GENERAL INSTRUCTIONS FOR KVPY TEST PAPER (STREAM-SA)

YEAR : 2008

1. In Year 2008, Question Number 1-60 each carries 1 (one) mark, Maths(1-15), Physics

(16-30), Chemistry(31-45), Biology(46-60) & Question Number 61 to 80 each carries

2 marks, Maths(61-65), Physics( 66-70), Chemistry(71-75), Biology(76-80).

2. Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other

electronic gadgets in any form is not allowed.

3. Write your Name and Roll No. in the space provided in the bottom of this booklet.

4. Before answering the paper, fill up the required details in the blank space provided in

the answer sheet.

5. There is negative marking for each wrong answer. For 1 mark question � 0.25 marks

will be deducted and for 2 mark question � 0.50 marks will be deducted. So attempt

each question carefully.

6. Do not forget to mention your roll number neatly and clearly in the blank space provided

in the answer sheet.

7. In case of any dispute, the answer filled in the OMR sheet available with the institute

shall be final.

Time : 3Hr. Max. Marks : 100

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PART-I (1 Mark)

MATHEMATICS

1. If a and b are any two real numbers with opposite signs, which of the following is the greatest ?

(A) (a�b)2 (B) (|a| � |b|)2 (C) |a2 � b2| (D) a2 + b2

2. The sum of the infinite series :

....10

n...

10

3

10

2101

n32!!!!!

(A) 91

(B) 8110

(C)81

(D) 2217

3. The number (1024)1024 is obtained by raising (16)16 to the power n. What is the value of n ?

(A) 64 (B) 642 (C) 6464 (D) 160

4. The smallest value the expression x2 + 6x+ 8 attains on the set { x" R | x2 � 2x � 8 # 0} is

(A) 0 (B) �1 (C) 8 (D) 3

5. Let P1 be the set of all prime numbers, i.e., P

1 = {2, 3, 5, 7,11, . . .}, Let Pn = {np | p " P

1|}, i.e., the set

of all prime multiples of n. Then which of the following sets is non empty ?

(A) 231 PP $ (B) 217 PP $ (C) 2012 PP $ (D) 2420 PP $

6. The number of integers a such that 1 # a # 100 and aa is a perfect square is :

(A) 50 (B) 53 (C) 55 (D) 56

7. On a card, the following three statements are found :

(1) On this card exactly one statement is false.

(2) On this card exactly two statements arc false.

(3) On this card exactly three statements are false.

The number of false statements on the card is exactly

(A) 0 (B) 1 (C) 2 (D) 3

8. In triangle ABC, with % A = 90°, the bisectors of the angles B and C meet at P. The distance from P to the

hypotenuse is 4 2 . The distance AP is :

(A) 8 (B) 4 (C) 8 2 (D) 4 2

YEAR-2008 (KVPY-STREAM-SA)

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9. In a rhombus one of the diagonals is twice the other diagonal. Let A be the area of the rhombus in square

units. Then each side of the rhombus is :

(A) A (B) A221

(C) A521

(D) A441

10. In the following figure, AE = EB, BD = 2DC What is the ratio of the areas of PED and ABC ?

A

B C

P

D

E

(A) 41

(B) 61

(C)91

(D)121

11. Let P be a point in the interior of the rectangle ABCD Which of the following sets of numbers can form the

areas of the four triangles PAB, PBC, PCD, PDA in same order ?

(A) 10,9,12,5 (B) 21,15,6,12 (C) 10,9,8,6 (D) 12,8,7,5

12. The sum of 7 consecutive positive integers is equal to the sum of the next five consecutive integers. What

is the largest among the 12 numbers ?

(A) 24 (B) 23 (C) 22 (D 21

13. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many

minutes will it take to fill the empty tanker if only B is used in the first-half of the time and A and B are both

used in the second-half of the time ?

