KVPY SA Stream paper-2007

 YEAR-2007  YEAR-20 07 (KVPY-STRE (KVPY-STREAM AM-SA) -SA) 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 s 2(n) be the sum of the first n term s of arithmetic progression 17, 19, 21 ......... If for some value of n, s 1(n) = s2(n) then this common sum is :

2.

(A) not uniquely determinable

(B) 260

(C) 216

(D) 200

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

3.

(B) 4

(C) 8

(D) 16

The set of real numbers r satisf ying :

3.r 2 – 8.r  5 4.r 2 – 3.r  7

0

is (A) the set of all real numbers (B) the set of all positive real numbers (C) the set of all real numbers str ictly between 1 and 5/3 (D) the set of all real numbers which are either less than 1 or greater than 5/3 4.

5.

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

How many positive real numbers x are there such that x x (A) 1

6.

(B) 2

x

x  x x  ?

(C) 4

(D) infinite

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

 n2     2  n 1  40

M



then M equals (A) 5700 7.

(B) 5720

(C) 5740

(D) 11060

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

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8.

Given a semicircle of radius 1, let

  be the side of an equilateral triangle which is inscribed in the

a

semicircle with its vertices on the boundary of the semicircle (boundary includes the bounding diameter  also). Then the set of possible values of  a is (A) {1} (B) {1,

2 3

}

(C) the set of all positive real num bers not exceeding

2 3

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

 9.

2 3

 A ray of light originating at the vertex A of a square ABCD passes through the vertex B after getting reflected by BC, CD and DA in that order. If   is the angle of the initial position of the ray with AB then sin  equals. (A) 2 / 13

10.

(C) 3/5

(D) 4/5

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

11.

(B) 3 / 13

(B) 9

(C) 48/5

(D) 10

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

12.

(C)

2  : 1

(D)

2  + 1 : 1

  and   are acute angles such that cos 2 + cos2 = 3/2 and sin   . sin   = 1/4, then  +  equals If   (A) 30°

13.

(B) 2 : 1

(B) 45°

(C) 60°

(D) 90°

There is a point inside an equilateral triangle which is at distances 1, 2 and 3 from the three sides. The area of the triangle is

14.

(A) not uniquely determinable

(B) 6

(C) 6 3

(D) 12 3

The wealth of a person A equals the sum of that of B and C . If he distributes half of his wealth between B 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 the wealth that A should distribute between B and C in t he ratio 1 : 2 so that the wealth of C equals the sum of that of A and B is (A) 1/2

15.

(B) 2/3

(C) 3/4

(D) 1

You have a measuring cup with capacity 25 ml and another with capacity 110 ml, the cups have no markings showing interm ediate volumes. Using large container and as much tap water as you wish. What is the sm allest amount of water you can measure accurately ? (A) 1 ml

(B) 5 ml

(C) 10 ml

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(D) 25 ml

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16.

 A person travels in a car from his his village to a town at a speed of 50 kms/hr for four hours. There he spends an hour moving about 20 kms. He then returns to his village at a speed 40 kms/ hr. His average speed over  the whole journey (in kms/hr) is (A) 44

17.

(B) 42

(C) 44

4 9

(D) 46

2 3

There are 20 unit cubes all of whose faces are white, and 44 unit cubes all of whose faces are r ed. They are put together to form a bigger cube (4 × 4 × 4). 4). What is the minimum number of white faces visible on this larger cube ? (A) 20

18.

(C) 12

(D) 8

The number of 2-digit numbers n such that 3 divides n – 2 and 5 divides n – 3 is (A) 5

19.

(B) 14

(B) 6

(C) 7

(D) 10

Let m be the number of ways in which two couples can be seated on 4 chairs in a row so that no wife is next to her husband and n be the number of ways in which they can be seated in 4 chairs in a circle. I n the latter case, rotations are considered differ ent configurations. Then (A) m = n

20.

(B) m = 2n

(C) m = 4n

(D) m = 8n

 A certain school has 300 students. Every student reads 5 newspapers newspapers and every newspaper newspaper is read by 60 students. 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 accelerated downward with an acceleration of 2ms –2 is (Take g = I0 ms –2) (A) 7�2 × 104 N

22.

(B) 4.8 × 104 N

(C) 6 × 104 N

(D) 1.2 × 104 N

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

(A) 23.

,

uv 2

(B)

v – u 2

(C)

u2

 v2 2

(D)

v 2 – u2 2

A ray of light light enters enters a slab slab of of material material with with incr increas easing ing refra refractiv ctive e index. index. Four Four poss possibi ibilit lities ies of of the traje trajector ctory y of the ray are shown below. below.

Slab with increasing Refractive index

 A

B

C

D

The correct choice is : (A) A

(B) B

(C) C

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( D) D

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24.

238 206 The isotope U92  decays through a chain of   and    emissions ending up at the product Pb82 . This

chain involves

25.

