BITSAT Sample Paper 01

Physics

01. The electric flux is given by the scalar product of the electric field strength and area. What are its dimensions? A. [A-2 M L3 T-2] B. [A-1 M L3 T-3] C. [A0 M2 L2 T-2] D. [A-1 M L2 T-3]

02. The component of the vector A = Axi + Ayj+ Azkalong the direction of

i+jis A. Ax+ Ay B. Ax Ay + Az C. (Ax+ Ay)/2 D. None of these

03. Three weights 1kg, 2kg, 4kg are connected to identical springs suspended

from a rigid horizontal rod. The assembly of rods and weights fall freely. The positions of the weights from the rod are such that : A. 4 kg will be the farthest B. 2 kg will be the farthest C. All the weights will be at the same distance D. 1 kg will be the farthest

04. A piece of blue glass is heated to a temperature of 800 K. It is taken with

a piece of red glass (at room temperature) to a dimly lit room. Then: A. The blue piece looks blue, and the red looks as usual B. The blue looks brighter blue and the red looks as usual. C. Both the pieces look red and shine the same. D. The blue piece shines brighter red than the red piece.

05. A man is sitting in a moving train. Comment on his momentum and KE. A. His momentum must be zero. B. His kinetic energy cannot be zero. C. His kinetic energy may not be zero. D. Both A & B.

06. The moment of inertia of a copper sphere depends upon

A. Its temperature B. Its angular velocity C. The position of the axis of rotation D. Both A & C

07. Two similar balls with angular velocities u and v collide with each other.

Then after the collision, A. unew= vnew B. unew>= vnew C. unew= vnew, only if the balls are smooth D. unew0. If the amplitude is a,then the time period T is proportional to A. 1/ B. Independent of a C. 1/a D. 1/a3/2

10. A spring of force constant k is cut into two pieces such that the longer

piece is thrice the length of the shorter one. The force constant of the longer piece is A. 4k B. k C. 4/3 k D. k

11. In each heartbeat, the heart pumps 80 mL of blood at an average pressure of 100 torr. What would be the power output of the heart, assuming that the average pulse is 72 bpm (beats per min)? A. 1.06 W B. 1.27 W C. 1.00 W D. 1.33 W

12. The Bernoulli equation is applicable to points

A. In a steadily flowing liquid B. In a streamline C. In a straight line, perpendicular to a streamline. D. In any non-viscous fluid

13. A body of mass 10 kg is attached to a wire of length 30 cm. What is the

maximum angular velocity with which it can be rotated in a horizontal circle? (Assume: Breaking stress of the wire = 48 million N/m2 and area of cross section of the wire is 10-6 m2) A. 4 rad/sec B. 2 rad/sec C. 8 rad/sec D. 1 rad/sec

14. If the linear strain in the x, y and z directions is given by a, b and c. Then

the volumetric strain is A. abc B. a2b2c2 C. (a+b+c)/3 D. a+b+c

15. What happens to the elastic property of a substance after annealing?

A. Increases B. Decreases C. No change D. Becomes zero

16. In a wave motion y = a sin(wt kx), y can be

A. Electric field B. Magnetic field C. Displacement D. All of the above

17. A string fixed at both ends vibrates in 4 loops, with the wavelength being

10cm. The length of the string is : A. 5 cm B. 10 cm C. 30 cm D. None of these

18. The displacement of a charge Q in the electric field E = ai+ b j + c k is

42 m in the direction r = (x j + y k)/2. The work done is: A. Q(ax+by) B. 4Q(ax+by) C. 4Q2 (ax+by) D. 4Q(bx+cy)

19. A rod has resistance 16 . If it is turned into a semi-circle, the resistance

along its diameter is : A. 3.12 B. 4.88 C. 8 D. 4

20. In a magnetic field of magnitude 0.05 T, the area of a coil changes from

101 sq.cm. to 100 sq.cm. The resistance remains a constant 2 ohm. The charge flow in this period is: A. 2.5 C B. 2 C C. 7.5 C D. 5 C

21. An ideal monoatomic gas is taken round the cycle ABCDA as shown in the P-V diagram (see figure). The work done during the cycle is

A. PV B. 2PV C. PV D. Zero

22. If 1 mole of a monoatomic gas ( = 5/3) is mixed with one mole of a diatomic gas ( = 7/5), the value of for the mixture is A. 1.40 B. 1.50 C. 1.53 D. 3.07

