KVPY SA Stream paper-2007

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PART-I (1 Mark)

MATHEMATICS

1. Let s1 (n) be the sum of the first n terms of the arithmetic progression 8, 12, 16, ....... and let s2(n) be thesum of the first n terms of arithmetic progression 17, 19, 21 ......... If for some value of n, s1(n) = s2(n) thenthis common sum is :(A) not uniquely determinable (B) 260(C) 216 (D) 200

2. The number of solutions are in [0, 2] such that (sin(2x))4 = 1/8 is(A) 2 (B) 4 (C) 8 (D) 16

3. The set of real numbers r satisfying :

07r.3–r.45r.8–r.3

2

2

is(A) the set of all real numbers(B) the set of all positive real numbers(C) the set of all real numbers strictly between 1 and 5/3(D) the set of all real numbers which are either less than 1 or greater than 5/3

4. If a, b and c are distinct real numbers such that a : (b + c) = b : (c + a) then(A) a, b, c are all positive (B) a, b, c are all negative(C) a + b + c = 0 (D) ab + bc + ca + 1 = 0

5. How many positive real numbers x are there such that xxx xxx ?

(A) 1 (B) 2 (C) 4 (D) infinite

6. Let [x] denote the greatest integer part of a real number x. If

40

1n

2

2nM

then M equals(A) 5700 (B) 5720 (C) 5740 (D) 11060

7. Suppose for fixed real numbers a and b.f(x) = x3 + ax2 + bx + chas 3 distinct roots for c = 0. Then(A) fc(x) has 3 distinct roots for all real c(B) fc(x) has 3 distinct roots for all real c > 0 or for all real c < 0, but not for both(C) fc(x) has 3 distinct roots for all real c in (p, q) for some p < 0 and q > 0(D) fc(x) need not have 3 distinct roots for any real c other than zero

YEAR-2007 (KVPY-STREAM-SA)


8. Given a semicircle of radius 1, let a be the side of an equilateral triangle which is inscribed in thesemicircle with its vertices on the boundary of the semicircle (boundary includes the bounding diameteralso). Then the set of possible values of a is(A) {1}

(B) {1, 32

}

(C) the set of all positive real numbers not exceeding 32

(D) the set of all real numbers which are greater than or equal to 1, but less than or equal to 32

9. A ray of light originating at the vertex A of a square ABCD passes through the vertex B after gettingreflected by BC, CD and DA in that order. If is the angle of the initial position of the ray with AB then sinequals.

(A) 13/2 (B) 13/3 (C) 3/5 (D) 4/5

10. Let ABC be triangle with AB = AC = 6. If the circumradius of the triangle is 5, then BC equals(A) 25/3 (B) 9 (C) 48/5 (D) 10

11. Let D and E be points on sides AB and AC of a triangle ABC such that(A) DE is parallel to BC(B) DE divides the area of the triangle ABC into two equal parts.The ratio of the distance from A to DE to the distance between DE and BC is

(A) 1 : 1 (B) 2 : 1 (C) 2 : 1 (D) 2 + 1 : 1

12. If and are acute angles such that cos2 + cos2 = 3/2 and sin . sin = 1/4, then + equals(A) 30° (B) 45° (C) 60° (D) 90°

13. There is a point inside an equilateral triangle which is at distances 1, 2 and 3 from the three sides. Thearea of the triangle is(A) not uniquely determinable (B) 6

(C) 36 (D) 312

14. The wealth of a person A equals the sum of that of B and C . If he distributes half of his wealth betweenB and C in the ratio 2 : 1 then the wealth of B equals the sum of that of A and C. Then the fraction of thewealth that A should distribute between B and C in the ratio 1 : 2 so that the wealth of C equals the sumof that of A and B is(A) 1/2 (B) 2/3 (C) 3/4 (D) 1

