Sainik School Class IX Entrance Examination-2015

Paper-I

Part-A : Mathematics

Directions (Qs. 1 to 20) : Bear 2 marks each.

1. Find two rational numbers between ¼ and 3/8 and represent them in number line.

3. Fifteen years from now Mohan’s age will be four times his present age. What is Mohan’s age after five years from now.

4. Find the least number of three digits which is greater than 100 and a perfect square.

5. Find the value of

6. Resolve into factors : 17 – 32y – 4y².

7. Find the cube root of 91125.

8. There are certain number rows of trees in a garden. The number of trees in each row is twice the number of rows. If the number of trees in the garden is 1250, then the number of rows in the garden is ………… .

9. The marked price of an item is Rs 1200. Find the discount percentage allowed on the item if it is sold for Rs 1050.

10. A man borrowed Rs 16000 at 10% per annum interest compounded half yearly. Find the amount repayable after one year.

11. The four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the measures of the angles.

12. What must be added to 4x² – 12x + 7 to make it a whole square.

13. (129⁸)⁹ is equal to

(a) 129¹⁷ (b) 129²

14. The mean of the first ten natural number sis:

(a) 5.10 (b) 5.5

15. Divide a sum of Rs 10 between two persons A and B such that A gets Re 1 more than B.

16. The sum of two number is 45 and their ratio is 7 : 8. Find the numbers.

17. If 56 men can do a piece of work in 42 days, how many men will do it in 14 days?

18.

19. In the above figure, ABCD is a parallelogram, find all the angles of the parallelogram if measure of angle DCX = 130°.

20. A man loses 20% of his money. After spending 25% of the remainder, he has Rs 480.00 left. How much money did he originally have?

By selling a towel for Rs 126.90 a shopkeeper loses 6%. For how much should he sell the towel to gain 4%.

Directions (Qs. 21 to 40) : Bear 3 marks each.

21. The digits of a two digit number are such that one is twice the other. When the digits are interchanged, the new number obtained is greater than the original number by 27. Find the number.

22.

23.

24. If then find the value of

25. A well is dug 20 m deep and has a diameter 7m. The earth which is so dug out is spread even on a rectangular plot 22 m long and 14 m broad. What is the height of the platform formed?

26. Find the area in sq cm of a rhombus whose side is 17 cm and one of its diagonals is 30 cm.

27. The marks obtained by 40 students in Mathematics are given below:

69, 59, 49, 39, 84, 68, 77, 48, 47, 57, 46, 41, 44, 67, 57, 45, 34, 36, 87, 89, 65, 41, 84, 78, 52, 49, 75, 37, 38, 42, 73, 31, 34, 37, 56, 59, 64, 85, 81 and 62.

Based on the above data, the frequency of the class 60 – 70 is ………… .

28. An article with a marked price of Rs 600 is available at a discount of 18%. Find the discount given and also the price at which the article is available for sale.

29. If 5^{3x + 4} = 25 × 5^{4x – 1}find the value of x.

30. Walking at 4 km an hour, a person reaches his office 5 minutes late. If he walks at 5 km an hour, he will be 4 minutes too early. Then the distance of his office from his residence is

31. The internal measures of a cuboidal room are 12 m × 8 m × 4 m. Find the total cost of whitewashing all four walls of the room, if the cost of whitewashing is Rs 5 per square metre. What will be the cost of whitewashing if the ceiling of the room is also whitewashed?

32. What least number must be subtracted from 2200 so as to get a perfect square?

33. A garrison of 2000 men has a provision for 15 weeks. How many men must leave so that the same provision may last for 20 weeks?

34. Multiply (a² + b² + c² – ab – bc – ca) by (a + b + c).

35. Construct a histogram for the frequency distribution below:

36.

37. Pipe A can fill a tank in 14 minutes, pipe B can fill it in 7 minutes and pipe C can empty the full tank in 28 minutes. If all of them are opened simultaneously, find the time taken to fill the empty tank.

38. Four pipes 5 cm each in diameter are to be replaced by a single pipe discharging the same quantity of water. If the speed of water remains same in both the case, find the diameter of the single pipe.