23. The radii of curvature of the left and right surface of the concave lens are

10 cm and 15 cm respectively. The radius of curvature of the mirror is 15 cm. A. equivalent focal length of the combination is -18cm B. equivalent focal length of the combination is +36 cm C. equivalent focal length of the combination is -36 cm D. None of the above

24. A wall has two layers A and B, each made of different materials. Both the

layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, if the temperature difference across layer A is 12 K, then that across B is A. 6 K B. 12 K C. 18 K D. 24 K

25. An electron enters an electric field E between the two plates (as shown)

at an angle such that tan =ld2

. What will be the angle at which

electron will move just at the end of the upper plate? A. 2tan-1() B. tan-1(/2) C. Zero D. tan-1()

26. A right angled triangular loop (as shown) enters uniform magnetic field

(at right angel to the boundary of the field) directed into the paper. Draw the graph between induced e.m.fe and the distance along the

perpendicular to the boundary of the field, (say x) along which loop moves.

27. A short circuited coil is placed in a time varying magnetic field. Electric power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be: A. Halved B. The same C. Doubled D. Quadrupled

28.

In an AC circuit shown below, the supply voltage has a constant r.m.s value V but variable frequency f. at resonance, the circuit

A. has a current I given by: RVI

B. has a resonance frequency 1000 Hz C. has a voltage across the capacitor which is 90o out of phase with that

across the inductor D. None of these

29. A magnetic needle is placed in a non-uniform magnetic field. It

experiences

A. A force and a torque B. Only a force C. Only a torque D. Neither

30. In a moving coil galvanometer, the deflection of the coil is related to the

current I by one of the following relations. A. I = k B. I = k tan C. I = k2 D. I = k

(N.B.: k>0 is a constant)

31. A voltmeter has resistance G and range V volt. The resistance used in series to convert it into a voltmeter of range nV volt is A. n G B. (n-1) G C. G/n D. G/(n-1)

32. A current I flows along the length of an infinitely long, straight, thin

walled pipe. Then the magnetic field A. At all points inside the pipe is same, but not zero. B. At any point inside the point is zero C. Is zero only on the axis D. Is different at different points

33. In a commonamplifier, the phase difference between the input signal

voltage and baseoutput voltage is (in degrees)

A. 180 B. 90 C. 45 D. 0

34. In an n-p-n transistor circuit, the collector current Is 10 mA. If 90% of the

electrons emitted reach the collector

A. the emitter current will be 9 mA B. the emitter current will be -11 mA C. the base current will be 1 mA D. the base current will be -1 mA

35. In a p-n junction, the depletion layer consists of

A. electrons B. protons C. mobile ions D. immobile ions

36. In an EM wave the electric field is given by E =E0(i-j) cos(wt-k(x+y)), and

the magnetic field is given by B = B0k cos (wt k(x+y)). The value of B0 is 5 x 10-3 (in SI units). Then E0 = A. 25 x 105 SI units B. 15 x 105 SI units C. 10 x 105 SI units D. None of these

37. Two small identical conducting balls A and B of charges of +10 C and

+30 C respectively are kept at a separation of 50 cm. these balls have been connected by a wire for a short time.The final charge on each ball A and B A. 10 C and 30 C, respectively

B. 20 C on each ball

C. 30 C and 10 C, respectively

D. -40C and 80 C, respectively

38. A strong argument for the particle nature of the cathode rays is A. Fluorescence B. Travel through vacuum C. Get deflected by electric and magnetic fields D. Cast a shadow

39. In a nuclear reaction involving the decay of 100 nuclei, marked 1 through

100, nuclei 1 decays after 1 sec. Then nuclei 2 will decay after A. 2 sec B. ln(2) sec C. 1 sec D. Cant say

40. The relation between Base current amplification factor a and emitter

current amplification factor bis A. a = b/(1-b) B. a = (1-b)/(1+b) C. b = a/(1-a) D. b = (1-a)/(1+a)

Chemistry

41.Pick out the incorrect statement:

A.MnO 24 is quite strongly oxidising and stable only in very strong alkalis. In dilute alkali or neutral solution it will disproportionate.

B. In acidic solutions, MnO 4 is reduced to Mn2+ and thus, KMnO4 is widely

used as oxidising agent

C. KMnO4 does not acts as oxidising agent in alkaline medium

D. KMnO4 is manufactured by the fusion of pyrolusite ore with KOH in presence of air or KNO3, followed by electrolytic oxidation in alkaline solution

42. )Y(AirCOK)X( Air32

Pink)Z(Cl)Y( 2

Which of the following is correct?

