ALL INDIA SAINIK SCHOOLS ENTRANCE EXAMINATION-2014FOR ADMISSION TO CLASS-IX

PAPER-I MATHEMATICS & SCIENCE

Time : 2.30 hrs. Max Marks : 275

(Maths : 200, Science : 75)

Name in Full __________________________________ Roll No. _______________

Signature of Invigilator _________________________ Code No. ______________(To be filled by the Office)

MATHEMATICS AND SCIENCE : CLASS IX

[Please DO NOT WRITE your name, roll number or any identificationtext/mark on any other page of this Answer Book]

FOR OFFICE PURPOSE ONLY

Code No. ___________________

MARKS OBTAINED

PART A PART B

Signature of the Examiner ______________ Checked by __________________

Note : (i) This paper contains two parts — Part 'A' : Mathematics and Part 'B' : General Science. You are to attempt ALL questions in each part.

(ii) Part 'A' bearing 200 marks, contains 50 questions. Q.No.1 to 20 carry two marks each, Q.No. 21 to 40 carry three marks each and Q.No. 41 to 50 carry ten marks each.

(iii) Part 'B' bearing 75 marks, contains 37 questions, Q.No. 1 to 15 carry one mark each, Q.No. 16 to 25 carry two marks each, Q.No. 26 to 35 carry three marks each, Q.No. 36 & 37 carry five marks each.

(iv) Write your answers in the question paper itself in the space provided.

(v) Rough work is to be done at space provided.

(vi) Write all your Answers in blue / black ink only. Do not use pencil.

(vii) This booklet contains 25 pages.

(1)

ROUGH WORK

(2)

(3)

PART — 'A' MATHEMATICS

200 Marks

(Instructions : Q1 to Q20 bear 2 marks each, i.e. 20 ´ 2 = 40 Marks)

Q1. Represent and on the number line.

Q2. Evaluate :

Q3. The sum of the squares of 3 consecutive odd numbers is 251. Find the numbers.

Q4. Simplify :-

6

5

2

5-

11 1

1 1

3 4

-- - üìï ïæ ö æ ö-í ýç ÷ ç ÷

è ø è øï ïî þ

( )(2 3 ) (2 3 )a b a b c a b c+ - + - -

(4)

Q5. If , find the value of

Q6. Factorise :

Q7. Solve :

Q8. If A's monthly income is 40% more than that of B, how much percent is B's income less than that of A ?

Q9. If 12% is allowed as discount on a radio and its selling price is ̀ 836, what is its marked price ?

1 1

2x

x

æ ö- =ç ÷

è ø

2

2

44x

x

æ ö+ç ÷

è ø

( )2 21 2x a a- - -

1 21

2 3

m mm

- -- = -

(5)

Q10. Find the Compound Interest on ` 5000 at 16% per annum for 1 year, compounded half-yearly.

Q11. Three angles of a quadrilateral are 80°, 95° and 120°. Find the fourth angle.

Q12. When a die is thrown. What is the probability of getting a number not greater than 5 ?

Q13. The multiplicative inverse of is :-

(a) (b) (c) (d) None of these

Q14. The sum of two numbers is 37 and their product is 342, then the numbers are :

(a) 19, 18 (b) 23, 14 (c) 24, 13 (d) 28, 9

5 3

8 7- ´-

15

56

56

15

35

24

(6)

Q15. Three coins are tossed simultaneously. What is the probability that at most 1 head comes ?

(a) (b) (c) (d)

Q16. What least number must be subtracted from 171 to make it a perfect square ?

(a) 2 (b) 3 (c) 4 (d) 5

Q17. is equal to :

(a) (b)

(c) (d)

Q18. If the perimeter of a rectangular field is 200 m and its breadth is 40 m, then 2

its area (in m ) is :

(a) 1200 (b) 2400 (c) 4800 (d) 6000

Q19. Find measure of Ðx in the figure given below :-

7

8

5

8

1

2

3

8

( )2

2x y-

2 24 4x y xy+ + 2 24 4x y xy- + -

2 24 4x y xy+ - 2 24 4x y xy- -

90°

50°

110°

x °

(7)

Q20. Find the smallest perfect square number which is divisible by 15, 18 and 25.

(Instructions : Q21 to Q40 bear 3 marks each i.e. 20 ́ 3 = 60 Marks)

Q21. Find three rational numbers between and .