15. You have a measuring cup with capacity 25 ml and another with capacity 110 ml, the cups have nomarkings showing intermediate volumes. Using large container and as much tap water as you wish.What is the smallest amount of water you can measure accurately ?(A) 1 ml (B) 5 ml (C) 10 ml (D) 25 ml


16. A person travels in a car from his village to a town at a speed of 50 kms/hr for four hours. There he spendsan hour moving about 20 kms. He then returns to his village at a speed 40 kms/hr. His average speed overthe whole journey (in kms/hr) is

(A) 44 (B) 42 (C) 4494

(D) 4632

17. There are 20 unit cubes all of whose faces are white, and 44 unit cubes all of whose faces are red. Theyare put together to form a bigger cube (4 × 4 × 4). What is the minimum number of white faces visible onthis larger cube ?(A) 20 (B) 14 (C) 12 (D) 8

18. The number of 2-digit numbers n such that 3 divides n – 2 and 5 divides n – 3 is(A) 5 (B) 6 (C) 7 (D) 10

19. Let m be the number of ways in which two couples can be seated on 4 chairs in a row so that no wife isnext to her husband and n be the number of ways in which they can be seated in 4 chairs in a circle. Inthe latter case, rotations are considered different configurations. Then(A) m = n (B) m = 2n (C) m = 4n (D) m = 8n

20. A certain school has 300 students. Every student reads 5 newspapers and every newspaper is read by 60students. Then the number of newspapers.(A) is at least 30 (B) is at most 20(C) is exactly 25 (D) cannot be determined by the data

PHYSICS

21. A fully loaded elevator has a mass of 6000 kg. The tension in the cable as the elevator is accelerateddownward with an acceleration of 2ms–2 is (Take g = I0 ms–2)(A) 7·2 × 104 N (B) 4.8 × 104 N (C) 6 × 104 N (D) 1.2 × 104 N

22. A body is moving with constant acceleration from A to B in a straight line. C is the mid-point of AB. If u andv are the speeds at A and B respectively. The speed at C is

(A)2

vu (B)

2u–v

(C)2

vu 22 (D)

2u–v 22

,23. A ray of light enters a slab of material with increasing refractive index. Four possibilities of the trajectoryof the ray are shown below.

Slab withincreasingRefractiveindex

DCBA

The correct choice is :(A) A (B) B (C) C ( D) D


24. The isotope 23892U decays through a chain of and emissions ending up at the product 206

82Pb . This

chain involves(A) 8 emission and 6 emissions(B) 8 emission and 8 emissions(C) 6 emission and 8 emissions(D) 6 emission and 6 emissions

25. Figure shows an assembly consisting of a number of pendulums of varying lengths. The driver pendulum ispulled aside and released so that it oscillates in a plane perpendicular to that of the diagram. It will beobserved that

String

Driverpendulum

(A) all pendulums oscillate with the frequency of the driver pendulum and have the same amplitude.(B) pendulums oscillate with different frequencies but equal amplitude, the shortest pendulum oscillatingwith the highest frequency.(C) all pendulums oscillate with the frequency of the driver pendulum; the pendulum with length equal tothat of the driver has the greatest amplitude.(D) pendulums oscillate with different frequencies and different amplitudes.

26. You are riding on your bicycle with inflated tyres. Your friend asks for a lift and sits on the carrier behindyou :(A) The air pressure in the tyres increases.(B) The air pressure in the tyres decreases.(C) The air pressure in the tyres remains the same.(D) Nothing in the system changes except the reaction of the ground

27. The circuit shown has 3 identical light bulbs A, B, C and 2 identical batteries E1, E2 . When the switch isopen, A and B glow with equal brightness. When the switch is closed:

A

B

C

S

E1

E2

(A) A and B will maintain their brightness and C will be dimmer than A and B.(B) A and B will become dimmer and C will be brighter than A and B.(C) A and B will maintain their brightness and C will not glow.(D) A, B and C will be equally bright.