A. X = black, MnO2, Y = Blue, K2CrO4, Z = KMnO4 B. X = green, Cr2O3, Y = Yellow, K2CrO4, Z = K2Cr2O7 C. X = black, MnO2, Y = green, K2MnO4, Z = KMnO4 D. X = black, Bi2O2, Y = colourless, KBiO2, Z = KBiO3

43. Select the correct relative stability:

A. [Cu(CN)4]3-> [Cd(CN)4]2-

B.PtCl 24 >NiCl2

4

C. [NiCl6]2-> [PtCl6]2-

D. [Cd(CN)4]2-> [Cu(CN)4]3-

44. Magnetic moment of [Ni(CN)4]2- is zero but that of [Ni(H2O)4] 2+ is

2.83 BM.It is because of

A. Different oxidation state of Ni in two complexes B. CN- is strong ligand making two unpaired electrons in Ni2+ paired while

in [Ni(H2O)4]2+, two electrons remain unpaired H2O being weak ligand C. Both (a) and (b) D. None of the above

45. If H2S gas is passed into a solution of Cu2+, Cd2+ having excess of KCN,

A.CuS and CdS both are precipitated.

B. Soluble complex [Cu(CN)4]3- and [Cd(CN)4]2- are forme d and no effect of passing H2S gas

C. Soluble complex [Cu(CN)4]3- and [Cd(CN4)2- are formed, of which CdS is precipitated as yellow ppt.

D. Soluble complex [Cu(CN)4]3- and [Cd(CN)4]2- are formed of which CuS is precipitated as black ppt.

46. Which of the following increasing order of oxidizing power is correct for the following species?

VO2+, MnO 4 , Cr2O2

7

A. 42722 MnOOCrVO

B. 27242 OCrMnOVO

C. 42272 MnOVOOCr

D. 24272 VOMnOOCr

47. IUPAC nomenclatureof the complex compound Na3[Cr(O)2(O2)(O2)2(NH3)] where half of the coordination number are occupied by neutral ligands with magnetic moment = 15 must be

A. sodium amminedioxodioxygensuperoxochromate (III)

B. sodium amminedioxygendioxodisuperoxochromate (III)

C. sodium amminebisdioxygendioxoperoxochromate (III)

D. sodium amminebisdioxygendioxoperoxochromium (III)

48. Arrange leaving power of these nucleophilic groups in decreasing order for nucleophilic substitution reactions:

(1) O SO2 (2)

3CHCO||O

(3) Br (4) OCH3

A. 1, 3, 4, 2

B. 1, 3, 2, 4

C. 4, 3, 2, 1

D. 1, 2, 3, 4

49. In the given reaction

33

SOHOsO)i(

SONa)ii(33

CHCH||

)B()A(CHCCCH 424

32

(B) Is:

A.

33

33

CHCH||

CHCCCH||OHOH

B.

33

33

CHCH||

CHCHCCH|OH

C.

3

33

3

CH|

CHCCCH|||CHO

D.

3

33

CH|

CHCHCCH||

O

50. In carbonyls, the carbon monoxide is linked to metal atom through

A. carbon atom forming a weak bond and a weak bond

B. carbon atom forming a strong bond and a strong bond

C. oxygen atom forming a weak bond and a weak bond

D. oxygen atom forming a strong bond and a strong bond

51. Two isomeric halo alkenes (A) and (B) have molecular formula C5H9Cl. (A) gives optically inactive compound while (B) gives optically active compound on hydrogenation. The two isomers respectively are:

A. 3-chloro-1-pentene and 4-chloro-2-pentene

B. 4-chloro-1-pentene and 2-chloro-2-pentene

C. 3-chloro-2-pentene and 1-chloro-2-pentene

D. 1-chloro-1-pentne and 5-chloro-1-pentene

52.

;productMajorDMSO/H

Which of the following is major product?

(a)

(b)

(c)

(d)

53. Which of the following plots represents the second order reaction for the dimerization of gas A where p stand for partial pressure?

54. Match the Column-I with Column-II:

Column-I Column-II

(A) Rate constant has the same unit as the rate of reaction. (p) First order reaction

(B) Reactions having apparent molecularity more than three. (q) Zero order reaction

(C) Reactions having molecularity two but order of reaction is one. (r) Complex reaction (D) For a reaction, AB, the

rate of reaction doubles as the (s) Pseudo unimolecular reaction concentration of A is doubled.

