Section I - Physics1. The ratio of the dimension of Planck ’s

constant and that of the moment of inertia isthe dimension of(a) time(b) frequency(c) angular momentum(d) velocity

2. The water drops fall at regular intervals from atap 5 m above the ground. The third drop isleaving the tap at an instant when the first droptouches the ground. How far above the groundis the second drop at that instant ? (Take g = 10m/sec2)(a) 1.25 m (b) 2.50 m(c) 3.75 m (d) 5.00 m

3. Two boys are standing at the ends A and B of aground where AB = a. The boy at B startsrunning in a direction perpendicular to AB withvelocity v1. The boy at A starts runningsimultaneously with velocity v and catches theother boy in a time t, where t is

(a) a v v/ 212+ (b) a/(v+v1)

(c) a/(v–v1) (d) a v v2 212/ ( )-

4. The coefficient of static friction, ms, betweenblock A of mass 2 kg and the table as shown inthe figure is 0.2. What would be the maximummass value of block B so that the two blocks donot move? The string and the pulley areassumed to be smooth and massless.(g = 10 m/s2)

A

B

2 kg

(a) 0.4 kg (b) 2.0 kg(c) 4.0 kg (d) 0.2 kg

5. A 5000 kg rocket is set for vertical firing. Theexhaust speed is 800 m/s. To give an initialupward acceleration of 20 m/s2, the amount ofgas ejected per second to supply the neededthrust will be (Take g = 10 m/s2)(a) 127.5 kg/s (b) 137.5 kg/s(c) 155.5 kg/s (d) 187.5 kg/s

6. Assuming the radius of the earth as R, thechange in gravitational potential energy of abody of mass m, when it is taken from the earth'ssurface to a height 3R above its surface, is

(a) 3 mg R (b) Rmg43

(c) 1 mg R (d) Rmg23

7. Imagine a new planet having the same densityas that of earth but it is 3 times bigger thanthe earth in size. If the acceleration due togravity on the surface of earth is g and thaton the surface of the new planet is g’, then(a) g’ = g/9 (b) g’ = 27g(c) g’=9g (d) g’=3g

8. A seconds pendulum is mounted in a rocket. Itsperiod of oscillation decreases when the rocket(a) comes down with uniform acceleration(b) moves round the earth in a geostationary

orbit(c) moves up with a uniform velocity(d) moves up with uniform acceleration

9. A linear harmonic oscillator of force constant2 × 106 N/m and amplitude 0.01 m has a totalmechanical energy of 160 J. Its(a) maximum potential energy is 160 J(b) maximum potential energy is 100 J(c) minimum potential energy is zero(d) minimum potential energy is 100 J

BITSAT MOCK TESTNo. of Questions : 150 Maximum Marks : 450

Deduct 1 mark for every wrong answer

2

10. If n1, n2 and n3 are the fundamental frequenciesof three segments into which a string is divided,then the original fundamental frequency n of thestring is given by(a) n = n1 + n2 + n3

(b)321 n

1n1

n1

n1

++=

(c)321 n

1n1

n1

n1

++=

(d) 321 nnnn ++=

11. The speed of a wave in a medium is 960 m/s. If3600 waves are passing through a point in themedium in 1 min., then the wavelength of thewave is(a) 8 m (b) 12 m(c) 16 m (d) 20 m

12. In case of a forced vibration, the resonance wavebecomes very sharp when the(a) quality factor is small(b) damping force is small(c) restoring force is small(d) applied periodic force is small

13. N molecules each of mass m of a gas A and 2Nmolecules each of mass 2m of gas B are containedin the same vessel which is maintained attemperature T. The mean square velocity ofmolecules of B type is v2 and the mean squarerectangular component of the velocity of A typeis denoted by w2. Then w2/v2

(a) 2 (b) 1(c) 1/3 (d) 2/3

14. The temperature of inversion of a thermo-couple is 620°C and the neutral temperatureis 300°C. What is the temperature of cold junc-tion?(a) 320°C (b) 20°C(c) –20°C (d) 40°C

15. The equation of state for 5 g of oxygen at apressure P and temperature T, when occupyinga volume V, will be(a) PV = (5/16) RT (b) PV = (5/32) RT(c) PV = 5 RT (d) PV = (5/2) RTwhere R is the gas constant.