(A) 8  em  emission

and

6    emissions

(B) 8  em  emission

and

8    emissions

(C) 6  em  emission

and

8    emissions

(D) 6  em  emission

and

6    emissions

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

String Driver  pendulum

(A) all pendulums oscillate with the frequency of the driver pendulum and have the sam e amplitude. (B) pendulums oscillate with different f requencies but equal amplitude, the shortest pendulum oscillating with the highest frequency. frequency. (C) all pendulums oscillate with the f requency of the driver pendulum; the pendulum with length equal to that 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 Your friend asks for a lift and sits on the carrier behind you : (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 E 1, E2 . When the switch is open, A and B glow with equal brightness. When the switch is closed:

C E1

 A

S E2

B

(A) A and B will maintain their brightness and C will be dimm er 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. glow. (D) A, B and C will be equally bright. CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892

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28.

 A boat at rest has two persons of unequal weights seated at either end. If they walk across the boat and interchange 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 new positions.

29.

 A physical quantity that is conserved in a process (A) must have the same sam e 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 prevent different parts of a plant from getting 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. conductivity. (D) low density and high thermal conductivity. conductivity.

CHEMISTRY

31.

60 The half-life of  60 27 Co  is 5.3 years. How much of 20 g of  27 Co  will remain radioactive after 21.2 years ?

(A) 10 g 32.

(D) S

(B) Cyclohexane

(C) Acetylene

(D) Glucose

(B) Na

(C) O

(D) F

(B) KCl

(C) KNO3

(D) KMnO4

 Among HCl, HBr, HBr, HF, HF, and HI the weakest acid in water is (A) HCl

37.

(C) Li

Chlorine gas is produced from HCI by the addition of (A) K2SO4

36.

(B) Mg

 An element which has 2 electrons less less than that in Ne is (A) Mg

35.

(D) 3.0 g

The compound having a triple bond is (A) Benzene

34.

(C) 2.5 g

The element element which which reac reacts ts both both with with acids acids and bases bases to to produ produce ce a salt salt and and hyd hydrog rogen en gas gas is (A) Zn

33.

(B) 1.25 g

(B) HF

(C) HBr

(D) HI

Products of the reaction Ca(OH) 2 + 2NH4Cl, are (A) CaCI2 + 2NH3 + 2H2O

(B) CaCl2 + NH4OH + H2

(C) CaO + 2NH 3  + 2H2O

(D) CaO + NH4OH + H2

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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) re r emains colorless

39.

40.

The reaction ZnO + C

(B) turns black

(C) turns blue

(D) turns white

 Zn + CO is an example of a

(A) Combination reaction

(B) Reduction-oxidation reaction

(C) Displacement reaction

(D) Decomposition Reaction

The monomer of Teflon is : (A)

(B)

(C) Cl

Me

CN

(D)

F

F

F

F

BIOLOGY 41.

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. Archaeopteryx one such example, which is connection connection link between :

43.

(A) Pisces and amphibian

(B) Amphibia and reptilia

(C) Reptilia and aves

(D) Aves and mammalian

Which of the f ollowing is a bacterial disease ? (A) Smallpox

44.

45.

46.

(B) Measles

(C) Meningitis

(D) Rabies

During photosynthesis, light energy : (A) Is converted to chemical energy

(B) Is converted to kinetic energy

(C) Is the catalyst

(D) Dissociates CO 2 directly

Majority of the world population depends largely on the following for their staple f ood : (A) Fungi and algae

(B) Animal products

(C) Dicotyledenous

(D) Monocotyledenous plants

 If you put a nail at the m iddle of a young plant and allow it to grow, then : (A) You 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 gr ound

47.

If you are asked to write on a topic of interest, you can read as many books as you want but never copy someone else’s writing on the same topic. The act is called plagiarism and is morally incorrect, as : (A) (A) Yo You are are stea steali lin ng som some eone one els else’ e’s s la labor bor

(B) (B) It It is is a pun punis isha habl ble e off offen ence ce in cour courtt

(C) You have not paid money to do so

(D) A patent ex exists on th the wr writing

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48.

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

49.

(B) 1/4

(C) 1/8

(D) 1/16

Grapes were put in a concentrated sugar solution. On examination after 12 hours, the grapes were shrunken. This is because :

50.

(A) Grapes become sweeter

(B) W ater evaporates from the solution

(C) (C) Sug Sugar ar indu induce ces s dis disin inte tegr grat atio ion n of grap grapes es

(D) (D) Los Loss s of of wat water er from from grap grapes es by osmo osmosi sis s

On a normal sunny day, day, rate of photosynthesis (per unit t ime) is maximum m aximum 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 = x 3 + y4 and y = 2xy is : (A) 5

52.

(B) 12

(C) 3

(D) 7

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 inf initely many such polynomials for each n   2 but not infinitely many for n = 1 53.

 A polynomial polynomial p(x) when divided by 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 r oot 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 ar e the midpoints of the sides BC and CD respectively. respectively. If  ANM = 90° then  AB : BC is : (A) 2 : 1

55.