39. Reduce the following expression into lowest term

40.

Directions (Qs. 41 to 50) : Bear 10 marks each.

41. A village, having a population of 4000. requires 150 litres of water per head per day. It has a tank which is 20 m long, 15 m broad and 6 cm high. For how many days will the water of this tank last? Given 1 m³ = 1000 litres.

42. The sum of the ages of a father and his son is 50 years. 5 years ago father’s age was 7 times the son’s age. Find their present ages.

43. (a) Solve the linear equation

x – 0.3 + 0.05x = 2 – 1 – 4x

(b) The sum of the digits of a certain two digits number is 7. Reversing its digits increases the number by 9. What is the number?

44. Construct a trapezium ABCCD in which AB &DC are parallel, AB = 6 cm, DC = 3.5 cm ∠A = 55°, AD = 3.5 cm.

45. Parikshit made a cuboid of plasticine having dimensions 2 cm, 5 cm, 5 cm. What is the minimum number of such cuboid required to make a cube?

46. A horse is tethered in a corner of rectangular plot 40 m by 36 m with a rope 14 m long. Find the area over which it can graze.

47. The pie chart below shows how Mr. Davis distributes his monthly income into different household expenses. See the pie chart to answer the following questions.

(a) In which of the above categories does Mr. Davis spend the greatest portion of his income?

(i) Grocery (ii) Entertainment

(iii) Eating out (iv) Rent

(b) What portion of the monthly income does Mr. Davis spend on entertainment?

(i) 10% (ii) 20%

(iii) 30% (iv) 25%

(i) ¼ (ii) ½

(iii) 1/10 (iv) ¾

(d) If Mr. Davis earns Rs 2,000/- per month, how much does he spend on groceries?

(i) Rs 1,000 (ii) Rs 250

(iii) Rs 500 (div Rs 700

(e) What is the ratio of expenditure between entertainment and grocery?

(i) 3:4 (ii) 4:5

(iii) 3: 5 (iv) none of these

48. A man bought a TV and washing machine for Rs 8000 each. He then sold the TV at a loss of 4% and the washing machine at a profit of Rs 8%. Find the overall gain or loss percent in the whole transaction.

49. Factorise the following:

(a) m² + n – mn – m

(b) x⁴ + 12x² + 64

50. (a) Solve : (4x² + 7x³y²) – (−6x² – 7x³y² – 4x) – (10x + 9x²)

(b) Using the identity:

(x + a) (x + b) = x² + (a + b)x + ab

Solve: 107 × 108

Part-B : Science

Note: Part ‘B’ contains 37 questions, bearing 75 marks. Question No. 1 to 15 are multiple choice questions carrying 1 mark each , Question No. 16 to 25 carry 2 marks each, Question No. 26 to 35 carry 3 marks each, Question No. 36 & 37 carry 5 marks each.

Fill in the blanks.

1. Blue green algae fix ……. directly from air to enhance fertility of soil.

2. Species found only in a particular area is known as ………… .

3. Synthetic fibres are synthesized from raw material called ………….. .

4. Phosphorus is a very ………… non metal.

5. Process of separation of different constituents from petroleum is called …………. .

Select the Correct Answer.

6. The most common carrier of communicable diseases is

(a) Ant (b) Housefly

Answer: (B)

7. Which of the following can be beaten into thin sheets

(a) Zinc (b) Phosphorus

Answer: (A)

8. Unwanted sound is called as

(a) Music (b) Pitch

Answer: (C)

9. The process of depositing a layer of any desired metal on another material by means of electricity is called

(a) Mixing (b) Electrolyting

Answer: (D)

10. Which of the following is NOT a planet of the sun?

(a) Sirius (b) Mercury

Answer: (A)

Mark ‘T’ if the statement is True and ‘F’ if it is False.