16. If g be the ratio of specific heats of a perfect gas,the number of degrees of freedom of a moleculeof the gas is

(a) )1(225

-g (b) 1213

-g-g

(c) 12-g (d) )1(

29

-g

17. Which of the following circular rods, (given ra-dius r and length l) each made of the same mate-rial and whose ends are maintained at the sametemperature will conduct most heat?(a) r = r0; l = l0 (b) r = 2r0; l = l0(c) r = r0; l = 2l0 (d) r = 2r0; l = 2l0

18. In BCC (Body Centred Cubic Crystal), distancebetween any two nearest atoms is

(a) a3 (b) a23

(c) a43

(d)2a

19. The coefficients of linear expansion of brass andsteel are a1 and a2 respectively. If we take abrass rod of length l1 and steel rod of length l2at 0°C, the difference in their lengths

)( 12 ll - will remain the same at sometemperature, if(a) 2211 ll a=a (b) 1221 ll a=a

(c) 2222

21 ll a=a (d) 2

12221 ll a=a

20. An electric dipole, consisting of two opposite

charges of 6102 -´ C each separated by adistance 3 cm is placed in an electric field of

5102´ N/C. Torque on the dipole is

(a) mN1012 1 -´ - (b) mN1012 2 -´ -

(c) mN1012 3 -´ - (d) mN1012 4 -´ -

21. Two charges q1 and q2 are placed 30 cm apart, asshown in the figure. A third charge q3 is movedalong the arc of a circle of radius 40 cm from C toD. The change in the potential energy of the

system is q

k3

04p Î, , where k is

3

q3

q2q1

40 cm

30 cmA B D

C

(a) 8q1 (b) 6q1(c) 8q2 (d) 6q2

22. If specific resistance of a potentiometer wire is10–7 Wm and current flow through it is 0.1 amp.,cross-sectional area of wire is 10–6 m2 thenpotential gradient will be(a) 10–2 volt/m (b) 10–4 volt/m(c) 10–6 volt/m (d) 10–8 volt/m

23. Two batteries, one of emf 18 volts and internal

resistance 2W and the other of emf 12 voltand internal resistance 1W, are connected asshown. The voltmeter V will record a readingof(a) 30 volt (b) 18 volt(c) 15 volt (d) 14 volt

24 Each corner of a cube of side l has a negativecharge, –q. The electrostatic potential energyof a charge q at the centre of the cube is

(a) l0

2

2q4pe

- (b) l0

2

4q3

pe

(c) l0

2

2q4pe

(d) l0

2

3q4pe

-

25. When a wire of uniform cross–section a,length l and resistance R is bent into acomplete circle, resistance between any twoof diametrically opposite points will be:

(a) R4

(b) 4R

(c) R8

(d) R2

26. If a negligibly small current is passed through awire of length 15 m and of resistance 5W havinguniform cross-section of 6 × 10–7 m2 , thencoefficient of resistivity of material, is(a) 1 × 10–7 W-m (b) 2 × 10–7 W-m(c) 3 × 10–7 W-m (d) 4 × 10–7 W-m

27. If 25W, 220 V and 100 W, 220 V bulbs areconnected in series across a 440 V line, then(a) Only 25W bulb will fuse(b) Only 100W bulb will fuse(c) Both bulbs will fuse(d) None of these

28. An electric kettle has two heating coils. Whenone of the coils is connected to an a.c. source,the water in the kettle boils in 10 minutes. Whenthe other coil is used the water boils in 40minutes. If both the coils are connected inparallel, the time taken by the same quantity ofwater to boil will be(a) 15 min (b) 8 min(c) 4 min (d) 25 min

29. A coil of one turn is made of a wire of certainlength and then from the same length a coil oftwo turns is made. If the same current is passedin both the cases, then the ratio of the magneticinductions at their centres will be(a) 2 : 1 (b) 1: 4(c) 4:1 (d) 1:2

30. Two magnets of magnetic moments M and 2Mare placed in a vibration magnetometer, with theidentical poles in the same direction. The timeperiod of vibration is T1. If the magnets areplaced with opposite poles together and vibratewith time period T2, then(a) T2 is infinite (b) T2 = T1(c) T2 > T1 (d) T2 < T1

31. For protecting a sensitive equipment from theexternal electric arc, it should be(a) Wrapped with insulation around it whenpassing current through it(b) Placed inside an iron can(c) Surrounded with fine copper sheet(d) Placed inside an aluminium can

4

32. Two coils have a mutual inductance 0.005 H.The current changes in the first coil accordingto equation I=I0 sin wt, where I0 = 10A and w =100p radian/sec. The maximum value of e.m.f. inthe second coil is(a) 2p (b) 5p(c) p (d) 4p

33. A capacitor of capacity C and reactance X, ifcapacitance and frequency become double, thenreactance will be(a) 4X (b) X/2(c) X/4 (d) 2X

34. An equiconvex lens is cut into two halves along(i) XOX' and (ii) YOY' as shown in the figure. Letf, f', f'' be the focal lengths of the complete lens,of each half in case (i), and of each half in case(ii), respectively.

