical Progression (G.P.) are 3 and 96 respectively. If the common ratio is 2, find: 

     (i) ‘n’ the number of terms of the G.P. 

     (ii) Sum of the n terms. 

(c) A hemispherical and a conical hole is scooped out of a solid wooden cylinder. 

     Find the volume of the remaining solid where the measurements are as follows: 

     The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm.

     Height of cone is 3 cm. Give your answer correct to the nearest whole number. Take π = 22/7

Q.7 (a) In the given figure AC is a tangent to the circle with center O.  

      If ∠ADB = 55o, find x and y. Give reasons for your answers. 

(b) The model of a building is constructed with the scale factor 1 : 30.  

      (i) If the height of the model is 80 cm, find the actual height of the building in  meters.  

     (ii) If the actual volume of a tank at the top of the building is 27 m3, find the volume  of the tank on the top of the                model. 

(c) Given  M  = 6 I, where M is a matrix and I is unit matrix of order 2 x 2. 

     (i) State the order of matrix M. 

    (ii) Find the matrix M. 

Q.8 (a) The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference. 

(b) The vertices of a ΔABC are A(3, 8), B(–1, 2) and C(6, –6). Find: 

      (i) Slope of BC. 

      (ii) Equation of a line perpendicular to BC and passing through A. 

(c) Using ruler and a compass only construct a semi-circle with diameter BC = 7cm.  

Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.  

Q.9 (a) The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method. Take the assumed mean as 45. Give your answer correct to 2 decimal places.

Number of patients  10 – 20  20 – 30  30 – 40  40 – 50  50 – 60  60 – 70
Number of Days  5

(b) Using properties of proportion solve for x, given 

(c) Sachin invests ₹ 8500 in 10%, ₹ 100 shares at ₹ 170. He sells the shares when the price of each share rises by ₹ 30. He invests the proceeds in 12% ₹ 100 shares at ₹ 125. Find: 

     (i) the sale proceeds. 

    (ii) the number of ₹ 125 shares he buys. 

    (iii) the change in his annual income. 

Q.10 (a) Use graph paper for this question. The marks obtained by 120 students in an English test are given below: 

Marks  0–10  10–20  20–30  30–40  40–50  50–60  60–70  70–80  80–90  90–100
No. of students 16  22  26  18  11  3

Draw the give and hence, estimate: 

     (i) the median marks. 

    (ii) the number of students who did not pass the test if the pass percentage was 50. 

    (iii) the upper quarterly marks. 

(b) A man observes the angle of elevation of the top of the tower to be 45o. He walks towards it in a horizontal line through its base. On covering 20 m the angle of  elevation changes to 60o. Find the height of the tower correct to 2 significant figures.

Q.11 (a) Using the Remainder Theorem find the remainders obtained when  x3 + (kx + 8)x + k is divided by x + 1 and x – 2. Hence find k if the sum of the two remainders is 1. 

(b) The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.  

(c) In the given figure, ABCDE is a pentagon inscribed in a circle such that AC is a diameter and side BC||AE. If ∠BAC = 50°, find giving reasons: 

     (i) ∠ACB 

    (ii) ∠EDC 

    (iii) ∠BEC 

    Hence prove that BE is also a diameter 




Click one of our representatives below to chat on WhatsApp or send us an email to info@vidhyarthidarpan.com