11. Generally, non metal react with acids. ( )

12. Coke is almost pure form of carbon ( )

13. Kerosene is not a fossil fuel. ( )

14. Unicellular organisms have one celled body. ()

15. An embryo is made up of a single cell. ( )

Write answers within the space provided under the questions:

16. Does pure water conduct electricity? If not what can we do to make it conductive.

17. Explain why sliding friction is less than static friction.

18. A pendulum oscillates 40 times in 4 seconds. Find its time period and frequency.

19. Define:

(a) Force of Gravity

(b) Pressure

20. Define adolescence.

21. Give two difference between Zygote and foetus.

22. Nylon is used for making parachutes, car seat belts and ropes for rock climbing. Why?

23. List condition under which combustion can take place.

24. List two advantages of using CNG & LPG as fuels.

25. What is malleability ? Give two examples of malleable metals.

Write answers within the space provided under each questions:

26. What is Marble Cancer? Write the air pollutants that are affecting the beauty of Tajmajal.

27. Why is the distance between stars is expressed in light years? What do you understand by the statement that a star is eight light years away from the earth?

28. Explain why plastic containers are favoured for storing food?

29. What are the major groups of micro organisms?

30. What is constellation? Name any two constellation.

31. Explain the reason why water is not used to control fires involving electrical equipment?

32. Why Sodium and Potassium are stored in kerosene?

33. Why are children?infants given vaccination?

34. Briefly explain types of combustion.

35. Draw labeled diagrams of plant cell and animal cell.

36. Write short notes on

(a) Cytoplasm (b) Nucleus of a Cell

37. Briefly answer the following questions.

(a) Why porters place a round piece of cloth on their head when they have to carry a heavy load?

(b) An inflated balloon was pressed against a wall after it had been rubbed with a piece of synthetic cloth. It was found that, the balloon sticks to the walls. What force might be responsible for attraction between the balloon and the wall?

Paper-II

Part-A : English Language

1. Read the following passage and answer the questions that follow. (3 × 5 = 15)

The beauties of nature are the greatest gifts of God to man. How unlucky are they who cannot enjoy and appreciate nature. Nature is all around us in varied aspects and shapes. We have the green charming hills, snow-capped mountains, and the rising and setting sun in its varied and unforgettable glory. The dew drops on the blades of grass look like iridescent pearls. The silvery moon and the twinkling starts bedeck the sky. The roaring waves in the vast ocean and the lakes which look like sheets of water add to the glorious treasure. Even the violent aspects of nature like the thundering clouds with dazzling flashes fighting, the torrential rain, and the all-powerful storm are some of the aspects of nature which Tennyson termed as nature “red in tooth and claw”. But they have their own charms which captivate man and even inspire in his heart.

One can enjoy the beauties of nature in an abundant measure at a hill station. The floating clouds, the dancing springs, the winding rivulets, the all pervading multicolour flowers, emitting sweet, soothing smell, the trees standing like sentinels with birds singing sweet harmonious songs in their branches, the cool breeze, the humming bees, the delicious fruits-all cater to human senses. Beauty lies in the eyes of the beholder on the earth, in the air, in the sky and in the ocean. His heart leaps up when he beholds a rainbow in the sky.

Nature teaches man the lesson of peace, innocence, purity, love, harmony, simplicity, hope and faith in the glory of God. Wordsworth believes that nature is the greatest store-house of wisdom, apart from being a source of eternal happiness:

(a) What is termed by Tennyson as “Red in tooth and Claw”?

(b) What are the captivating beauties of Hills?

(d) Write synonyms for the following words which means in above passage:

(i) Dazzling …………..

(ii) Capped ………….

(iii) Soothing ………..

(e) Pick out words opposite to following words from the passage:

(i) Calm …………..

(ii) Faded ……………..

(iii) Limited …………….

2. Write a para in about 100 words on ONE of the following given topics. (10)

(a) Hazards of Polythene

(b) Role of Media

3. Write a letter to collector inviting him for the children’s day function at your school. (limit your answer to 150 words) (15)

4. Fill in the blanks with suitable articles/ prepositions in the brackets. (2 × 5 = 10)

(a) Who has kept ……… eggs in fruit basket. (a/an/the)

(b) We have turned ……… better ways of living. (towards/about/back)

(d) In the busy road many were passing ………. (out/by/off/on)

(e) Indian food appeals ………… anybody’s taste. (after/to /into/in)

5. Change into passive voice: (2 × 5 = 10)

(a) Which team won the final match last year?