Y

Y'

XX' O

Choose the correct statement from the following(a) f' = 2f, f'' = 2f (b) f' = f, f'' = 2f(c) f' = 2f, f'' = f (d) f' = f, f'' = f

35. The angular resolution of a 10 cm diametertelescope at a wavelength of 5000 Å is of theorder of(a) 106 rad (b) 10–2 rad(c) 10–4 rad (d) 10–6 rad

36. The stable nucleus that has a radius half that ofFe56 is(a) Li7 (b) Na21

(c) S16 (d) Ca40

37. The mass number of He is 4 and that of sulphuris 32. The radius of sulphur nucleus is largerthan that of helium by a factor of

(a) 8 (b) 8(c) 4 (d) 2

38. In the case of a common emitter transistoramplifier the ratio of the collector current to theemitter current Ic /Ie is 0.96. The current gain ofthe amplifier is(a) 6 (b) 48(c) 24 (d) 12

39. Of the diodes shown in the following diagrams,which one is reverse biased ?

(a)+5 V

+10 V

R

(b)–12 V

–5 V

R

(c)

–10 V

R

(d)

+5 V

R

40. An electron of mass m and charge e is acceleratedfrom rest through a potential difference of V voltin vacuum. Its final speed will be

(a)m2

eV (b)meV

(c)meV2 (d)

m2eV

Section II - Chemistry41. The vapour pressure of two liquids ‘P’ and ‘Q’

are 80 and 60 torr, respectively. The total vapourpressure of solution obtained by mixing 3 moleof P and 2 mole of Q would be(a) 72 torr (b) 140 torr(c) 68 torr (d) 20 torr

42. What is the weight of oxygen required for thecomplete combustion of 2.8 kg of ethylene ?(a) 2.8 kg (b) 6.4 kg(c) 9.6 kg (d) 96 kg

5

43. The oxide, which cannot act as a reducing agent,is(a) NO2 (b) SO2(c) CO2 (d) ClO2

44. The energy of second Bohr orbit of the hydrogenatom is -328 kJ mol-1; hence the energy of fourthBohr orbit would be:(a) -41 kJ mol-1 (b) -82 kJ mol-1

(c) -164 kJ mol-1 (d) -1312 kJ mol-1

45. The dipole moments of diatomic molecules ABand CD are 10.41 and 10.27 D, respectively whiletheir bond distances are 2.82 and 2.67 Å,respectively. This indicates that(a) bonding is 100% ionic in both the molecules(b) AB has more ionic bond character than CD(c) AB has lesser ionic bond character than

CD(d) bonding is nearly covalent in both the

molecules46. For the cell reaction,

Cu2+ (C1, aq) + Zn(s) = Zn2+ (C2, aq) + Cu(s) of anelectrochemical cell, the change in free energy,DG, at a given temperature is a function of(a) ln (C1) (b) ln (C2/C1)(c) ln (C2) (d) ln (C1 + C2)

47. The standard e.m.f. of a galvanic cell involvingcell reaction with n = 2 is found to be 0.295 V at25°C. The equilibrium constant of the reactionwould be

(a) 11100.2 ´ (b) 12100.4 ´

(c) 2100.1 ´ (d) 10100.1 ´(Given F = 96500 C mol–1; R = 8.314JK–1mol–1)

48. The equilibrium constant for the reaction A2

2A at 500 K and 700 K are 1 × 10–10 and 1× 10–5 respectively. The given reaction is(a) exothermic (b) slow(c) endothermic (d) fast

49. The solubility products of CuS, Ag2S and HgSare 10–31, 10–44, 10–54 respectively. Thesolubilities of these sulphides are in the order(a) Ag2S > HgS > CuS(b) Ag2S > CuS > HgS(c) HgS > Ag2S > CuS(d) CuS > Ag2S > HgS

50. Considering entropy (S) as a thermodynamicparameter, the criterion for the spontaneity ofany process is

(a) 0SS gssurroundinsystem >D+D

(b) 0SS gssurroundinsystem >D-D

(c) only0Ssystem >D

(d) only0S gssurroundin >D

51. The molar heat capacity of water at constantpressure C, is 75 JK–1 mol–1. When 1kJ of heat issupplied to 100 g of water, which is free toexpand, the increase in temperature of water is(a) 6.6 K (b) 1.2 K(c) 2.4 K (d) 4.8 K

52. Which reaction is not feasible?(a) 22 IKBr2BrKI2 +®+

(b) 22 BrKI2IKBr2 +®+

(c) 22 BrKCl2ClKBr2 +®+

(d) 222 OHF4F2OH2 +®+53. Which of the following order is wrong?

(a) NH3 < PH3 < AsH3 – Acidic(b) Li < Be < B < C – First IP(c) Al2O3 < MgO < Na2O < K2O – Basic(d) Li+ < Na+ < K+ < Cs+ – Ionic radius

54. The first ionization potentials (eV) of Be and Brespectively are(a) 8.29, 9.32 (b) 9.32, 9.32(c) 8.29, 8.29 (d) 9.32, 8.29

55. Which one of the following statements aboutthe zeolites is false ?(a) They are used as cation exchangers(b) They have open structure which enables

them to take up small molecules(c) Zeolites are aluminosilicates having three

dimensional network

(d) Some of the -44SiO units are replaced by

-- 96

54 AlOandAlO ions in zeolites

56. The most convenient method to protect thebottom of ship made of iron is(a) Coating it with red lead oxide(b) White tin plating(c) Connecting it with Mg block(d) Connecting it with Pb block