(B)

2 :1

(C)

(D) 1: 1

3 :1

Consider the triangle OAB in t he xy - plane where O = (0, 0), A = (6, 0), B =

 



2, 3 . 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) 3 / 2

56.

(B)

9 4

(C)

3 5 2 2

(D) 2

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

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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

58.

(B) 11 : 10

(C) 16 : 11

(D) 17 : 13

Given a sphere, a cone is constructed so that the cone and the sphere have the same volume, but the total surface area of the cone is k times that of the sphere, where k is determined so that there is a unique cone satisfying this property. Then k equals : (A) 1

59.

(B)

(C)

2

3

(D)

3

2

How many 4-digit numbers are there with the property that it is a square and the number obtained by increasing all its digits by 1 is also a square ? (A) 0

60.

(B) 1

(C) 2

(D) 4

The number of positive fractions m/n such that 1/3 < m/n < 1 and having the property that the fraction remains the same by adding some positive integer to the numerator and multiplying the denominator by the 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 wheels during the braking period is about (A) 48

62.

(B) 96

(C) 32

(D) 12

The energy released in a modest size atomic bomb (20 kiloton) is about 10 14 J. On a monsoon day in Mumbai, there was a heavy rainfall of about 100 cm over an area of about 100 km 2. The energy released in the atmosphere on that day is roughly equivalent to that released in

63.

(A) 2000 atomic bombs.

(B) 100 atomic bombs

(C) atomic bomb

(D) negligible compared to an atomic bomb.

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

 A 10V

(A) 0.83 A

(B) 12 A

(C) 1 A

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(D) 4 A

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64.

Light incident incident on a rotating mirror M is reflected to a fixed mirror N placed 22.5 km away from M. The fixed mirror reflects ref lects it back to M (along the sam e path) which in turn reflects the light again along a direction that makes an angle of 27° with the incident direction. The speed of rotation of the mirror is:

65.

(A) 250 revolutions s –1

(B) 500 revolutions s –1

(C) 1000 revolutions s –1

(D) 125 revolutions s –1

In aerial mapping a camera uses a lens with a 100 cm focal length. The height at which the airplane must fly, fly, so that the photograph of a 1 km long strip on the graund fits exactly on Ihe 20 cm long film strip of the camera, is: (A) 200 km

(B) 20km

(C) 5 km

(D) 1 km

CHEMISTRY 66.

67.

68.

 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  to 240 ml

(B) 10 ml of the conc. H2SO4 to 240 ml

(C) 1 ml of the conc. H2SO4 to  to 36 ml

(D) 20 ml of the conc. H2SO4 to 36 ml

The gas responsible for under water corrosion of iron and the product of corrosion, respectively, respectively, are (A) Dissolved oxygen and Fe 2O3

(B) Dissolved hydrogen and Fe 2O3

(C) Dissolved oxygen and Fe(OH) 3

(D) Dissolved nitrogen and Fe(OH) 3

The solubility curve of KNO 3 as a function of tem perature is given below 250

     )     r     e      t     a200     w      l     m      0 150      0      1      /     g 100      (     y      t      i      l      i 50      b     u      l     o      S 0

0

20

40

60

80

100

Temperature (°C)

The amount of KNO 3 that will crystallize when a saturated solution of KNO3 in 100 ml of water is cooled from 90°C to 30 °C, is (A) 16 g 69.

(B) 100 g

(C) 56 g

(D)160 g

In the reaction.

yeast X KMnO 4 Y Glucose                   the products X and Y, respectively, are (A) EtOH, CH3COOH

(B) MeOH, HCOOH

(C) EtOH, CH3CHO

(D) EtOH, HOCH2CH2OH

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70.

 A sample of water was checked for suitability suitability for drinking and was subjected to a chemical test. Pure zinc granules and sulphuric acid were added to the water sample. The effervescence that resulted from t he reaction was bubbled through a tube containing lead acetate solution. A black precipitate appeared. The outgoing gas was subsequently passed through a heated copper tube, a black mirror appeared on the wall of the tube. The first and second black substances, respectively, 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 muscle armors and is forc ed to discontinue. Which of the following options given’ below could give rise to this problem :

72.

(A) Muscle tear

(B) Sea winter diffusion into muscles

(C) Bite of pirranahas

(D) Lactic acid accumulation

In an experiment to monitor the ascent of sap, the following treatments were carr ied out to a twig dipped in water. In which case wilting will be observed ?

73.

(A) Bark removed

(B) Pith removed

(C) Twig cut into half

(D) Glucose added to water  

Root pressure on a tree is typically typically about 2-6 atm. This is sufficient to raise the water level upto a few f eet. Tall trees get water at the top due to :

74.

(A) Capillary rise and suction

(B) A pump operating in the growing tree

(C) Fed by rain water

(D) W ater content in the atmosphere

 A patient patient given given broad broad spectrum antibiotic 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 harm ful 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 f unction of liver can be taken over by kidneys

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