VITEEE Examination Previous Year Question Paper 2018 With Answer Key

VITEEE SOLVED PAPER-2018

PART –I (PHYSICS)

1. The resistance of a wire is ‘R’ ohm. If it is melted and stretched to ‘n’ times its original length, its new resistance will be

(a)   R/n

(b)   n2R

(c)   R/n2

(d)   nR

Answer: (b)

2. A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is

(a)   20 seconds

(b)   5 seconds

(c)   1/5 seconds

(d)   40 seconds

Answer: (b)

3. Which of the following is the correct lens formula?

(a)     

(b)    

(c)   v – u = f

(d)   v + u = f

Answer: (a)

4. The magnetic field at a point due to a current carrying conductor is directly proportional to

(a)   resistance of the conductor

(b)   thickness of the conductor

(c)   current flowing through the conductor

(d)   distance from the conductor

Answer: (c)

5. A metallic sphere is placed in a uniform electric field. The line of force follow the path (s) shown in the figure as

(a)   1

(b)   2

(c)   3

(d)   4

Answer: (d)

6. Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelength λ1 : λ2 emitted in the two cases is

(a)   7/5

(b)   27/20

(c)   27/5

(d)   20/7

Answer: (c)

7. In a common emitter transistor amplifier β = 60, Ro = 5000 Ω and internal resistance of a transistor is 500 Ω. The voltage amplification of amplifier will be

(a)   500

(b)   460

(c)   600

(d)   560

Answer: (c)

8. A machine gun has a mass 5 kg. It fires 50 gram bullets at the rate of 30 bullets per minute at a speed of 400 ms1. What force is required to keep the gun in position?

(a)   10 N

(b)   5 N

(c)   15 N

(d)   30 N

Answer: (a)

9. The activity of a radioactive sample is measured as 9750 counts per minute at t = 0 and as 975 counts per minute at t = 5 minutes. The decay constant is approximately.

(a)   0.922 per minute

(b)   0.691 per minute

(c)   0.461 per minute

(d)   0.230 per minute

Answer: (c)

10. The equivalent capacitance between a and b for the combination of capacitors shown in figure where all capacitances are in microfarad is

(a)   6.0 μF

(b)   4.0 μF

(c)   2.0 μF

(d)   3.0 μF

Answer: (a)

11. Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I = I0 sin ωt, where I0 = 10A and ω = 100 π radian/sec. The maximum value of e.m.f. in the second coil is

(a)   2 π

(b)   5 π

(c)   π

(d)   4 π

Answer: (b)

12. In Young’s double slit experiment intensity at a point is (1/4) of the maximum intensity. Angular position of this point is (separation between slits is d)

(a)   sin1 (λ/d)

(b)   sin1 (λ/2d)

(c)   sin1 (λ/3d)

(d)   sin1 (λ/4d)

Answer: (c)

13. Two batteries of emf 4 V and 8 V with internal resistance 1 Ω and 2 Ω are connected in a circuit with a resistance of 9 Ω as shown in figure.

The current and potential difference between the points P and Q are

(a)    

(b)    

(c)    

(d)    

Answer: (a)

14. The horizontal component of the earth’s magnetic field is 3.6 × 105 tesla where the dip angle is 60°. The magnitude of the earth’s magnetic field is

(a)   2.8 × 104 tesla

(b)   2.1 × 104 tesla

(c)   7.2 × 1045tesla

(d)   3.6 × 105 tesla

Answer: (c)

15. The velocity of water in a river is 18 km/hr near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water = 102

(a)   101 N/m2

(b)   102 N/m2

(c)   103 N/m2

(d)   104 N/m2

Answer: (b)

16. The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength is

(a)   3 V/m

(b)   6 V/m

(c)   9 V/m

(d)   12 V/m

Answer: (b)

17. The V-I characteristic of a diode is shown in the figure.

The ratio of forward to reverse bias resistance is :