6

57. Which of the following statement is not correct?(a) La (OH)3 is less basic than Li(OH)3(b) La is actually an element of transition series

rather lanthanides(c) Atomic radius of Zr and Hf are same

because of lanthanide contraction(d) In lanthanide series ionic radius of Ln+3

ions decreases58. Oxidation of thiosulphate by iodine gives

(a) tetrathionate ion (b) sulphide ion(c) sulphate ion (d) sulphite ion

59. Which of the following does not have a metal-carbon bond?(a) 352 )HOC(Al (b) MgBrHC 52

(c) ]Cl)HC(Pt[K 342 (d) 4)CO(Ni60. Name of the compound given below is

CH3

CH3

CH3

H3C

(a) 5-ethyl-6-methyloctane(b) 4-ethyl-3-methyloctane(c) 3-methyl-4-ethyloctane(d) 2, 3-diethylheptane

61. Among the following compounds (I - III), theease of their reaction with electrophiles is,

OCH3 NO2

I II III

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

62. Which one of the following orders is correctregarding the —I effect of the substituents ?(a) —NR2 <—OR >—F(b) —NR2 > —OR >—F(c) —NR2 <—OR <—F(d) —NR2 >—OR <—F

63. Which of the following compounds reacts slowerin electrophilic substitution?(a) C6H5NO2 (b) C6H5OH(c) C6H5CH3 (d) C6H5NH2

64. Using anhydrous AlCl3 as catalyst, which oneof the following reactions producesethylbenzene (PhEt)?

(a) 6623 HCOHCHCH +-(b) 6623 HCCHCHCH +=-

(c) 6622 HCCHCH +=

(d) 6633 HCCHCH +-

65. 3|

23 CHH

Cl

CCHCH --- obtained by

chlorination of n-butane, will be(a) l-form (b) d-form(c) Meso form (d) Racemic mixture

66. Correct order of stability is :(a) cis -2- butene > 1-butene > trans -2-butene(b) trans-2-butene > cis-2-butene > 1-butene(c) 1-butene > cis-2-butene > trans-2- butene(d) cis-2-butene > trans-2-butene > 1-butene

67. Which of the following is incorrect?(a) NaHSO3 is used in detection of carbonyl

compound(b) FeCl3 is used in detection of phenolic group(c) Tollen reagent is used in detection of

unsaturation(d) Fehling solution is used in detection of

glucose68. Consider the following transformations :

CH COOH A 3 B C¾¾¾ ®¾ 3CaCO ¾¾ ®¾heat

NaOH

I2¾®¾

The molecular formula of C is

(a) 3|

|3 CH

OH

I

CCH -- (b) ICH2 — COCH3

(c) CHI3 (d) CH3I69. In the reaction

CN)OH(CHCHHCNCHOCH 33 ®+

COOH)OH(CHCH3OH.H ¾¾ ®¾

an asymmetric centre is generated. The acidobtained would be(a) 20 % D + 80 % L-isomer(b) D-isomer(c) L-isomer(d) 50% D + 50% L-isomer

7

70. Aniline when diazotized in cold and whentreated with dimethyl aniline gives a colouredproduct. Its structure would be

(a) CH3NH N=N NHCH3

(b) CH3 N=N NH2

(c) (CH3)2N N=N

(d) (CH3)2N NH71. Electrolytic reduction of nitrobenzene in weakly

acidic medium gives(a) N-Penylhydroxylamine(b) Nitrosobenzene(c) Aniline(d) p-Hydroxyaniline

72. Polarization of electrons in acrolein may bewritten as:

(a)+d-d

== OCH—CHHC 2

(b) OCH—HCHC 2 ==-d+d

(c)-d+d

== OCH—CHHC 2

(d) OHC—HCHC 2 ==+d-d

73. Which of the following is correct about H-bonding in nucleotide?(a) A --- A and T --- T(b) G --- T and A --- C(c) A --- G and T --- C(d) A --- T and G --- C

74. Which one of the following monomers gives thepolymer neoprene on polymerization ?(a) CF2 = CF2(b) CH2 = CHCl(c) CCl2 = CCl2

(d) 2|

2 CHCH—

Cl

CCH ==

75. In DNA the complementary bases are(a) adenine and thymine ; guanine and

cytosine(b) uracil and adenine ; cytosine and guanine(c) adenine and guanine; thymine and cytosine(d) adenine and thymine ; guanine and uracil

76. According to the adsorption theory of catalysis,the speed of the reaction increases because-(a) Adsorption lowers the activation energy

of the reaction(b) The concentration of reactant molecules at

the active centres of the catalyst becomeshigh due to strong adsorption

(c) In the process of adsorption, the activationenergy fo the molecules becomes large