Q22. Factorise :

Q23. Find :

Q24. If , find the value of

1

4

1

2

2

2

13x

x

æ ö+ -ç ÷

è ø

2 3 5 3 1

3 5 2 5 6- ´ + - ´

12x

x

æ ö+ =ç ÷

è ø

3

3

1x

x

æ ö+ç ÷

è ø

(8)

3 3 3 Q25. If x + y + z = 9 & xy + yz + zx = 23, then find the value of (x + y + z - 3xyz)

Q26. In a rhombus, whose area is 144 sq.cm., one of its diagonal is twice as long as the other. Find the length of its diagonals.

Q27. Simplify :

Q28. By selling 100 pencils, a shopkeeper gains the selling price of 20 pencils. Find his gain percent.

Q29. Express the following numbers in usual form :

5(i) 3.52 ́ 10

-5(ii) 3 ́ 10

5 5

7 5

3 10 125

5 6

- -

- -

´ ´

´

(9)

2Q30. Divide : z (5z - 80) by 5z (z + 4)

Q31. Pipe A can fill a tank in 20 hours while pipe B alone can fill it in 30 hours and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, how much time will be needed to make the tank full ?

2Q32. The area of a trapezium shaped field is 480 m , the distance between two

parallel sides is 15 m and one of the parallel side is 20 m. Find the other parallel side.

3 2Q33. Find the height of a cuboid whose volume is 275 cm and base area is 25 cm .

(10)

Q34. Find the least number that must be added to 1300 so as to get a perfect square.

Q35. Simplify : (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y

Q36. A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder.

(Take p = )

Q37. 94 is divided into two parts in such a way that the fifth part of the first and the eighth part of the second are in the ratio 3 : 4. Find the first part.

22

7

(11)

Q38. ` 770 have been divided among A, B, C in such a way that A receives th of what B and C together receive. Find A's share.

Q39. If 15 men can build a wall 108 m long in 6 days, what length of similar wall can be built by 25 men in 3 days ?

Q40. An aquarium is in the form of a Cuboid whose external measures are 80 cm

´ 30 cm ́ 40 cm. The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed ?

2

9

(12)

(Instructions : Q 41 to Q 50 bear 10 Marks each i.e., 10 ́ 10 = 100 Marks)

Q41. The sum of three consecutive multiples of 11 is 363. Find these multiples .

Q42. In the following figure, both RISK and CLUE are parallelograms. Find the

value of Ðx.

K

R

E

I

S

C

U

L

120°

70°

x°

(13)

Q43. Waheeda bought an air cooler for ` 3300 including a tax of 10%. Find the price of the air cooler before VAT was added.

Q44. Simplify :

Q45. A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

2 2 2 3 2( ) 2m n m m n- +

(14)

Q46. A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same ?

Q47. The digits of a two digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number ?

Q48. Mohan buys an article with 25% discount on its marked price. He makes a profit of 10% by selling it at ̀ 660. Find the Marked Price.

Q49. Factorise the expressions and divide as directed.

Q50. A godown is in the form of a cuboid of measures 60m ´ 40m ´ 30m. How 3

many cuboidal boxes can be stored in it if the volume of one box is 0.8 m ?

(15)

2 212 (9 16 ) 4 (3 4 )xy x y xy x y- ¸ +

Select the correct answer:- (15 ´ 1 = 15 Marks)

[ Mark Your Answer by putting a Tick Mark (3) on the correct option - Overwriting is NOT permitted]

Q1. The angle of reflection is equal to the angle of incidence :

a) Always b) Sometimes

c) Under special conditions d) Never

Q2. A charged object attracts an uncharged object by producing opposite charges in the nearer end of the uncharged object by the process of

a) Electric Potential b) Electric Induction

c) Friction d) Electromagnetic Induction.

Q3. Which of the following does not conduct electricity?

a) Vinegar solution b) Sugar solution

c) Lemon juice d) Caustic Soda solution.

Q4. When we change a feeble sound to a loud sound , we increase its

a) Frequency b) Speed

c) Timbre d) Amplitude

Q5. A spring balance can used to measure:

a) Mass of an object b) Volume of an object

c) Weight of an object d) Density of an object.

Q6. The same force F acts on four different objects having areas given below, one by one. In which case the pressure exerted will be maximum?

2 2a) 100 cm b) 50 m 2 2c) 10 m d) 20 m

PART 'B' (SCIENCE)

Max Marks : 75

Note :- Part 'B' bearing 75 marks, contains 37 questions. Q.No. 1to 15 carry one mark each, Q.No. 16 to 25 carry two marks each, Q.No. 26 to 35 carry three marks each, Q.No. 36 & 37 carry five marks each.