(a)   10

(b)   106

(c)   106

(d)   100

Answer: (b)

18. The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact

(a)   is extremely small

(b)   is moderately small

(c)   is extremely large

(d)   depends on particular case

Answer: (a)

19. The current sensitivity of a moving coil galvanometer depends on

(a)   the number of turns in the coil

(b)   moment of inertia of the coil

(c)   current sent through galvanometer

(d)   eddy current in Al frame

Answer: (a)

20. The length of elastic string, obeying Hooke’s law is ℓ1 metres when the tension 4 N and ℓ2 metres when the tension is 5N. The length in metres when the tension is 9 N is-

(a)   5 ℓ1 – 4 ℓ2

(b)   5 ℓ2 – 4 ℓ1

(c)   9 ℓ1 – 8 ℓ2

(d)   9 ℓ2 – 8 ℓ1

Answer: (b)

21. A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance d from the conductor as shown in figure. The loop will experience

(a)   a net repulsive force away from the conductor

(b)   a net torque acting upward perpendicular to the  horizontal plane

(c)   a net torque acting downward normal to the horizontal plane

(d)   a net attractive force towards the conductor

Answer: (d)

22. The temperature of equal masses the three different liquids A, B and C are 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C and when B and C are mixed is 23° The temperature when A and C are mixed is

(a)   18.2°C

(b)   22°C

(c)   20.2°C

(d)   25.2°C

Answer: (c)

23. An alternating voltage of 220 V, 50 Hz frequency is applied across a capacitor of capacitance 2 μ The impedence of the circuit is

(a)   π/5000

(b)   1000/π

(c)   500 π

(d)   5000/π

Answer: (d)

24. The molar specific heats of an ideal gas at constant pressure and volume are denoted by Cp and Cv, respectively. If γ = Cp/Cv and R is the universal gas constant, then Cv is equal to

(a)   

(b)    

(c)   γR

(d)     

Answer: (a)

25. The ratio of radii of the first three Bohr orbits is

(a)   1 : 1/2 : 1/3

(b)   1 : 2 : 3

(c)   1 : 4 : 9

(d)   1: 8 : 27

Answer: (c)

26. The given electrical network is equivalent to :

(a)   OR gate

(b)   NOR gate

(c)   NOT gate

(d)   AND gate

Answer: (b)

27. A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given, surface tension of liquid T, density ρ)

(a)    

(b)    

(c)     

(d)    

Answer: (d)

28. Find the magnetic field at P due to the arrangement shown

(a)     

(b)    

(c)     

(d)    

Answer: (a)

29. The Binding energy per nucleon  of nuclei are 5.60 MeV and 7.06 MeV, respectively.

In the nuclear reaction  the value of energy Q released is :

(a)   19.6 MeV

(b)   −2.4 MeV

(c)   8.4 MeV

(d)   17.3 MeV

Answer: (d)

30. A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in the figure and emerges from the other refracting face AC as RS such that AQ = AR. If the angle of prism A = 60° and the refractive index of the material of prism is √3, then the angle of deviation of the ray is

(a)   60°

(b)   45°

(c)   30°

(d)   None of these

Answer: (a)

31. Ina photoelectric effect measurement, the stopping potential for a given metal is found to be V0 volt when radiation of wavelength λ0 is used. If radiation of wavelength 2λ0 is used with the same metal then the stopping potential (in volt) will be

(a)   V0/2

(b)   2 V0

(c)    

(d)     

Answer: (d)

32. In the circuit shown the cells A and B have negligible resistances, For VA = 12 V, R1 = 500 Ω and R = 100 Ω the galvanometer (G) shows no deflection. The value of VB is:

(a)   4 V

(b)   2 V

(c)   12 V

(d)   6 V

Answer: (b)

33. A steel wire of length ℓ has a magnetic moment M. It is then bent into a semicircular arc. The new magnetic moment is