(d) Adsorption produces heat which increasesthe speed of the reaction

77. Specific volume of cylindrical virus particle is6.02 × 10–2 cc/gm. whose radius and length 7 Å& 10 Å respectively. If NA = 6.02 × 1023, findmolecular weight of virus(a) 3.08 × 103 kg/mol(b) 3.08 × 104 kg/mol(c) 1.54 × 104 kg/mol(d) 15.4 kg/mol

78. When a substance A reacts with water itproduces a combustible gas B and a solution ofsubstance C in water. When another substanceD reacts with this solution of C, it also producesthe same gas B on warming but D can producegas B on reaction with dilute sulphuric acid atroom temperature. A imparts a deep goldenyellow colour to a smokeless flame of Bunsenburner. A, B, C and D respectively are(a) Na , H2, NaOH, Zn(b) K, H2, KOH, Al(c) Ca, H2, Ca(OH)2, Sn(d) CaC2, C2H2, Ca(OH)2, Fe

79. H2S gas when passed through a solution ofcations containing HCl precipitates thecat ions of second group of qual itat iveanalysis but not those belonging to the fourthgroup. It is because(a) presence of HCl decreases the sulphide

ion concentration.(b) solubility product of group II sulphides

is more than that of group IV sulphides.(c) presence of HCl increases the sulphide

ion concentration.(d) sulphides of group IV cat ions are

unstable in HCl.80. Which one of the following forms micelles in

aqueous solution above cer ta inconcentration?(a) Dodecyl trimethyl ammonium chloride(b) Glucose(c) Urea(d) Pyridinium chloride

8

Section III - Mathematics

81. The number of all possible selections of one ormore questions from 10 given questions, eachquestion having one alternative is(a) 310 (b) 210 – 1(c) 310 – 1 (d) 210

82. The polynomial 2k31n3m3 xxx ++ ++ , is

exactly divisible by 1xx 2 ++ if(a) m n, k are rational(b) m, n, k are integers(c) m, n, k are positive integers(d) none of these.

83. If ax2 + 2bx + c = 0 and a1x2 + 2b1x + c1 = 0 have

a common root and 111 cc,

bb,

aa are in A.P., then

a1, b1, c1 are in(a) A.P. (b) G.P.(c) H.P. (d) none

84. If a an b be the roots of 0qpxx 2 =++

then

ab+

ba

wb+awbw+wa22

22 ))((

(a) pq

- (b) ab

(c) qp

(d) w

[w, w2 are complex cube roots of unity]85. If n arithmetic means are inserted between 1 and

31 such that the ratio of the 1st mean and nth

mean is 3 : 29, then the value of n is(a) 14 (b) 15(c) 30 (d) 13

86. The number of dissimilar terms in the expansionof (a + b)n is n + 1, therefore number of dissimilarterms in the expansion of (a + b + c)12 is(a) 13 (b) 39(c) 78 (d) 91

87. a C0 + (a + b) C1 + (a + 2b) C2 + .... + (a + nb) Cn isequal to(a) (2a + nb) 2n (b) (2a + nb) 2n – 1

(c) (na + 2b) 2n (d) (na + 2b) 2n – 1

88. Which of the following is INCORRECT?(a) If A is a skew-symmetric matrix and n is a

positive integer, then An is alwayssymmetric

(b) If A and B are two matrices such that AB =B and BA = A, then A2 + B2 = A + B

(c) If A and B are two matrices such that AB =O, then : |A| = 0 or |B| = 0.

(d) All three are correct89. The general solution of the equation

cos x cos 6x = – 1 is :(a) IÎp+= n,)n(x 12

(b) IÎp= n,nx 2

(c) IÎp÷øö

çèæ -= n,nx

2

12

(d) none of these.

90. The value of ( )xsinxcos2cos 11 -- + at x = 5

1

is

(a)5

62- (b) 62-

(c)5

6- (d) None

91. The set of values of x for which

1x2tanx3tan1x2tanx3tan

=+

- is

(a) f

(b)þýü

îíì p4

(c)þýü

îíì =

p+p ,......,,n:n 321

4

(d)þýü

îíì =

p+p .....,,n:n 321

42

92. The value of sin (cot–1 (cos (tan–1x)) is

(a)1x2x

2

2

+

+ (b)2x1x

2

2

+

+

(c)2x

x2 +

(d)2x

12 +

93. If A = sin8 q + cos14 q, then for all values of q :(a) A ³ 1 (b) 0 < A £ 1(c) 1< 2A £ 3 (d) none of these

994. Two sides of a triangle are given by the roots of

the equation 02x32x2 =+- . The angle

between the sides is 3p

. The perimeter of the

triangle is(a) 32 (b) 6

(c) 632 + (d) )63(2 +95. The value of

6532cos

6516cos

658cos

654cos

652cos

65cos pppppp

is equal to

(a) 641

(b) 651

(c)2

1(d) None

96. The equation of the straight line whoseintercepts on the axes are twice the intercepts ofthe straight line 3x + 4y = 6 on the axes is(a) 3x + 44y = 3 (b) 3x + 4y = 12(c) 6x + 8y = 9 (d) None of these