(A) 15 (B) 20 (C) 27.5 (D) 30

14. Let 0 < a < b < c be 3 distinct digits. The sum of all 3-digit numbers formed by using all the 3 digits once

each is 1554. The value of c is :

(A) 3 (B) 4 (C) 5 (D) 6

15. Let a sequence have 200 zeroes to start with. In step 1, to every position in the sequence we add1. In

step2, to every even position in the sequence we add1. In step 3, to every position which is a multiple of

3, we add 1. This is continued up to 200-th step. After the 200-th step, what will be the value in the 128th

position ?

(A) 8 (B ) 16 (C) 128 (D) 200

PHYSICS

16. A ball is thrown vertically upwards with a certain initial velocity. Assume that there is no resistance dueto air. Among the graphs below, the graph that is not an appropriate representation of the motion of theball is :

(i)

Kin

etic

Ene

rgy

Time

(ii) )

Pot

entia

l Ene

rgy

Time

(iii)

Kin

etic

En

ergy

Height of the ball

(iv)

Pot

entia

l Ene

rgy

Speed of the ball

(A) A (B) B (C) C (D) D

17. An electron of mass me initially at rest takes time t

1 to move a distance s in a uniform electric field in the

same field environment, a proton of mass mp initially at rest takes time t

2 to move the same distance (in

the opposite direction). lgnoring gravity, the ratio t2/t

1 is :

(A) 1 (B)

2/1

p

e

mm

&&'

())*

+(C)

e

p

m

m(D)

2/1

e

p

m

m&&'

())*

+

18. A simple camera with a converging lens of 60 mm focal length is focused on very far objects. To focus thecamera on a nearby object 1.5 m away, the distance between the film and lens will have to be:(A) decreased by 2.5 mm(B) increased by 2.5 mm(C) kept fixed as before. but aperture increased by a factor of 2.5(D) kept fixed as before, hut aperture decreased by a factor of 2.5

19. A molecule of gas in a container hits one wall (1) normally and rebounds back. It suffers no collision andhits the opposite wall (2) which is at an angle of 30º with wall 1.

30º

Wall 1

Wall 2

Assuming the collisions to be elastic and the small collision time to be the same for both the walls, themagnitude of average force by wall 2. (F

2) provided to the molecule during collision satisfy :

(A) F1 > F

2(B) F

1 < F

2

(C) F1 = F

2, both non-zero (D) F

1 = F

2 = 0

20. A stone dropped from the window of a stationary train hits the ground and comes to rest. An identical

stone is dropped from the window when the same train is moving with speed v and it comes to rest on the

ground. Assume that in each case, the entire energy lost in impact goes into heating the stone. Then

(A) The first stone is is slightly more heated than the second.

(B) The second stone is slightly more heated than the first.

(C) Both the stones will be raised to the same slightly higher) temperature.

(D) The second stone will be slightly more heated than the first only if its horizontal speed during fall is

more than the final vertical speed.

21. A negatively charged particle initially at rest is placed in an electric field that varies from point to point.

There are no other fields. Then :

(A) the particle moves along the electric line of force passing through it.

(B) the particle moves opposite to the electric line of force passing through it.

(C) the direction of acceleration of the particle is tangential to the electric line of force at every instant.

(D) the direction of acceleration of the particle is normal to the electric line of force at every instant.

22. There is a steady water flow in a horizontal tube in which one part has cross sectional area A1 and the

other part has cross sectional area A2. Assume that water is incompressible.

If A1/A

2 = 16, the ratio of the speed u

1 in part 1 and the speed u

2 in part 2, i.e. u

1/u

2 is :

(A) 161

(B) 4 (C) 41

(D) 1

23. Positive point charges of magnitude are placed at all the twelve �hour� positions of a clock of radius r. The

clock is mounted on a wall in the normal way. The charge at the position �6� is removed. The resulting

electric field at the centre of the clock is :

(A) 0 (B) 2o r

q4

1,- in the horizontal direction.