(a)   M/π

(b)   2M/π

(c)   3M/π

(d)   4M/π

Answer: (b)

34. A running man has half the kinetic energy of that of body of half of his mass. The man speeds up by 1 m/s so as to have same K.E. as that of the boy. The original speed of the man will be

(a)   √2 m/s

(b)   (√2 – 1) m/s

(c)    

(d)     

Answer: (c)

35. In Young’s double slit experiment the two slits are illuminated by light of wavelength 5890Å and the distance between the fringes obtained on the screen is 0.2°. If the whole apparatus is immersed in water then the angular fringe width will be, if the refractive index of water is 4/3.

(a)   0.30°

(b)   0.15°

(c)   15°

(d)   90°

Answer: (b)

36. Four point charges –Q, −q, 2q and 2Q are placed one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

(a)   Q = −q

(b)   Q = −1/q

(c)   Q = q

(d)   Q = 1/q

Answer: (a)

37. In the given circuit the reading of voltmeter V1 and V2 are 300 volt each. The reading of the voltmeter V3 and ammeter A are respectively

(a)   150 V and 2.2 A

(b)   220 V and 2.2 A

(c)   220 V and 2.0 A

(d)   100 V and 2.0 A

Answer: (b)

38. A body cools from 50.0°C to 49.9°C in 5s. How long will it take to cool from 40. 0°C to 39.9°C? Assume the temperature of surroundings to be 30.0°C and Newton’s law of cooling to be valid

(a)   2.5 s

(b)   10 s

(c)   20 s

(d)   5 s

Answer: (b)

39. Consider the junction diode as ideal. The value of current flowing through AB is

(a)   0 A

(b)   102 A

(c)   101 A

(d)   103 A

Answer: (b)

40. A metal disc of radius 100 cm is rotated at a constant angular speed of 60 rad/s in a plane at right angles to an external field of magnetic induction 0.05 Wb/m2. The emf induced between the centre and a point on the rim will be

(a)   3 V

(b)   1.5 V

(c)   6 V

(d)   9 V

Answer: (b)

PART – II (CHEMISTRY)

41. Ionisation energy of He+ is 19.6 × 1018 J atom1. The energy of the first stationary state (n = 1) of Li2+ is

(a)   4.41 × 1016 J atom1

(b)   −4.41 × 1017 J atom1

(c)   −2.2 × 1015 J atom1

(d)   8.8 × 1017 J atom1

Answer: (b)

42. The chirality of the compound

(a)   R

(b)   S

(c)   E

(d)   Z

Answer: (a)

43. Which of the following compounds is formed when a mixture of K2Cr2O7 and NaCl is heated with conc. H2SO4?

(a)   CrO2Cl2

(b)   CrCl3

(c)   Cr2(SO4)3

(d)   Na2CrO4

Answer: (a)

44. For the process H2O(l) (1 bar, 373 K) → H2O(g) (1 bar, 373 K), the correct set of thermodynamic parameter is

(a)   ∆G = 0, ∆S = +ve

(b)   ∆G = 0, ∆S = −ve

(c)   ∆G = +ve, ∆S = 0

(d)   ∆G = −ve, ∆S = +ve

Answer: (a)

45. Compound ‘A’ of molecular formula C4H10O on treatment with Lucas reagent at room temperature gives compound ‘B’. When compound ‘B’ is heated with alcoholic KOH, it gives isobutene. Compound ‘A’ and ‘B’ are respectively

(a)   2-methyl-2 propanaol and 2-methyl-2-chloropropane

(b)   2-methyl-1 propanol and 1-chloro-2-methylpropane

(c)   2-methyl-1-propanol and 2-methyl-2-chloropropane

(d)   butan-2-ol and 2-chlorobutane

Answer: (a)

46. The reagent(s) which can be used to distinguish acetophenone from benzophenone is (are)

(a)   2, 4-dinitrophenylhydrazine

(b)   aqueous solution of NaHSO3

(c)   benedict reagent

(d)   I2 and Na2CO3

Answer: (d)

47. In the extraction of Cu, the metal is formed in the Bessemer converter due to the reaction:

(a)   Cu2S + 2Cu2O → 6Cu + SO2

(b)   Cu2S → 2Cu +S

(c)   Fe + Cu2O → 2Cu + FeO

(d)   2Cu­2O → 4Cu + O2

Answer: (d)

48. For which one of the following systems at equilibrium, at constant temperature will the doubling of the volume cause a shift to the right?