97. The equation of pair of lines through origin andperpendicular to the pair of lines

0byhxy2ax 22 =++ is

(a) 0byhxy2ax 22 =+-

(b) 0ayhxy2bx 22 =-+

(c) 0ayhxy2bx 22 =--

(d) 0ayhxy2bx 22 =+-98. The four points of intersection of the lines

0)3y2x()1yx2( =+-+- with the axes lie ona circle whose centre is the point

(a) ÷øö

çèæ

45,

43

(b) ÷øö

çèæ-

45,

47

(c) (2, 3) (d) None of these

99. If the line 222 bmamxy -+= touches the

hyperbola 1by

ax

2

2

2

2=- at the point j . Then

j =

(a) )m(sin 1- (b) ÷øö

çèæ-

bmasin 1

(c) ÷øö

çèæ-

ambsin 1

(d) ÷øö

çèæ-

abmsin 1

100. The equation of the ellipse whose axes are alongthe coordinate axes, the length of the latus rectum

is 5 and the eccentricity is 32

is

(a) 445y

81x 22

=+ (b)41

45y

81x 22

=+

(c) 345y

81x 22

=+ (d)23

45y

81x 22

=+

101. The line joining (5, 0) to ( )sin10,cos10( qq isdivided internally in the ratio 2 : 3 at P. If qvaries, then the locus of P is(a) a pair of straight lines(b) a circle(c) a straight line(d) None of these

102. If the lines 0cybxa 111 =++ and

0cybxa 222 =++ cut the co-ordinate axes inconcylic points, then

(a) 2211 baba = (b)2

1

2

1bb

aa

=

(c) 2121 bbaa +=+ (d) 2121 bbaa =

103. The function ïî

ïíì

>+£=

0xforxa20xfor5.6)x(f

x

will be continuous at x = 0 if a =(a) 3 (b) 2(c) 1 (d) 0

104. The number of points at which the function f (x)=|x – 0.5| + | x – 1| + tan x does not have aderivative the interval (0, 2) is(a) 0 (b) 1(c) 2 (d) 3

105. If 0xatdxdythen,

212tany 1x2

x1 =÷

÷ø

öççè

æ

+=

+- is :

(a) 1 (b) 2(c) log 2 (d) None

106. The abscissa of the point on the curve ay2 = x3,the normal at which cuts off equal interceptsfrom the coordinate axes is

(a) 9a2

(b) 9a4

(c) 9a4

- (d) 9a2

-

10107. If A > 0, B > 0 and A + B = p/3, then the maximum

value of tan A tan B is

(a) 31

(b) 31

(c) 3 (d) 3

108. The derivative of x1x1tan 1

+-- with respect to

sin–1x is :

(a) 1 (b)21

-

(c)21

(d) None

109. Let f(x) = x |x|. The set of points where f(x) istwice differentiable is(a) R (b) R – {0}(c) R – {1} (d) none of these.

110. If ,x1xy 2m/1úûù

êëé ++=

then 122 xyy)x1( ++ is equal to

(a) m2y (b) my2

(c) m2y2 (d) None

111. If ,c)p(fdp1p1p

p21

+=+-

= òI then f(p) is

equal to :

(a) úûù

êëé -- 1ppn

21 2l

(b) psec21pcos

21 11 -- +

(c) psec211ppn 12 ---+l

(d) none of the above.

112. If ( )

ò-

+ -dx

x91

x3cosx2

21

2x91A -= + B (cos–13x)3 + c,where c is integration constant, then the valuesof A and B are :

(a) A = 91B,

91

-=-

(b) A = 91B,

91

=-

(c) 91B,

91A -==

(d) none of the above.

113. If ò -+=f xcotxcot31xdxcot)x( 34 and

)x(then22

fp

=÷øö

çèæ p

f is

(a) x-p (b) p-x(c) x2/ -p (d) None

114. If f (x) ò >=x

x/12

dx)x(dfthen),0x(dttcos is

(a) xx2)xcos(2xcos3 2-+

(b) 2

2

x2)xcos(2xcosxx -+

(c) ÷øö

çèæ-

x1cos

x2xcosx2

(d) none of the above

115. The value of ò-

+-

n/)1an(

n1

dxxxa

x is

(a) a/2 (b) )2na(n2

1+

(c) n2

2na -(d) none of these.