(b) We have sold all the tickets of the show.

(d) We do not accept ATM cards.

(e) We will sell all kinds of clothes here.

6. Following sentences are INCORRECT. Find out the error and rewrite the following sentences correctly. (2 × 5 = 10)

(a) He gave me some advices.

(b) Will you tell me the reason of an earthquake?

(d) All but I were present in class.

(e) The flower pot is placed in the centre.

7. Write one word for the following group of words. (1 × 5 = 5)

(a) One who is all powerful

(b) A study of body

(d) That through which light cannot pass

(e) One who looks at the dark side of things

8. Frame a meaningful sentence by using each word. (2 × 5 = 10)

(a) Ode, Owed (b) Ceiling, Sealing

(e) Cite, Sight

9. Change the following DIRECT sentences into INDIRECT sentence. (1 × 5 = 5)

(a) Ruby said, “Raj, how is your knee today?”

(b) Raman said, “Let us decide on the place.”

(d) I said “Did you call at my house last night?”

(e) He said, “Please lend me your umbrella”.

10. Look at the picture critically, think of a suitable theme and write a story. (in approx. 100 words) (10)

PART-B : Social Studies

1. State True or False. (1 × 15 = 15)

(a) James Mill glorified India and its culture in his book “A HISTORY OF BRITISH INDIA”.

(b) The Maratha power a crushed in the third Anglo – Maratha war.

(d) The tribal chiefs lost their authority under the British rule.

(e) Birsa Munda was convicted on the charges of rioting.

(f) After the revolt of 1857 the Governor- general of India was given the title of Admiral General.

(g) The Tata iron and steel company began to produce steel after the First World War.

(h) Raja Ram Mohan Roy founded the Aryasamaj in 1975.

(i) The Simon commission had two Indian representatives.

(j) The Jalianwalabagh massacre occurred in Amritsar on Baishakhi day.

(k) All natural resources of energy are renewable.

(l) Chile and Peru are leading producers of copper.

(m) Bauxite is the ore of aluminum.

(n) Our constitution guarantees rights of minorities against the majority.

(o) The total membership of the Loksabha is 500.

2. Fill in the blanks. (1 × 15 = 15)

(a) The court language of Mughals was ………… .

(b) The coin of Rupa was first issued by ………. .

(d) The title of Governor General changed to that of Viceroy in the year ………. .

(e) Delhi became the capital of India in ……… .

(f) Type of party system that has evolved in India is ………. .

(g) The first General Election in India was held in ………. .

(h) Panchayati Raj was first introduced in the state of …………… .

(i) The last Moughal Emperor was ……… .

(j) The third research centre of India in Antarctica is ………. .

(k) ………. is the latest established High Court in India.

(l) ………… is often referred to as ‘Manchester of India’.

(m) The president of the constituent assembly was …………

(n) ………. allowed the company to use the vast revenue resources of Bengal.

(o) …… was the capital of British India before Delhi.

3. Expand the abbreviations. (1 × 10 = 10)

(a) RTI (b) SAARC

(e) BARC (f) NATO

(g) UNO (h) IPL

(i) TISCO (j) UNICEF

4. Match the following columns. (1 × 10 = 10)

(a) Rocks and minerals (i) Bangalore

(b) Tiger of Mysore (ii) Productive use of land

(d) Humus (iv) Bihar

(e) William Jones (v) a biotic resources

(f) The arms act (vi) South Africa

(g) Simon commission (vii) a linguist

(h) Cholera (viii) 1878

(i) Diamond mines (ix) 1927

(j) Silicon Valley (x) Tipu sultan

5. Write short notes on ANY FIVE of the following topics (limit 50 words) (5 × 5 = 25)

(a) Women Empowerment.

(b) Revolt of 1857.

(d) Green Earth

(e) Cultural Diversity

(f) Conventional and non-conventional sources of energy.

(g) Panchayati Raj.

(h) Battle of Plassey.

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