A. Aq;Br;Cp; Ds

B. Ar; Bq;Cs; Dp

C. Aq; Bp;Cr; Ds

D. Aq; Br; Cs; Dp

55. When the same quantity of electricity is passed through aq. AgNO3

and H2SO4 solutions connected in series, 50.4 mg of H2 is liberated. What

is the mass of silver deposited (in grams)?

(Eq. weight of hydrogen = 1, silver = 108)

A. 54

B. 0.54

C. 5.4

D. 10.8

56.Assertion (A): The aqueous solution of sodium acetate is alkaline in

nature.

Reason (R): Acetate ion undergoes anionic hydrolysis.

A. Both A and R are correct, R is not the correct explanation for A.

B. Both A and R are correct, R is the correct explanation for A.

C. A is true, R is false.

D. R is true, A is false.

57.The pH of N/10 HCl is:

A. 3

B. 4

C. 2

D. 1

58. Boron halides behave as Lewis acids because of their _____ nature.

A. Proton donor

B. Covalent

C. Electron deficient

D. Ionising

59. For a crystal, the angle of diffraction (2) is 90 and the second order line has d = .228 nm. The wavelength in is

A. 1.612

B. 2.00

C. 2.28

D. 4.00

60. Hardening stage of plaster of Paris is a

A. Hydration process

B. Crystalline change from orthorhombic gypsum to monoclinic gypsum

C. Crystalline change from monoclinic gypsum to orthorhombic gypsum

D. Dehydration process

61. Which amongst the following metal carbonyls are inner orbital complexes with diamagnetic property?

(I) Ni(CO)4; (II) Fe(CO)5; (III) V(CO)5; (IV) Cr(CO)6

Select the correct answer from the codes gives below:

A. I and II only B. II, III and IV only C. II and IV only D. I, II and IV only

62. The number of chloride ions which would be precipitated, when CrCl3.4NH3 is treated with silver nitrate solution are

A. 3 B. 2 C. 0 D. 1

63. On increasing the temperature of a substance, the vapour pressure:

A. Always increases B. Always decreases C. May increase or decrease D. Independent of temperature

64. When zeolite, which is hydrated sodium aluminium silicate, is treated with hard water, the sodium ions are exchanged with

A. H+ B. K+ C. SO4 2- D. Mg2+

65. The degree of ionisation of a weak electrolyte depends upon

A. Size of solute B. Nature of solute C. Nature of vessel D. Amount of electricity passed

66. An organic compound A (C6H12O) neither decolourise bromine water nor changes the colour of acidic dichromate solution. A on heating with H2SO4 produces an alkene which on oxidative ozonolysis gives B(C6H10O3), which gives a yellow precipitate with NaOH/I2. The most probable structure of A is:

(a)

(b)

(c)

(d)

67. In the reaction sequence:

)B()A(CHCHCHCH HClClNH

ClCu

4

22

(B) will be:

(a) CHCCHCH

|C

3

(b)

22 CHCHCCH|C

(c) ClCCCHCH 2 (d) ClCCCHCH 23

68. Which of the following statement(s) is incorrect?

(a) The complexes [NiCl4]2- and [NiCN4]2- differ in the magnetic properties

(b) The complexes [NiCl4]2- and [NiCN4]2- differ in the geometry

(c) The complexes [NiCl4]2- and [NiCN4]2- differ in the primary valencies of nickel

(d) The complexes [NiCl4]2- and [NiCN4]2- differ in the state of hybridization of nickel

69. Which of the following has the slowest rate of the hydrogenation?

(a) I (b) II (c) III (d) IV

70. What, in the following, is most adsorbed by charcoal?

A. SO2 B. CO2 C. CO D. Water vapour

71. One of the following properties is not shown by colloids in general

A. Adsorption B. Flocculation C. Paramagnetism D. Tyndall effect

72.Which of the following statements is incorrect?