(a)   H­2(g) + Cl2(g) ⇌ 2HCl(g)

(b)   2CO(g) + O2(g) ⇌ 2CO2­­(g)

(c)   Fe + Cu2O → 2Cu + FeO

(d)   2Cu2O → 4Cu + O2

Answer: (d)

49. The molecular formula of diphenyl methane,

How many structural isomers are possible when one of the hydrogens is replaced by a chlorine atom?

(a)   6

(b)   4

(c)   8

(d)   7

Answer: (b)

50. Calculate enthalpy change for the change 85(g) → S8(g), given that

H2S2(g) → 2H(g) + 2S(g), ∆H = 239.0 k cal mol1

H2S(g) → 2H(g) + S(g), ∆H = 175.0 k cal mol1

(a)   +512.0 k cal

(b)   −512.0 k cal

(c)   508.0 k cal

(d)   −508.0 k cal          

Answer: (b)

51. Which of the following is best method for reducing 3-bromopropanal to 1-bromopropane-

(a)   Wolf-Kishner reduction

(b)   Clemmenson reduction

(c)   Either (a) or (b)

(d)   Stephen’s reduction

Answer: (b)

52. Which one of the following has an optical isomer?

(a)   [Zn(en) (NH3)2]2+

(b)   [Co(en)3]3+

(c)   [Co(H2O)4(en)]3+

(d)   [Zn(en)2]2+

Answer: (b)

53. An element occurring in the bcc structure has 12.08 × 1023 unit cells. The total number of atoms of the element in these cells will be

(a)   24.16 × 1023

(b)   36.18 × 1023

(c)   6.04 × 1023

(d)   12.08× 1023

Answer: (a)

54. Te major product of the following reaction is

(a)   a hemiacetal

(b)   an acetal

(c)   an ether

(d)   an ester

Answer: (b)

55. Standard cell voltage for the cell Pb |Pb2+|| Sn2+| Sn is – 0.01 V. If the cell is to exhibit Ecell = 0, the value of [Sn2+]/[Pb2+] should be antilog of-

(a)   +0.3

(b)   0.5

(c)   1.5

(d)   −0.5

Answer: (a)

56. HBr reacts with CH2 = CH – OCH3 under anhydrous conditions at room temperature to give

(a)   BrCH2 – CH2 – OCH3

(b)   H3C – CHBr – OCH3

(c)   CH3CHO and CH3Br

(d)   BrCH2CHO and CH3OH

Answer: (b)

57. Acetic anhydride reacts with diethyl ether in the presence of anhydrous AlCl3 to give:

(a)   CH3CH2COOH

(b)   CH3CH2COOH2H5

(c)   CH3COOCH3

(d)   CH3COOC25

Answer: (d)

58. The resistance of 0.01 N solution of an electrolyte was found to be 220 ohm at 298 K using a conductivity cell with a cell constant of 0.88 cm1. The value of equivalent conductance of solution is-

(a)   400 mho cm2 g eq1

(b)   295 mho cm2 g eq1

(c)   419 mho cm2 g eq1

(d)   425 mho cm2 g eq1

Answer: (a)

59. p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is

(a)  

(b)  

(c)  

(d)  

Answer: (c)

60. The radius of La3+ (Atomic number of La = 57) is 1.06Å. Which one of the following given values will be closest to the radius of Lu3+ (Atomic number of Lu = 71)?