(C) 2o r

q4

1,- vertically upward. (D) 2

o r

q4

1,- vertically downward

24. The pair of quantities that do not have the same dimensions is :

(A) Latent heat, specific heat

(B) Gravitational force, Coulomb force

(C) Kinetic energy pf a freely falling body, potential energy of a compressed spring

(D) Coefficient of friction, number of molecules in a container.

25. A block of wood is floating on oil with half of its volume submerged. If the density of oil 840 kg m�3, the

relative density of wood (relative to water) is :

(A) 0.84 (B) 0.42 (C) 0.21 (D) 1.00

26. We are given n resistors, each of resistance R. The ratio of the maximum to minimum resistance that can

be obtained by combining them is :

(A) nn (B) n (C) n2 (D) logn

27. A light string goes over a frictionless polley. At its one end hangs a mass of 2 kg and at the other end

hangs a mass of 6 kg. Both the masses are supported by hands to keep them at rest. When the masses

are released, they being to move and the string gets taut.

(Take g = 10 ms�2) The tension in the string during the motion of the masses is :

(A) 60 N (B) 30 N (C) 20 N (D) 40 N

28. The escape speed of a body from the earth regarded as a uniform (non-rotating) sphere depends on :

(A) the mass of the body.

(B) the direction of projection.

(C) the location of the projection on the earth's surface.

(D) the height of location from the earth�s surface from where the body is launched.

29 . On a day during the Monsoon season, the relative humidity at a place is 90% and the temperature is

15°(C) The saturation vapour pressure of water at this temperature is 0.0169 × 105 Pa. The partial pressure

of water vapour in the air on that day is

(A) 0.9 × 105 Pa (B) 0.0169 × 105 Pa (C) 0.0152 x 105 Pa (D) 1.0 x 105 Pa

30. It is now known that a proton and a neutron consist of three elementary units called 'quarks'. Two types

of quarks are involved: the 'up' quark (u) of charge + 32

e and the �down� quark (d) of charge �31

e, where

e is the magnitude of election's charge. u and d are their antiparticles. An antiparticle has the same

magnitude of charge as the particle but of opposite sign. The possible compositions of a proton and a

neutron are :

(A) p : uud ; n : udd

(B) p : uuu ; n : ddd

(C) p : uu d ; n : ud d

(D) p : uu u ; n : ud d

CHEMISTRY

31. The volume of 0.5 M aqueous NaOH solution required to neutralize 10 ml of 2 M aqueous HCl solution is:

(A) 20ml (B) 40ml (C) 80ml (D) 120ml

32. The compound that can be purified by sublimation is :

(A) Ammonium Sulphate (B) Calcium Carbonate

(C) Calcium Oxide (D) Aluminium Chloride

33. Penicillin was discovered by :

(A) Alexander G. Fleming (B) Emil Fisher

(C) Robert B. Woodward (D) van�t Hoff

34. Among butane,1-butene,1-butanol and butanal, the compound which is most polar is

(A) butane (B) 1-butene (C) 1-butanol (D) butanal

35. Among ethanol, dimethyl ether, methanol, and propanal, the isomers are :

(A) ethanol, dimethyl ether, methanol and propanal

(B) ethanol and methanol

(C) ethanol, dimethyl ether, and methanol

(D) ethanol and dimethyl ether

36. Among Li, Be, N and F, the element having the largest atomic radius, is :

(A) Li (B) Be (C) N (D) F

37. The proof of oxidizing action of hydrogen peroxide in acid solution is in the formation of :

(A) O2

(B) H2O

(C) both H2O and O

2(D) both H

3O+ and O

2

38. A gel toothpaste is a mixture of a :

(A) liquid in a solid (B) solid in a gas (C) liquid in a liquid (D) gas in a solid

39. 3.01×1023 molecules of elemental Sulphur will react with 0.5 mole of oxygen gas completely to produce