(a) Transition elements exhibit higher enthalpies atomization as they have stronger interatomic interaction

(b) IE2 of 23V

(d) The elements which gives the greatest number of oxidation states occurs in or near the middle of the series

73. KMnO4 on treatment with conc. H2SO4 forms a compound (X) which decomposes explosively on heating forming (Y). Then (X) and (Y) are, respectively,

(a) Mn2O7, MnO2

(b) Mn2O7, Mn2O3

(c) MnSO4, Mn2O3

(d) Mn2O3, MnO2

74. Statement -1: Treatment of 2-chlorobutane with t-butoxide ion produces 1-butene as the major product.

Statement-2: Bulky bases always produce Saytzeff product.

(a) Statement-1 is True, Statement-2 is True, Statement-2 is correct explanation for Statement-1

(b) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Satement-1

(c) Statement-1 is True, Statement-2 is False (d) Statement-1 is False, Statement-2 is True

75. Arrange the basicity of the following compounds in decreasing order:

I II III IV

(a) (i) > (iv) > (iii) > (ii) (b) (iv) > (i) > (ii) > (iii)

(c) (i) > (iv) > (ii) > (iii) (d) (iv) > (ii) > (iii) > (i)

76. The time required for 10% completion of a first-order reaction at 300 K is equal to that required for it 25% completion at 310 K. If the pre-exponential factor for the reaction is 4 108 sec1. If the rate constant at 320 K is A 104 sec1 approximate. What will be the value of A? (log 2.7 = 0.4)

A. 3 B. 6 C. 9 D. 0.3

77. Alumina, in column chromatography, is used as:

A. Mobile phase B. Eluting agent C. Colouring agent D. Adsorbent

78. Which of the following does not show positive Lassaignes test?

A. Urea B. Hydrazine C. Phenylhydrazine D. Azobenzene

79. Tetrafluoroethene is a monomer of

A. Orlon B. Polystyrene C. Teflon D. Neoprene

80. Dipole moment of cis-2,3-chloro-2-butene is _____ than the dipole moment of cis-1,2-dichloro-ethene

A. More B. Less C. Depends on the concentration D. Equal

Math

81.f(x) = x3 x and g(x) = sin 2x then g (2) is

A. Zero B. Positive

C. Negative D. Sometime negative sometime positive

82. Let f(x) = ln(2x x2) + sin2x , then, which of the following is incorrect?

(A) Graph of f(x) is symmetrical about the line x = 1

(B) Graph of f(x) is symmetrical about the line x = 2

(C) maximum value of f is 1

(D) minimum value of f does not exist.

83. If b,a and c

are three mutually perpendicular unit vectors and d

is a unit

vector which makes equal angle with b,aand c

, then | dcba

|2 is

equal to

A. 4 B. 4 3

C. 4 2 3 D. none of these

84. The vector k3j2i2 is rotated about origin through an angle and

becomes k2j3i2 . Then angle is not equal to

A. = cos-1

1716

B. = sin-11743

C. = sin-11733

D. = tan-1

1633

85. ABCD is a rectangle with A(1, 2), B(3, 7) and AB : BC 4 :3. If d is the distance of the origin from the centre of the rectangle then [d] is equal to (where [.] denotes the greatest integer function).

A. 4 B. 5 C. 8 D. 7

86. If sin-1(3/x) + sin-1(4/x) = /2 , then x is A. 3 B. 5 C. 7 D. 11

87. If the sum of distances from two perpendicular lines in a plane is 1, then the locus of P is:

A. Rhombus B. Circle C. Straight line D. Ellipse

88. The quartile deviation for the data

x: 2 3 4 5 6

y: 3 4 8 4 1 is:

A. 0 B. C. D. 1

89. A party of n persons sits at a round table, the odds against two specified individuals sitting next to each other are

A. 2 : n-1 B. 2 : n-2 C. 2 : n-3 D. None of these

90. If normal of f(x) at x = 0 be given by 3x y + 3 = 0 then the value of

x2{f (x2) 5 f (4x2) + 4 f (7x2)}-1 is

A. 1/6 B. 1/3 C. 1/6 D. 1/3

91. In any ABC, if 2cosB = a/c, then the triangle is

A. Right Angled B. Isosceles C. Equilateral D. Both A and B

0xlim

92. (1+ cos 22.5) (1+cos 67.5) (1+cos 112.5) (1+cos157.5) = A. B. cos 22.5 C. 1/8 D. (1+2)/22

93. 2cosx + 2cos3x = cosy;

2sinx + 2sin3x = siny

The value of cos 2x is

A. -7/8 B. 1/8 C. -1/8 D. 7/8

94. If c = c1 kcjci 32 is perpendicular to both a

= a1 kajai 32 and b

= b1

kbjbi 32 (wherea, c,b

are unit vectors) and

5xx

321

321

321

2

cbcbbbaaa

= 1 for all

real x, then the angle between a and b

, is

(A) 6 (B)