28. A boat at rest has two persons of unequal weights seated at either end. If they walk across the boat andinterchange their positions,(A) the boat will move in the direction of walking of the lighter person.(B) the boat will move in the direction of walking of the heavier person.(C) the boat will not move at all.(D) the boat will oscillate about a mean position and stop once the persons have moved to the newpositions.

29. A physical quantity that is conserved in a process(A) must have the same value for all observers.(B) can never take negative values.(C) must be dimensionless.(D) need not necessarily be a scalar.

30. A coolant in a chemical or nuclear plant is a liquid that is used to prevent different parts of a plant fromgetting too hot. One important property of coolant is that it(A) should have low specific heat.(B) should have high specific heat.(C) high density and low thermal conductivity.(D) low density and high thermal conductivity.

CHEMISTRY

31. The half-life of Co6027 is 5.3 years. How much of 20 g of Co60

27 will remain radioactive after 21.2 years ?

(A) 10 g (B) 1.25 g (C) 2.5 g (D) 3.0 g

32. The element which reacts both with acids and bases to produce a salt and hydrogen gas is -(A) Zn (B) Mg (C) Li (D) S

33. The compound having a triple bond is -(A) Benzene (B) Cyclohexane (C) Acetylene (D) Glucose

34. An element which has 2 electrons less than that in Ne is -(A) Mg (B) Na (C) O (D) F

35. Chlorine gas is produced from HCI by the addition of -(A) K2SO4 (B) KCl (C) KNO3 (D) KMnO4

36. Among HCl, HBr, HF, and HI the weakest acid in water is -(A) HCl (B) HF (C) HBr (D) HI

37. Products of the reaction Ca(OH)2 + 2NH4Cl, are(A) CaCI2 + 2NH3 + 2H2O (B) CaCl2 + NH4OH + H2

(C) CaO + 2NH3 + 2H2O (D) CaO + NH4OH + H2


38. When a few drops of concentrated sulphuric acid are added to a few drops of a clear sugar (sucrose)solution in a test tube, the solution(A) remains colorless (B) turns black (C) turns blue (D) turns white

39. The reaction ZnO + C Zn + CO is an example of a(A) Combination reaction (B) Reduction-oxidation reaction(C) Displacement reaction (D) Decomposition Reaction

40. The monomer of Teflon is :

(A)Me

(B)Cl

(C) CN (D)FF

FF

BIOLOGY41. In a wound, 'pus' is a :

(A) A mixture of destroyed germs, killed leucocytes and damaged tissue cells(B) Concentrated blood plasma(C) Thick mucus secretion(D) Concentrated secretion of the sebaceous gland

42. Discovery of fossils has provided biologists with significant clues as in the steps in evolution. Archaeop-teryx one such example, which is connection link between :(A) Pisces and amphibian (B) Amphibia and reptilia(C) Reptilia and aves (D) Aves and mammalian

43. Which of the following is a bacterial disease ?(A) Smallpox (B) Measles (C) Meningitis (D) Rabies

44. During photosynthesis, light energy :(A) Is converted to chemical energy (B) Is converted to kinetic energy(C) Is the catalyst (D) Dissociates CO2 directly

45. Majority of the world population depends largely on the following for their staple food :(A) Fungi and algae (B) Animal products(C) Dicotyledenous (D) Monocotyledenous plants

46. If you put a nail at the middle of a young plant and allow it to grow, then :(A) You will find the nail at the same position after the tree is fully grown(B) The nail will fall out(C) The nail will rise along with the tree(D) The nail will come closer to the ground

47. If you are asked to write on a topic of interest, you can read as many books as you want but never copysomeone else's writing on the same topic. The act is called plagiarism and is morally incorrect, as :(A) You are stealing someone else's labor (B) It is a punishable offence in court(C) You have not paid money to do so (D) A patent exists on the writing


48. A couple has 8 children, all boys. What is the chance that their ninth child will be another boy ?(A) 1/2 (B) 1/4 (C) 1/8 (D) 1/16