116. The function òq

q-q=q

0 xcoscos1dx

dd)(f

satisfies the differential equation ;

(a) 0cot)(f2ddf

=qq+q

(b) 0cot)(f2ddf

=qq-q

(c) 0)(f2ddf

=q+q

(d) 0)(f2ddf

=q-q

117. The solution to the differential equation

2x3 )1x(eydxdy)1x( +=-+ is

(a) ce)1x(y x3 ++=

(b) ce)1x(y3 x3 +++=

(c) ce1x

y3 x3 +=+

(d) c)1x(3ye x3 ++=-

11

118. A vector of magnitude 3, bisecting the angle

between the vectors kji2a -+= and

kj2ib +-= and making an obtuse angle with

b is

(a)6

ji3 -(b)

14k2j3i -+

(c)14

)k2j3i(3 -+(d)

10ji3 -

119. Let candb,a be three non-coplanar

vectors, and let randq,p be the vectors

defined by the relations ]cba[

cbp ´= ,

]cba[

acq ´= and

]cba[

bar ´= . Then the

value of the expression

r.)ac(q).cb(p.)ba( +++++ isequal to(a) 0 (b) 1(c) 2 (d) 3

120. Consider the parallelopiped with side

k3j3icandk2jib,kj2i3a ++=++=++=

then the angle between a and the plane

containing the face determined by b and c is

(a) 31sin 1- (b)

149cos 1-

(c)149sin 1- d) 3

2sin 1-

121. The projection of a line PQ, where P is(0, –1, 3) and Q is (4, 5, 6) on a line whosedirection ratios are 1, 2, 3 is

(a) 1412

(b) 149

(c) 1425

(d) None

122. Let d1, d2, be the intercepts of the sphere

014y13x5zyx 222 =---++ on x-axis andy-axis, then(a) d1 = 9, d2 = 13 (b) d1 = 5, d2 = 13(c) d1 = 9, d2 = 15 (d) none of these.

123. A speaks the truth in 70 percent cases and B in80 percent. The probability that they willcontradict eact. other when describing a singleevent is(a) 0.36 (b) 0.38(c) 0.4 (d) 0.42

124. The two vectors kxj)2x(i)1x( 22 +++- and

k3jxi2 +- are orthogonal(a) for no real value of x(b) for x = –1

(c) for x = 21

(d) for x = – 21

and x = 1

125. Let wandv,u be vectors such that

0wvu =++ . If

5|w|and4|v|,3|u| === , then

u.ww.vv.u ++ is

(a) 47 (b) –25(c) 0 (d) 25

Section IV - English Proficiency &Logical Reasoning

English Proficiency

126. Choose the correct synonym for the givenword.FOIBLE(a) separate (b) minor fault(c) indignity (d) illusion

127. Choose the correct antonym for the givenword.LIVID(a) undiscoloured (b) senseless(c) larger (d) outrageous

12

128. Directions: Choose the option which containsa pair of words related to each other in thesame way as the pair given in capital letters.DILATE : CONTRACT(a) hock : pawn(b) wax : wane(c) contaminate : spread(d) intrude : disturb

129. Directions: In each of these questions, eachsentence has four underlined words or phrasesmarked A, B, C and D. Choose the word orphrase that must be changed for the sentenceto be correct.He suggested us

Athat we should try to improve

B

our condition by beginning to work hard.C

No errorD

(a) A (b) B(c) C (d) D

130. Directions: Arrange the sentences, A, B, C andD to form a logical sequence between sentences1 and 6.1. I was awakened in the night by a noise in

the house.P : I quickly put on my dressing gown and

crept downstairs.Q : In the living room I discovered two burglars

breaking into my desk.R : As I switched on the light I saw that it was

2 o’clock.S : They were both tall, dark men.6. As soon as they saw me standing there,

they rushed to the window and jumped out.(a) PQRS (b) PQSR(c) PSRQ (d) RPQS

131. Directions : In each of the following quesitons,a sentence has been given in Active (or Passive)Voice. Out of the four alternative suggestedselect the one which best expresses the samesentence in Passive (or Active) voice.The clown was being laughed at by them.(a) They were laughing at the clown.(b) They were laughing on the clown.(c) They laughed at the down.(d) The clown was laughed at by them.

132. Directions : The question has four items. Selectthe item that does not bolong to the group.(a) anarchy (b) chaos(c) pandemonium (d) shield

133. Directions : In the following question, a part ofthe sentence is italicised. Below are givenalternatives to the italicised part which mayimprove the sentence. Choose the correctalternativeNewton wanted to know why did the apple fallto the ground.(a) Know that why did the apple fall(b) Know why the apple fell(c) know that why the apple fell(d) No improvement

134. Directions: In the following question, you aregiven oneblank. The question is followed byfour choices, only one of which fits the blankappropriately. That correct choice is youranswer.The man who is ...... hesitating which of the twothings he will do first, will do neither.(a) persistently (b) constantly(c) insistently (d) consistently

135. Directions: In the following question, you aregiven oneblank. The question is followed byfour choices, only one of which fits the blankappropriately. That correct choice is youranswer.The pilot had been warned about the stormbefore he....(a) took up (b) took away(c) took off (d) took over

136. Directions: : In the question below are giventwo sentences numbered I and II. In thesesentences, two homonyms are given in italicstype, which may be either mis-spelt orinappropriate in the context of the sentences.Read both the sentences carefully and decideon their correctness on the basis of the italicisedwords.I. He drank a draut of wine.II. Crops failed due to drout.(a) if only sentence I is correct;(b) if only sentence II is correct;(c) if both the sentences I and II are correct;(d) if I as well as II are incorrect, but both could

be made correct by interchanging theitalicised words;

(e) if either I nor II is correct and the sentencecould not be made correct by interchangingthe italicised words.