3 (C)

4 (D)

2

95. Let f:[2, ) ),1[ defined by f(X) =24 x4x2

Then f-1(x) is

(A) xlog42 2

(B) xlog42 2

(C) xlog42 2

(D) None of these

96. If the area of a triangle ABC is a-(b-c)2, then tan A =

A. -8/15 B. 15/16 C. 8/15 D. 15/8

97. y2 2x 2y + 5 = 0 is

A. Circle with centre (1,1)

B. Parabola with vertex (1,2) C. Parabola with directrix x = 3/2 D. Parabola with directrix x = -1/2

98. The coefficient of n-r in log10(n/n-1) is

A. 1/(r ln10) B. -1/(r ln10) C. -1/(r! ln10) D. None of these

99. If f (x) = , then

is (where [.] denotes the greatest integer function)

A. 0 B. 1 C. -1 D. Does not exist

100. The tangent vector to r(t) = 2t2i + (1-t) j + (3t2 + 2)k at (2, 0, 5) is

A. 4i + j 6k B. 4i j + 6k C. 2i j + 6k D. 2i + j 6k

101. Let f :

1,21

[-1, 1] is given by f (x) = 4x3 3x, then f-1 (x) is given by

(A) cos

xcos31 1 (B) 3 cos (sin-1 x) (C) 3 sin-1 (cos x) (D) none

of these

102. Let f : N N defined by f (x) = x + (-1)x + 1. Then

(A) f-1 (x) = x + (-1)x (B) f-1 (x) = x + (-1)x + 1

(C) f-1 (x) = x + (-1)x 1 (D) f-1 (x) does not exist

103. Let PQRS be a square with length of the side 10. The point A and B are taken on the side PQ and C is taken in the side RS. Then the circumradius of the triangle ABC can be

0x,

xxsinlim

0x,xt

t

x

xflim0x

(A) 3.1

(B) 4.2

(C) 5.5

(D) 8

104. If f(x) = dt)1t(2x

x

, 1 x 2, then global maximum value of f(x) is

A. 2 B. 4 C. 8 D. 1

105. The minimum value of 22 2 2

2 1 1 2x x 1 x 4 x is equal to

A. 1 B. 2 C. 4 D. None of these

106. The projections of the line segment AB on the coordinate axes are 9, 12, -8 respectively. The direction cosines of the line segment AB are:

(A) 9 12 8, ,17 17 17

(B) 9 12 8, ,289 289 289

(C) 9 12 8, ,17 17 17

(D) None of these

107. The direction ration of a normal to the plane passing through (1, 0, 0), (0,

1, 0) and making an angle 4 with the plane x + y = 3 are:

(A) (1, 2, 1)

(B) (1,1, 2)

(C) (1,1, 2)

(D) ( 2,1, 1)

108. The line of intersection of planes r (i j k) 3 and r (2i 3 j k) 9

is

perpendicular to plane r (ai bj 4k) 5

then value of a + b is equal to k then k is equal to

A. 2 B. 3

C. 1 D. 4

109. If d is the distance between the point (-1, -5, -10) and the point of

intersection of the line 12

24

13

2

zyxwith the plane x y + z = 5, then d

7 is equal to

A. 3 B. 9 C. 6 D. 4

110. If a.(bxc) = 0, then

A. Any two of the 3 vectors are parallel B. All three are coplanar C. Any two are equal D. None of these

111. Let f (x + y) + f (x y ) = 2 f (x) f (y) x, y R and f (0) = k, then

(A) f is even if k = 2

(B) f is odd if k = 0

(C) f is always odd

(D) f is neither even nor odd for any value of k

112. The horizontal distance between two towers is 60 m and theangle of depression of the top of the first tower as seen from the top of the second is 30. If the height of the second tower be 150 m, then the height of the first tower is

(a) 90m

(b) (150 603) m (c) (150 + 203) m (d) None of these

113. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80 . Then which one of the following gives possible values a and b?