(a)   1.40 Å

(b)   1.06 Å

(c)   0.85 Å

(d)   1.60 Å

Answer: (c)

61. In a compound, atoms of element Y from ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be

(a)   X4Y3

(b)   X2Y3

(c)   X2Y

(d)   X3Y4

Answer: (a)

62. An organic compound (C3H9N) (A), when treated with nitrous acid, gave an alcohol and N2 gas was evolved. (A) on warming with CHCl3 and caustic potash gave (C) which on reduction gave isopropylmethylamine. Predict the structure of (A).

(a)  

(b)   CH3CH2 – NH – CH3

(c)    

(d)   CH3CH2CH2 – NH2

Answer: (a)

63. For the reaction 2N2O5 → 4NO2 + O2, rate and rate constant are 1.02 × 104 mol lit1 sec1 and 3.4 × 105 sec1 respectively then concentration of N2O5 at that time will be

(a)   1.732 M

(b)   3 M

(c)   3.4 × 105M

(d)   1.02 × 104 M

Answer: (b)

64. The complex showing a spin-only magnetic moment of 2.82 B.M. is :

(a)   Ni(CO)4

(b)   [NiCl4]2

(c)   Ni(PPh3)4

(d)   [Ni(CN)4]2

Answer: (b)

65. What is order with respect to A, B, C, respectively

[A]          [B]       [C]       rate (M/sec)

0.2          0.1       0.02     8.08 × 103

0.1          0.2       0.02     2.01× 103

0.1          1.8       0.18     6.03 × 103

0.2          0.1       0.08     6.464 × 102

(a)   −1, 1, 3/2

(b)   −1, 1, 1/2

(c)   1, 3/2, −1

(d)   1, −1, 3/2

Answer: (d)

66. In the silver plating of copper, K[Ag(CN)2] is used instead of AgNO3. The reason is

(a)   a thin layer of Ag is formed on Cu

(b)   more voltage is required

(c)   Ag+ ions are completely removed from solution

(d)   less availability of Ag+ ions, as Cu cannot displace Ag from [Ag(CN)2] ion

Answer: (d)

67. Nitrosoamines (R2N – N = 0) are soluble in water. On heating them with concentrated H2SO4, they give secondary amines. This reaction is called

(a)   Perkin reaction

(b)   Sandmeyer’s reaction

(c)   Fitting reaction

(d)   Liebermann nitroso reaction

Answer: (d)

68. The energies E1 and E2 of two radiations are 25 eV and 50 eV, respectively. The relation between their wavelengths i.e., λ1 and λ2 will be

(a)   λ1 = λ2

(b)   λ1 = 2λ2

(c)   λ1 = 4λ2

(d)     

Answer: (b)

69. In the reaction:

(a)   SiC

(b)   H2SO4

(c)   KMnO4

(d)   Fe + HCl

Answer: (d)

70. Nucleotide in DNA are linked by-

(a)   hydrogen bond

(b)   3’-5’ phosphodiester bond

(c)   glycosidic bond

(d)   peptide bond

Answer: (b)

71. The correct order of the thermal stability of hydrogen halides (H – X) is

(a)   HI > HCl < HF < HBr

(b)   HCl < HF > HBr < HI

(c)   HF > HCl > HBr > HI

(d)   HI < HBr > HCl < HF

Answer: (c)

72. The values of ∆H and ∆S for the reaction, C(graphite) + CO2(g) → 2CO(g) are 170 kJ and spontaneous at

(a)   910 K

(b)   1110 K

(c)   510 K

(d)   710 K

Answer: (b)

73. The following carbohydrate is

(a)   a ketohexose

(b)   an aldohexose

(c)   an α-furnaose

(d)   an α-pyranose

Answer: (b)

74. Given that the equilibrium constant for the reaction 2SO2(g) + O2(g) ⇌ 2SO3(g) has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature?