(16)

Q7. Malaria is caused by

a) Bacteria b) Virus

c) Worms d) Protozoan

Q8. Which of the following does not show metamorphosis?

a) Fish b) Frog

c) Silk moth d) Mosquito

Q9. The nonliving part of a tomato cell is its

a) Cell membrane b) Nucleus

c) Chloroplasts d) Cell wall

Q10. The national park which is located in Rajasthan

a) Corbett National Park b) Kanha National Park

c) Satpura National Park d) Sariska National Park

Q11. Which of the following burns without producing a flame?

a) Camphor b) Coke

c) Cooking gas d) Kerosene

Q12. Which of the following is used as a reducing agent in the extraction of iron metal?

a) Coal b) Bitumen

c) Coke d) Charcoal

Q13. Which of the following elements will produce an oxide that will dissolve in water to form an acid?

a) Calcium b) Zinc

c) Carbon d) Copper

Q14. The synthetic polymer which can be used as a substitute for wool for making sweaters and shawls is

a) Nylon b) Polyester

c) Terylene d) Acrylic

Q15. Ursa Major is a :

a) Star b) Planet

c) Constellation d) Satellite

(17)

Note :- Write your answers within the space provided under the questions :-

(10 ´ 2 = 20 Marks)

Q16. What is an artificial satellite? Name any two artificial satellites launched by our country.

Q17. The distance between the object and a plane mirror is 80 m .

a) What is the image distance if the plane mirror is moved 5 m towards the object ?

b) What is the distance of the image from the object if the object is moved 5 m away from the plane mirror?

Q18. A tuning fork vibrates 18000 times in one minute. What is the frequency of the sound produced by it? What is the time period of the sound produced.

Q19. Explain how the use of oil reduces friction between two surfaces in contact with each other?

(18)

Q20. Explain why, the walls of a dam are thicker near the bottom than at the top.

Q21. What is the function of adrenaline hormone in the body?

Q22. Give two differences between a zygote and a foetus.

Q23. What is meant by endangered species? Name two endangered animals.

Q24. What happens when a fresh iron nail is placed in copper sulphate solution ?

(19)

Q25. The metal X reacts with dilute sulphuric acid to produce a gas Y . When a burning match stick is brought near to it burns with a 'pop' sound.

a) Name the metal Xb) Name the gas Y.

Note :- Write your answers within the space provided under the questions :-

(10 ´ 3 = 30 Marks) Q26. Farmers in Northern India grow legumes as fodder in one season and

wheat in the next season. a) what is this practice known as? b) how does this process help cultivation.

Q27. Name three human diseases caused by virus. Also name the mode of transmission and preventive measures for each of these diseases.

(20)

Q28. A strip of impure copper metal is given to you. Describe briefly how you will purify it by using the chemical effect of electric current. Draw a labelled diagram of the experimental set up for this purpose.

Q29. Explain the term 'fertilisation' . Describe the process of fertilisation in human beings.

Q30. What are the major products of petroleum refining? Give one use of each of petroleum product.

(21)

Q31. What is 'Global Warming' ? Name the main gas responsible for this. State the harmful effect caused by global warming?

Q32. Draw a labelled diagram of a human nerve cell. What are its functions?

Q33. What is meant by 'Reproductive Health' ? State the conditions necessary for maintaining good reproductive health during adolescence ?

(22)

Q34. What are the forces acting on a plastic bucket containing water held above the ground level in your hand . Why the forces acting on the bucket do not bring a change in its state of motion?

Q35. What happens to the needle of a magnetic compass kept nearby the electric circuit.

a) When electric current is switched on in a wire ?

b) When the direction of current is reversed in the wire ?

c) Why does this happen?

Note :- Write your answers within the space provided under the questions :-

(2 ´ 5 = 10 Marks)

Q36. a) How many images of an object will be formed when the object is placed obetween two plane mirrors which are inclined at an angle 60 .

(23)

b) What is dispersion of light? Name the natural phenomenon caused by dispersion of light .

oc) A ray of light is incident on a plane mirror with angle of incidence 40 .

oIf the mirror is rotated by an angle 5 clockwise find the angle of refraction. (1+2+2 =5)

Q37. a) Explain why a speedboat has a streamlined shape?

(24)

b) Explain with a labelled diagram the reproduction of Hydra. (2+3 =5)

(25)