49. Grapes were put in a concentrated sugar solution. On examination after 12 hours, the grapes wereshrunken. This is because :(A) Grapes become sweeter (B) Water evaporates from the solution(C) Sugar induces disintegration of grapes (D) Loss of water from grapes by osmosis

50. On a normal sunny day, rate of photosynthesis (per unit time) is maximum during :(A) Early morning (B) Between late morning to before noon(C) Midday (D) Late evening

PART-II (2 Mark)

MATHEMATICS

51. The number of distinct pairs (x, y) of the real numbers satisfying x = x3 + y4 and y = 2xy is :(A) 5 (B) 12 (C) 3 (D) 7

52. We want to find a polynomial f(x) of degree n such that f(1) = 2 and f(3) = . Which of the following is

true ?(A) There does not exist such a polynomial(B) There is exactly one such polynomial and it has degree 1(C) There are infinitely many such polynomials for each n 1(D) There are infinitely many such polynomials for each n 2 but not infinitely many for n = 1

53. A polynomial p(x) when divided by x2 – 3x + 2 leaves remainder 2x – 3. Then :(A) p(x) must have a root between 0 and 3(B) p(x) cannot have a root between 0 and 3(C) p(x) must have a real root but may or may not be between 0 and 3(D) p(x) need not have a real root

54. In a rectangle ABCD , M and N are the midpoints of the sides BC and CD respectively. If ANM= 90° thenAB : BC is :

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

55. Consider the triangle OAB in the xy - plane where O = (0, 0), A = (6, 0), B = 3,2 . A square PQRS is

inscribed in the square with P, Q on OA, R on AB and S on BO. Then the side of the square equals:

(A) 2/3 (B)49

(C)25

23

(D) 2

56. Let a semicircle with centre O and diameter AB. Let P and Q be points on the semicircle and R be a point

on AB extended such that OA = QR < PR. If POA = 102° then PRA is :(A) 51° (B) 34°(C) 25.5° (D) not possible to be determined


57. Let A, B, C, D be collinear points in that order. Suppose AB : CD = 3 : 2 and BC : AD = 1 : 5. Then AC :BD is :(A) 1 : 1 (B) 11 : 10 (C) 16 : 11 (D) 17 : 13

58. Given a sphere, a cone is constructed so that the cone and the sphere have the same volume, but thetotal surface area of the cone is k times that of the sphere, where k is determined so that there is a uniquecone satisfying this property. Then k equals :

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

59. How many 4-digit numbers are there with the property that it is a square and the number obtained byincreasing all its digits by 1 is also a square ?(A) 0 (B) 1 (C) 2 (D) 4

60. The number of positive fractions m/n such that 1/3 < m/n < 1 and having the property that the fractionremains the same by adding some positive integer to the numerator and multiplying the denominator bythe same positive integer is :(A) 1 (B) 3 (C) 6 (D) infinite

PHYSICS

61. The rear wheels of a car are turning at an angular speed of 60 rad/s. The brakes are applied for 5s,causing a uniform angular retardation of 8 rads–2. The number of revolutions turned by the rear wheelsduring the braking period is about(A) 48 (B) 96 (C) 32 (D) 12

62. The energy released in a modest size atomic bomb (20 kiloton) is about 1014 J. On a monsoon day inMumbai, there was a heavy rainfall of about 100 cm over an area of about 100 km2. The energy releasedin the atmosphere on that day is roughly equivalent to that released in(A) 2000 atomic bombs. (B) 100 atomic bombs(C) atomic bomb (D) negligible compared to an atomic bomb.