(a)   1.8 × 103

(b)   3.6 × 103

(c)   6.0 × 102

(d)   1.3 × 105

Answer: (c)

75. Which one of the following statements is correct?

(a)   All amino acids except lysine are optically active

(b)   All amino acids are optically active

(c)   All amino acids except glycine are optically active

(d)   All amino acids except glutamic acids are optically active

Answer: (c)

76. In case of nitrogen, NCl3 is possible but not NCl5 while in case of phosphorus, PCl3 as well as PCl5 are possible. It is due to

(a)   availability of vacant d orbitals in P but not in N

(b)   lower electronegativity of P than N

(c)   lower tendency of H-bond formation in P than N

(d)   occurrence of P in solid while N in gaseous state at room temperature.

Answer: (a)

77. For the reaction :

2BaO2(s) ⇌ 2BaO(s) + O2(g);

∆H = +ve. In equilibrium condition, pressure of O2 is dependent on

(a)   mass of BaO2

(b)   mass of BaO

(c)   temperature of equilibrium

(d)   mass of BaO2 and BaO both

Answer: (c)

78. In the series of reaction

                 X and Y are respectively

(a)   C6H5 – N = N – C6H5, C­6H5N2Cl

(b)   C6H5N2Cl, C6H5 – N = N – C6H5

(c)   C6H5N2Cl, C6H5NO2

(d)   C6H5NO2, C6H6

Answer: (c)

79. In XeF2, XeF4, XeF6 the number of lone pairs on Xe are respectively

(a)   2, 3, 1

(b)   1, 2, 3

(c)   4, 1, 2

(d)   3, 2, 1

Answer: (c)

80. In Wiliamson synthesis if tertiary alkyl halide is used than

(a)   ether is obtained in good yield

(b)   ether is obtained in poor yield

(c)   alkene is the only reaction product

(d)   a mixture of alkene as a major product and ether as a minor product forms.

Answer: (c)

PART-III (MATHEMATICS)

81. If 12 cot2θ – 31 cosec θ + 32 = 0, then the value of sin θ is

(a)   3/5 or 1

(b)   2/3 or −2/3

(c)   4/5 or 3/4

(d)   ±1/2

Answer: (c)

82. Amplitude of  is:

(a)   π/6

(b)   π/4

(c)   π/3

(d)   π/2

Answer: (c)

83. The value of is

(a)   1

(b)   −2

(c)   2

(d)   0

Answer: (c)

84. The connective in the statement :

“ 2 + 7 > 9 or 2 + 7 < 9” is

(a)   and

(b)   or

(c)   >

(d)   <

Answer: (b)

85. The number of ways in which 3 prizes can be distributed to 4 children, so that no child gets all the three prizes, are

(a)   64

(b)   62

(c)   60

(d)   None of these

Answer: (c)

86. If A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. then,

(I) P(not A) = 0.58

(II) P(not B) = 0.52

(III) P(A or B) = 0.47

(a)   Only I and II are correct.

(b)   Only II and III are correct.

(c)   Only I and III are true.

(d)   All three statements are correct.

Answer: (a)

87. The focus of the curve y2 + 4x – 6y + 13 = 0 is

(a)   (2, 3)

(b)   (–2, 3)

(c)   (2, –3)

(d)   (–2, –3)

Answer: (b)

88. If the parabola y2 = 4ax passes through the point (1, –2), then the tangent at this point is

(a)   x + y – 1 = 0

(b)   x – y – 1 = 0

(c)   x + y + 1 = 0

(d)   x – y – 1 = 0

Answer: (c)

89. The no. of points of discontinuity of the function f(x) = x – [x] in the interval (0, 7) are

(a)   2

(b)   4

(c)   6

(d)   8

Answer: (c)

90. A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is_______ π cm/s

(a)   0

(b)   2

(c)   8

(d)   9

Answer: (c)