(A) 6.02 × 1023 molecules of SO3

(B) 6.02 × 1023 molecules of SO2

(C) 3.01 × 1023 molecules of SO3

(D) 3.01 x 1023 molecules of SO2

40. The pair of metals which will produce hydrogen gas in reaction with acid is :

(A) Mg, Cu (B) Mg, Ag (C) Zn, Pb (D) Cu, Zn

41. The correct order of pH is :

(A) Lemon juice < water < Milk of Magnesia (B) Lemon juice > water > Milk of Magnesia

(C) Water > lemon juice > milk of Magnesia (D) Milk of Magnesia > lemon juice > water

42. The solubility of a gas in a solution is measured in three cases as shown in the figure given below where

w is the weight of a solid slab placed on the top of the cylinder lid. The solubility will follow the order :

gas

solution

w

gas

solution

w w

gas

solution

w w w

(A) a > b > c (B) a < b < c (C) a = b = c (D) a >b < c

43. A Daniel cell converts :

(A) electrical energy to chemical energy (B) chemical energy to electrical energy

(C) mechanical energy to chemical energy (D) potential energy to electrical energy

44. One of the major components in compressed natural gas (CNG) is :

(A) carbon dioxide (B) acetylene (C) methane (D) water gas

45. Dehydration of 2-pentanol gives :

(A) pentane (B) Only 1-pentene

(C) Only 2-pentene (D) A mixture of 1-pentene and 2-pentene

BIOLOGY

46. A cancer which is not a tumor is :

(A) Lymphoma (B) Leukemia (C) Prostate cancer (D) Oral cancer

47. The phase of the cell cycle in which DNA synthesis takes place is :

(A) G1 phase (B) S phase (C) G2 phase (D) G0 phase

48. You have a tube containing 102 bacteria. You have taken out 102 bacteria. How many bacteria are left in

the tube ?

(A) approximately 107 (B) approximately 106 (C) approximately 105 (D) approximately 109

49. Association in which both the organisms get benefited is :

(A) Commensalism (B) Mutualism (C) Ammensalism (D) Parasitism

50. You are part of a scientific expedition that has ventured deep into the Amazon rain forest. You spot a tree

with branches spread over a large area. What can you conclude about the root structure of the tree?

(A) It is dicotyledonous

(B) It is monocotyledonous

(C) It may be either monocotyledonous or dicotyledonous

(D) There is no correlation between foliage and root structure

51. Alleles are :

(A) Different forms of the same protein (B) Two different genes

(C) Different forms of the same gene (D) Two different proteins

52. Diet rich in carotenoids is beneficial because :

(A) They act as free radical scavengers (B) They absorb harmful UV rays

(C) They help in curing cancer (D) They are rich source of iron

53. The amount of CO2 plant is greater at night than during the day because :

(A) The rate of respiration is higher at night.

(B) More CO2 is produced because it is colder during the night.

(C) Photosynthesis during the day uses up some of the CO2 produced by respiration.

(D) More glucose is available for respiration during the night

54. Osmosis takes place between two solutions separated by a semipermeable membrane because.

(A) Water molecules move from the more dilute solution to the less dilute solution

(B) Solute molecules move from the less dilute solution to the more dilute solution

(C) Water molecules move from the less dilute solution to the more dilute solution

(D) Solute molecules move from the more dilute solution to the less dilute solution

55. Arteries do not have valves but veins do, because :

(A) Arteries have a narrower lumen than veins

(B) Arteries have thicker walls than veins

(C) Arteries carry oxygenated blood whereas veins carry deoxygenated blood

(D) Valves prevent backflow of blood in veins

56. If a person's spinal cord is injured which of the following functions might be affected ?

(A) Talking (B) Seeing (C) Sneezing (D) Hearing

57. Use of an insecticide in an island made a certain insect species extinct. A few years later a tree species

was also found to be extinct. This may be because :