A. a = 1, b = 6

B. a = 3, b = 4

C. a = 0, b = 7

D. a = 5, b = 2

114. The equation 2 sinx + cosx = 3 has

(a) only one solution

(b) no solution

(c) infinitely many solution

(d) finitely many solution

115. If f(x) = 3x + 2/5x - 3, then

(a) f-1(x) = f(x)

(b) f-1(x) = - f(x)

(c) f (f(x)) = - x

(d) f-1(x) = -1/19

116. The function f(X) = |x|3 is increasing in

(a) (0, )

(b) (-, 0)

(c) (-,)

(d) (-,1) (1, )

117. The number of real roots of the equation (x - 1)2 + (x + 2)2 + (x - 3)2 = 0 is

(1) 1

(b) 2

(c) 3

(d) None of these

118.The number of values of c such that the straight line y = 4x + c touches the curve

(a) 0

(b) 1

(c) 2

(d) infinite

119. If cos (2 sin-1x) = 1/9, then x =

(a) 2/3

(b) -2/3

(c) 2/3

(d) none of these

120. The period of function f(x) = sin2 + tan x is

(a)

(b) 2

(c) 3

(d) None of these

121. In (0,/2) , the function f(x) = x/sin x is

(a) An increasing function

(b) A decreasing function

(c) A constant function

(d) None of these

122. The values of cos 52 + cos 68 + cos 172 is equal to

(a) 0

(b) 2

(c) 1/2

(d) None of these

123. If x sin (a + y) = sin y, then dy/dx is equal to

(a) sin2 (a + y) /sin a

(b) sin a/sin2 (a + y)

(c) sin (a + y)/sin a

(d) sin a/sin (a + y)

124. The range of the function f(x) = cos [x], where - /2 < x < /2, is

(a) {-1, 1, 0}

(b) {cos 1, 1 ,cos 2)

(c) {cos 1, - cos 1, 1}

(d) none of these

125. Covariance (x,y) between x and y if = 15, = 40, = 110, n=5 is,

(a) 22 (b) 2 (c) -2 (d) -22

English

Directions: Choose the most appropriate alternative to fill the blank

126. In a published deal, Coca-Cola has ___ the entire soft drink market.

A. Conquered B. Swallowed C. Captured D. Occupied

127. She expects that her son ____

A. May return B. Can return C. Will return D. Should return

128. His life consists of ____ of drinking punctuated by periods of drunken sleep.

A. Barrels B. Bouts C. Bowls D. Pints

129. He lives in a world of ______

A. Allusions B. Illusions C. Conclusions D. Delusions

130. While you were young, you _____ cultivated good habits.

A. Ought to B. Ought to have C. Should have D. Must have

Directions: Find the synonyms of the following words.

131. EXODUS

A. Invasion B. Intrusion C. Immigration D. Expulsion

132. CONJECTURE

A. Certainty

B. Guess C. Position D. Form

133. GIMCRACK

A. Expensive B. Worthless C. Rare D. Smuggled

Directions: Find the antonyms of the following words.

134. HINDER

A. Abhor B. Aid C. Accentuate D. None of these

135. OBLIGATORY

A. Advisable B. Unnecessary C. Superfluous D. Optional

136. LANGUID

A. Energetic B. Lazy C. Liquid D. Slow

Directions: Rearrange these parts in such a way that the statement makes sense.

137. Since life has now become intensely competitive (P) not only by the grades he obtains (Q) but also by his skill of observation and logical reasoning (R) we judge a persons intellectual worth(S)

A. SQRP B. PSRQ C. PQRS D. PSRQ

138. Its known that the worlds greatest men(P) becoming rich (Q) with a view(R) have not laboured(S)

A. PRQS B. RQPS C. PSRQ D. RQSP

Directions: Choose the word which can be substituted for the group word.

139. A government made of nobles.

A. Democracy B. Monarchy C. Autocracy D. Aristocracy

140. A short story, typically with animals as characters, conveying a moral

A. Anecdote B. Tale C. Fable D. Allegory

Logical Reasoning

Directions Q. 141 - 144: Given below are sets of six sentences that form part of a paragraph. The first and the last sentences (S1 and S6) are at their right places. Arrange P, Q, R and S, the four sentences so that the given sentences constitute a coherent paragraph.

141.

S1. In other words, grammar grows and changes, and there is no such thing as correct use of English for the past, the present and the future.

P. The door is broken.

Q. Yet this would have been correct in Shakespeares time

R. Today, only an uneducated person would say, my arm is broken.

S. For example, in Shakespeares play Hamlet, there is a line.

S6. All the words that man has invented are divided into eight classes, which are called parts of speech.