91. The interval in which the function  is decreasing is :

(a)   (−1/2, 1/2)

(b)   [−1/2, 1/2]

(c)   (−1, 1)

(d)   [−1, 1]

Answer: (a)

92. The eccentricity of the ellipse whose major axis is three times the minor axis is:

(a)   √2/3

(b)   √3/2

(c)   2√2/3

(d)   2/√3

Answer: (c)

93. The equation of the hyperbola with vertices (3, 0), (−3, 0) and semi-latus rectum 4 is given by:

(a)   4x2 – 3y2 + 36 = 0

(b)   4x2 – 3y2 + 12 = 0

(c)   4x2 – 3y2 – 36 = 0

(d)   4x2 + 3y2 – 25 = 0

Answer: (c)

94. at x = 0 is

(a)   continuous as well as differentiable

(b)   differentiable but not continuous

(c)   continuous but not differentiable

(d)   neither continuous nor differentiable

Answer: (c)

95. If then the value of B is

(a)   3

(b)   4

(c)   6

(d)   8

Answer: (d)

96. The vector equation of the symmetrical form of equation of straight line  is

(a)    

(b)     

(c)    

(d)     

Answer: (d)

97. Let the line  lie in the plane x + 3y – αz + β = 0. Then (α, β) equals

(a)   (−6, 7)

(b)   (5, −15)

(c)   (−5, 5)

(d)   (6, −17)

Answer: (a)

98. The principal value of 

(a)   −5π/3

(b)   5π/3

(c)   −π/3

(d)   4π/3

Answer: (c)

99. If  then x is

(a)   −1/2

(b)   1/2

(c)   1

(d)   −1

Answer: (b)

100. If  then which statement is true?

(a)   AAT = I

(b)   BBT = I

(c)   AB ≠ BA

(d)   (AB)T = I

Answer: (d)

101. The value of c in Rolle’s Theorem for the function

f(x) = ex sin x, x ∈ [0, π] is

(a)   π/6

(b)   π/4

(c)   π/2

(d)   3π/4

Answer: (d)

102. The area of the region bounded by the curve x = 2y + 3 and lines y = 1 and y = −1 is

(a)   4 sq. units

(b)   3/2 sq. units

(c)   6 sq. units

(d)   8 sq. units

Answer: (c)

103. A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is given, then the probability that the original signal is green, is

(a)   3/5

(b)   6/7

(c)   20/23

(d)   9/20

Answer: (c)

104. The value of the determinant  is

(a)   2

(b)   4

(c)   6

(d)   8

Answer: (c)

105. If the equation x + ay – z = 0, 2x – y + az = 0, ax + y + 2z = 0 have non-trivial solutions, then a =

(a)   2

(b)   −2

(c)   √3

(d)   −√3

Answer: (b)

106. If the I.F. of the differential equation  then A=

(a)   0

(b)   1

(c)   3

(d)   5

Answer: (d)

107. What is the length of the projection of  on the xy-plane?

(a)   3

(b)   5

(c)   7

(d)   9

Answer: (b)

108. The radius of the sphere

x2 + y2 + z2 = 49, 2x + 3y – z – 5√14 = 0 is

(a)   √6

(b)   2√6

(c)   4√6

(d)   6√6

Answer: (b)

109. One of the values of  is

(a)     

(b)   −i

(c)   i

(d)   −√3 + i

Answer: (a)

110. The value of does the line y = x + λ touches the ellipse 9x2 + 16y2 = 144 is/are

(a)   ±2√2

(b)   2 ± √3

(c)   ±5

(d)   5 ± √2

Answer: (c)

111. The combined equation of the asymptotes of the hyperbola 2x2 + 5xy + 2y2 + 4x + 5y = 0 is-

(a)   2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0

(b)   2x2 + 5xy + 2y2 + 4x + 5y − 2 = 0

(c)   2x2 + 5xy + 2y2 = 0

(d)   None of these

Answer: (a)