(A) The tree is pollinated by the insect (B) The insect used to live on the tree

(C) The insect used to eat the leaves of the tree (D) The tree is insectivorous

58. Why is it advisable to take antibiotics if someone is suffering from gastric ulcers ?

(A) Antibiotics reduce gastric acid secretion

(B) antibiotics prevent ulcers from being infected

(C) Antibiotics reduce gastric enzyme secretion

(D) Gastric ulcers are caused by bacteria

59. You are synthesizing a 5 amino acid containing peptide from the pool of 20 standard amino acids by

choosing amino acids randomly. What is the probability of selecting Gly�Gly�Gly-Gly

(A) 0 (B) 1/205 (C) 1/20 (D) 1/(20 × 5)

60. The appropriate description of animal hormones is,

(A) Have size smaller than 5 kDa (B) Comprise of proteins only

(C) Comprise of lipid molecule only (D) Are pour directly into the blood

PART-II (2 Mark)

MATHEMATICS

61. Five real numbers x1, x

2, x

3, x

4, x

5 are such that :

16x49x34x21x 4321 .!.!.!. + 5 25x5 . = 2

xxxxx 54321 !!!!

The value of 2

xxxxx 54321 !!!!is

(A) not uniquely determined (B) 55

(C) 110 (D) 210

62. The coefficient of x30 in the expansion of :

(1 + 2x + 3x2 + .... 21x20)2 is :

(A) 2706 (B) 2450 (C) 1481 (D) 256

63. A billiards table of grid size 8 × 10 has four holes in the A, B, C, D. A ball starting from the point P on the

side AD, as in the figure, strikes against CD at an angle� 45°, gets reflected and moves on striking against

the other sides. Which hole will the ball fall into ?

P

D C

BA

(A) B (B) C (C) D (D) no hole

64. In triangle ABC, the coordinates of A and B are respectively (2,3) and (8,10). It is known that C also

has integer coordinates. The minimum possible area of ABC is :

(A) 0 (B) 21

(C) 1 (D) 23

65. A shop-keeper increases the price of a commodity by x%. some time later, he reduces the new price

by y% and notices that the price is now the same as it was originally. The value of x1

y1 . is :

(A) 100

1. (B) 0 (C) 100

1(D) not uniquely determinable

PHYSICS

66. An Insulated vessel contains 0.4 kg of warer at 0ºC. A piece of 0.1 kg ice at �15°C is put into it and

steam at 100ºC is bubbled into it until all ice is melted and finally the contents are liquid water at 40ºC.

Assume that the vessel does not give or take any heat and there is no loss of matter and heat to the

surroundings. Specific heat of ice is 2.2 × 103 J kg-1K-1, heat of fusion of water is 333 × 103 J kg�1 and heat

of vaporization of water is 2260 × 103 J kg�1. The amount of steam that was bubbled into the water is

about :

(A) 34.7 gram (B) 236.0 gram (C) 0.023 gram (D) 48.0 gram

67. A light source is placed 100 cm away from a screen. A converging lens placed at a certain position

between the source and the screen focuses the image of the source on the screen. The lens is moved a

distance of 40 cm and it is found that it again focuses the image of the source on the screen. The focal

length of the lens is :

(A) 21 cm (B) 30 cm (C) 40 cm (D) 67 cm

68. A rubber pipe with a diameter of 10 cm is connected to a nozzle 2 cm in diameter. Water flowing through

the. pipe at a speed of 0.6 ms�1, comes out like a jet through the nozzle. The backward force of the

nozzle is about :

(A) 7.7 N (B) 67.9 N (C) zero (D) 2.8 N

69. A power supply of fixed emf E is connected to a variable resistor (resistance = R) and an ammeter of

resistance RA. The internal resistance of the supply is r. The potential difference bctween the terminals of

the power supply in closed circuit is denoted by V and the current in the circuit is denoted by I. A graph

is obtained between V and I by drawing varying amount of current from the supply. The correct V-I graph

for the given situation is :

E

V

E/r I

E

V

I(I) (II)

V

I

V

I

E/r

(III) (IV)

(A) Graph 1 (B) Graph II (C) Graph III (D) Graph IV

70. A thermometer uses �density of water� as thermometric property. The actual reading in the thermometer

is �height of water�(h) which is inversely proportional to density of water (d). In a certain temperature

range, density of water varies with temperature as shown. The graph is symmetric about the maximum

d

De

nsity

of

wat

er

Tempeature

T1 T2

Two identical bodies (of same mass and specific heat) at different temperatures T1 and T

2 show the same

reading of height h1 = h

2 in the thermometer. The bodies are brought into contact and allowed to reach

thermal equilibrium. The thermometer reading �height of water for final equilibrium state h1 satisfies.