A. PSQR

B. QPSR

C. RSPQ

D. SPRQ

142.

S1. The Bhagvad Gita recognizes the nature of man and the needs of man. P. All these three aspects continue the nature of man.

Q. It shows how the human being is a rational one, an ethical one and a spiritual one.

R. More than all, it must be a spiritual experience.

S. Nothing can give fulfilment unless it satisfies his reason and his ethical conscience.

S6. A man who does not harmonies them, is not truly human.

(A) PSQR

(B) PSRQ

(C) QSRP

(D) RSPQ

143.

S1. Silence is unnatural to man.

P. even his conversation is in great measure a desperate attempt to prevent a dreadful silence.

Q. In the interval he does all he can to make a noise in the world.

R. There are few things of which he stands in more fear than of the absence of noise

S. He being life with a cry and ends it in stillness.

S6. He knows that ninety-nine percent of human conversation means no more than the buzzing of a fly, but he longs to join in the buzz and to prove that he is a man and not a waxwork figure.

(A) PQRD

(B) PRQS

(C) QPRS

(D) SQRP

144.

S1. During the Middle Ages the production of cloth was divided amongst a number of associations of skilled works who performed different operations required in its production.

P. But the association of skilled workers lacked capital to butt it.

Q. Consequently, he began to assume the role of the employer.

R. With the mechanization of these operations, capital became necessary for economic production.

S. The banker, therefore stepped in to finance the industrialization of these operations.

S6. This was one of the reasons why the industry flourished in such rich countries as Flanders, Italy and Britain.

(A) PRQS

(B) PRSQ

(C) RPQS

(D) RPSQ

145. Generalization: Professors with tenure dont work as hard as professors without tenure.

(1) The possibility of losing ones job is an incentive to work hard.

(2) Professors Smith, who is tenured, works 14 hours a day.

What type of support does statement (1) provide for this generalization?

(A) Confirms

(B) Disconfirms

(C) Irrelevant

(D) None of these

146. Generalization: Professors with tenure dont work as hard as professors without tenure.

(1) The possibility of losing ones job is an incentive to work hard.

(2) Professors Smith, who is tenured, works 14 hours a day. What type of support does statement provide for this generalization?

(A) Confirms

(B) Disconfirms

(C) Irrelevant

(D) None of these

147. Volt: Voltage :: Biot : ?

A. Current B. Resistance C. Magnetic Field Intensity D. Magnetic Permeability

148. 0,2,10,30,68,130, ?

A. 178 B. 180 C. 222 D. 224

149. Look carefully at the sequence of symbols to find the pattern. Select correct pattern.

A. 1 B. 2 C. 3 D. 4

150. In each of the following questions you are given a combination of alphabets and/or numbers followed by four alternatives (1), (2), (3) and (4). Choose the alternative which closely resembles the mirror image of the given combination.

A. 1 B. 2 C. 3 D. 4

Answer Key 01

01. B 02. C 03. C 04. D 05. C 06. D 07. C 08. C 09. A 10. C 11. B 12. B 13. A

14. B 15. B 16. D 17. D 18. D 19. C 20. A 21. A 22. B 23. B 24. D 25. C 26. C 27. B 28. A 29. A 30. A 31. B 32. B 33. D 34. C 35. D 36. D 37. B 38. C 39. D 40. C 41. C 42. C 43. A 44. B 45. C 46. A 47. C 48. B 49. C 50. A 51. A 52. C 53. C 54. D 55. C 56. B 57. D 58. C 59. D 60. B 61. C 62. D 63. A 64. D 65. B 66. B

67. B 68. C 69. A 70. A 71. C 72. B 73. A 74. C 75. A 76. C 77. D 78. B 79. C 80. A 81. C 82. B 83. C 84. B 85. A 86. C 87. A 88. D 89. C 90. D 91. C 92. C 93. A 94. D 95. B 96. C 97. C 98. A 99. A 100. C 101. A 102. B 103. C 104. B 105. A 106. A 107. B 108. D 109. C 110. B 111. B 112. C 113. B 114. B 115. A 116. A 117. D 118. C 119. C

120. A 121. A 122. A 123. A 124. B 125. C

126. C 127. A

128. B

129. D

130. C

131. C

132. A

133. B

134. B

135. D

136. A

137. D

138. C

139. D

140. C

141. D

142. C

143. C

144. D

145. A

146. B

147. A

148. C

149. C

150. B