63. A battery of 10 V and negligible internal resistance is connected across the diagonally opposite corncr ofa cubical network consisting of 12 resistors each of resistance 1 . The total current I in the circuitexternal to the network is :

A

10V

(A) 0.83 A (B) 12 A (C) 1 A (D) 4 A


64. Light incident on a rotating mirror M is reflected to a fixed mirror N placed 22.5 km away from M. The fixedmirror reflects it back to M (along the same path) which in turn reflects the light again along a directionthat makes an angle of 27° with the incident direction. The speed of rotation of the mirror is:(A) 250 revolutions s–1 (B) 500 revolutions s–1

(C) 1000 revolutions s–1 (D) 125 revolutions s–1

65. In aerial mapping a camera uses a lens with a 100 cm focal length. The height at which the airplane mustfly, so that the photograph of a 1 km long strip on the graund fits exactly on Ihe 20 cm long filmstrip of thecamera, is:(A) 200 km (B) 20km (C) 5 km (D) 1 km

CHEMISTRY

66. A 3 N solution of H2SO4 in water is prepared from Conc. H2SO4 (36 N) by diluting -(A) 20 ml of the conc. H2SO4 to 240 ml (B) 10 ml of the conc. H2SO4 to 240 ml(C) 1 ml of the conc. H2SO4 to 36 ml (D) 20 ml of the conc. H2SO4 to 36 ml

67. The gas responsible for under water corrosion of iron and the product of corrosion, respectively, are -(A) Dissolved oxygen and Fe2O3 (B) Dissolved hydrogen and Fe2O3

(C) Dissolved oxygen and Fe(OH)3 (D) Dissolved nitrogen and Fe(OH)3

68. The solubility curve of KNO3 as a function of temperature is given below

0 20 40 60 80 100

0

50

100

150

200

250

Temperature (°C)

Sol

ubili

ty(g

/100

mlw

ater

)

The amount of KNO3 that will crystallize when a saturated solution of KNO3 in 100 ml of water is cooledfrom 90°C to 30 °C, is(A) 16 g (B) 100 g (C) 56 g (D)160 g

69. In the reaction.

Glucose yeast X 4KMnO Y

the products X and Y, respectively, are -

(A) EtOH, CH3COOH (B) MeOH, HCOOH(C) EtOH, CH3CHO (D) EtOH, HOCH2CH2OH


70. A sample of water was checked for suitability for drinking and was subjected to a chemical test. Pure zincgranules and sulphuric acid were added to the water sample. The effervescence that resulted from thereaction was bubbled through a tube containing lead acetate solution. A black precipitate appeared. Theoutgoing gas was subsequently passed through a heated copper tube, a black mirror appeared on thewall of the tube. The first and second black substances, respectively, are :(A) HgS and CuS (B) PbS and CuS (C) As and Hg (D) PbS and As

BIOLOGY

71. A swimmer crossing the British channel after 2 hrs of vigorous swimming experiences severe musclearmors and is forced to discontinue. Which of the following options given' below could give rise to thisproblem :(A) Muscle tear (B) Sea winter diffusion into muscles(C) Bite of pirranahas (D) Lactic acid accumulation

72. In an experiment to monitor the ascent of sap, the following treatments were carried out to a twig dippedin water. In which case wilting will be observed ?(A) Bark removed (B) Pith removed(C) Twig cut into half (D) Glucose added to water

73. Root pressure on a tree is typically about 2-6 atm. This is sufficient to raise the water level upto a few feet.Tall trees get water at the top due to :(A) Capillary rise and suction (B) A pump operating in the growing tree(C) Fed by rain water (D) Water content in the atmosphere

74. A patient given broad spectrum antibiotic suffered from vitamin deficiency because :(A) Antibiotic inactivated the vitamins(B) Antibiotic inhibited the synthesis of vitamins(C) Antibiotics killed the commensals in the gut which produced vitamins(D) Antibiotics killed the vitamin producing cells in liver

75. Partial removal of liver is not harmful because :(A) Liver being a large organ can suffice the functions even if a part is removed(B) Liver is not a very essential organ of the body

(C) Liver has regenerative capacity and will grow after partial hepatectomy

(D) The function of liver can be taken over by kidneys

KVPY SA Stream paper-2007

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