(A) hf =

2hh 21 ! = 21 hh /

(B) hf > h

1 = h

2

(C) hf < h

1 = h

2

(D) hf may be greater or less than h

1 = h

2 , depending on the specific heat of the bodies.

CHEMISTRY

71. The density of a salt solution is1.13 g cm�3 and it contains 18% of NaCI by weight. The volume of the

solution containing 36.0 g of the salt will be :

(A) 200 cm3 (B) 217 cm3 (C) 177 cm3 (D) 157cm3

72. Esterification of a compound ��X�� with molecular formula C3H

6O

2 with an alcohol ��Y�� produces a com-

pound with molecular formula C5H

10O

2. X and Y, respectively, are :

(A) propanoic acid and methanol (B) propanoic acid and ethanol

(C) acetic acid and ethanol (D) butyric acid and methanol

73. 10 g of a crystalline metal sulphate salt when heated generates approximately 6.4 g of an anhydrous salt

of the same metal. The molecular weight of the anhydrous salt is 160 g. The number of water molecules

present in the crystal is :

(A) 1 (B) 2 (C) 3 (D) 5

74. In the reaction of FeSO4 with K

2Cr

2O

7 in the presence of an acid, the changes in the formal oxidation

numbers of Cr and Fe, respectively, are :

(A) 1 and 5 (B) 3 and 1 (C) 5 and 1 (D) 1 and 3

75. An aqueous solution of a metal salt (X) reacts with carbon dioxide to give a water soluble compound (Y)

which on heating gives the starting metal salt back. Y when present in water does not produce lather with

soap. The compounds X and Y, respectively are

(A) CaCO3 and Ca(HCO

3)2

(B) Mg (HCO3)

2 and MgCO

3

(C) Ca(HCO3)

2 and CaCO

3(D) MgCO

3 and Mg (HCO

3)

2

BIOLOGY

76. Plasmolysis is not observed in boiled plant tissue because :

(A) The cell wall becomes impermeable to water

(B) The cell membrane disintegrates

(C) The cell wall disintegrates

(D) The cell membrane becomes impermeable to water

77. If the analogy of a city is applied to a eukaryotic cell then which of the following statements is correct ?

(A) Nucleus as a library and ribosome as a slaughter house

(B) Nucleus as a police station and mitochondria as powerhouse

(C) Mitochondria as powerhouse and Golgi as a cargo sorting facility

(D) Mitochondria as powerhouse and nucleus as slaughter house

78. The placenta tissue in mammals originates from :

(A) The mother only

(B) The foetus only

(C) Both the mother and the foetus

(D) Originates from the mother but taken over by the foetus

79. Both bacteria and amoeba are unicellular organisms which may live in aqueous environment. Bacteria do

not burst by taking up water from the surrounding because they have cell walls. Amoeba do not have cell

walls but yet do not burst because :

(A) Amoeba eliminates excess water by the help of contractile vacuoles.

(B) The cytoplasm of amoeba is isotonic to surrounding water.

(C) The cytoplasm of amoeba is hypotonic to surrounding water.

(D) Amoeba does not take up water from the surroundings.

80. In the lunch, you ate boiled green vegetables, a piece of cooked meat, one boiled egg and a sugar candy.

Which one of these foods may have been digested first ?

(A) Boiled green vegetables (B) The piece of cooked meat

(C) Boiled egg (D) Sugar candy