13

137. Directions: The following question has anidiomatic expression followed by four options.Choose the one closest to its meaning.To wrangle over an ass’s shadow(a) To act in a foolish way(b) To do something funny(c) To quarrel lover trifles(d) To quarrel over the possession of an ass

Directions for the Q. 138 to 140: Read the followingpassage carefully and answer the questions givenbelow the passage. Certain words/phrases in thepassage are given in bold to locate them whileanswering some of the questions :

A man may usually be known by the books he reads aswell as by the company he keeps; for there is acompanionship of books as well as of men and oneshould always live in the best company, whether it beof books or of men. A good book may be among thebest of friends. It is the same today that it always wasand it will never change. It is the most patient andcheerful of companions. It does not turn its back uponus in times of adversity or distress. It always receivesus with the same kindness; amusing and interestingus in youth, comforting and consoling us in age.

138. “A man may usually be known by the books hereads” because(a) books provide him a lot of knowledge(b) the books he reads affect his thinking and

character(c) his selection of books generally reveals his

temperament and character(d) his reading habit shows that he is a scholar

139. Which of the following statement is not true ?(a) good books as well as good men always

provide the finest company.(b) we have sometimes to be patient with a

book as it may bore us(c) a good book serves as a permanent friend.(d) a good book never betrays us

140. The statement “A good book may be among thebest friend” in the middle of the passage, meansthat,(a) a good book can be included among the

best friends of mankind.(b) our best friends read the same good books(c) there can bot be a better friend than a good

book(d) books may be good friend, but not better

than good man.

Logical Reasoning141. In the following question there is some relation-

ship between the two terms to the left of : : andthe same relationship obtains between the twoterms to its right. In this quesion the fourth termis missing. This term is one of the alternativeamong the four terms given below. Find out thisterm.LXNU : NYPV : : QTBR : ?(a) SDSU (b) RSUD(c) RUSD (d) SUDS

142. Which one is different from the rest three?(a) 54–28 (b) 34-17(c) 42-21 (d) 22-11

143. Which one of the number is wrong in the series?0, 1, 3, 6, 10, 15, 21, 28, 37, 45(a) 0 (b) 10(c) 45 (d) 37

Directions : In this question a passage is given andan inference is also given which can be drawn fromthe facts stated in the passage. You have to examinethe inference in the context of the passage and de-cide upon its degree of truth or falsity.In the overall economy of India, agriculture is the larg-est sector of economic activity. It plays a crucial rolein the country’s economic development by providingfood to its people and raw materials to industry. Itaccounts for the largest share to the national income.The share of the various agricultural commodities,animal busbandry and ancillary activities has beenmore than 40 percent since independence. During thedecade of the fifties, it actually contributed about halfof the national output.Inference : Agriculture is the only source of nationalincome in India.

Mark answer.144. (a) if the inference is ‘definitely true’, i.e. it

properly follows from the statement offacts given.

(b) if the inference is ‘probably true’ thoughnot ‘definitely true’ in the light of the factsgiven.

(c) if the ‘data are inadequate’, i.e. from thefacts given you cannot say whether theinference is likely to be true or false.

(d) if the inference is ‘probably false’ thoughnot ‘definitely false’ in the light of thefacts given.

(e) if the inference is ‘definitely false’, i.e. itcannot possibly be drawn from the factsgiven or it contradicts the given facts.

14

145. In the following question, a set of figures carry-ing certain characters, is given. Assuming thatthe characters in each set follow a similar pat-tern, find the missing character.

11 6 817 12 ?25 34 1919 28 11

(a) 9 (b) 13(c) 15 (d) 16

146. Complet the following figure with correct option.

?

(a) (b)

(c) (d)

147. In the following quesiton, find out which of thealternatives will exactly make up the key figure

(X)

(a) (b)

(c) (d)

148. This question contains a set of three figures X,Y and Z showing a sequence of folding of apiece of paper. Fig. (Z) shows the manner in whichthe folded paper has been cut. These three fig-ures are followed by four answer figures fromwhich you have to choose a figure which wouldmost closely resemble the unfolded form of fig.(Z).

X Y Z

(a) (b)

(c) (d)

149. In the following question, select the answer fig-ure that will fit in the blank space in the questionfigure, maintaining the pattern in the proper se-quence.

?

(a) (b)

(c) (d)

150. The following question contains four rows offigures, as four alternatives . Each row containsthree different designs. You have to study care-fully each row and judge which series of figuresfollows the stated rule exactly.Rule : Any figure can be traced by a single un-broken line without retracing.

(a)

(b)

(c)

(d)

15

Useful Books