112. The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of

(a)   π/4

(b)   π/3

(c)   π/2

(d)   π/6

Answer: (c)

113. If at x = 1, the function x4 – 62x2 + ax + 9 attains its maximum value on the interval [0, 2], then the value of a is

(a)   110

(b)   10

(c)   55

(d)   None of these

Answer: (d)

114. The value of  (where [.] denotes greatest integer function) is

(a)   0

(b)   1

(c)   2

(d)   None of these

Answer: (b)

115. The correct evaluation of  is

(a)   8π/3

(b)   2π/3

(c)   4π/3

(d)   3π/8

Answer: (d)

116. The order and degree of the differential equation whose solution is y = cx + c2 – 3c3/2 + 2, where c is parameter, is

(a)   order = 4, degree = 4

(b)   order = 4, degree = 1

(c)   order = 1,degree = 4

(d)   None of these

Answer: (c)

117. The solution of  is

(a)    

(b)    

(c)    

(d)     

Answer: (a)

118. A unit vector perpendicular to the plane formed by the points (1, 0, 1), (0, 2, 2) and (3, 3, 0) is

(a)     

(b)    

(c)    

(d)   None of these

Answer: (b)

119. If  then

(a)     

(b)     

(c)     

(d)    

Answer: (c)

120. The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P(X = 1) is

(a)   1/4

(b)   1/32

(c)   1/16

(d)   1/8

Answer: (a)

PART-IV (ENGLISH)

Directions (Qs. 121-123): Study the paragraph and answer the questions that follow:

Judiciary has become the centre of controversy, in the percent past, on account of the sudden ‘Me’ in the level of judicial intervention. The area of judicial intervention has been steadily expanding through the device of public interest litigation. The judiciary has shed its pro-status-quo approach and taken upon itself the duty to enforce the basic rights of the poor and vulnerable sections of society, by progressive interpretation and positive action. The Supreme Court has developed new methods of dispensing justice to the masses through the public interest litigation. Former Chief Justice PN. Bhagwat, under whose leadership public interest litigation attained a new dimension comments that “the Supreme Court has developed several new commitments. It has carried forward participative justice.”

121. The steady expansion of judicial intervention is the result of

(a)   excessive laws

(b)   public interest litigation

(c)   Supreme Court’s new methods of dispensing justice

(d)   new commitments of Supreme Court

Answer: (b)

122. According to the author, judiciary has become the center of controversy because of

(a)   problems arising in dispensing justice in the recent past

(b)   public interest litigation

(c)   sudden ‘Me’ in the level of judicial intervention

(d)   Supreme Court’s supremacy

Answer: (c)

123. According to Justice PN. Bhagwat, Supreme Court has developed

(a)   judicial intervention

(b)   various new commitments

(c)   participative judicial approach to dispense justice

(d)   public interest litigation

Answer: (b)

Directions (Q. 124) : In the questions below, a sentence is given, a part of which is printed in bold and underline. his part may contain a grammatical error. Each sentence is followed by phrases a, b, c and d. Find out which phrase should replace the phrase given in bold/underline to correct the error, if there is any to make the sentence grammatically meaningful and correct.

124. Recent incidents of tigers straying have brought to focus the lack of proper regulatory mechanism

and powers with the forest department to take action against the resorts mushroom in forest fringes.

(a)   and powers with the forest department to taking action against the resorts mushroom in forest fringes.

(b)   and powers with the forest departments to take action against the resorts mushroom in forest fringes.

(c)   and powers with the forest department to take action for the resorts mushroom in forest fringes.

(d)   and powers with the forest department to take action against the resorts mushrooming in forest fringes.

Answer: (d)

125. Choose the best pronunciation of the word ‘Mischievous’ from the following options.

(a)   Mis-chuh-vus

(b)   Mis-chi-vius

(c)   Mis-chi-vus

(d)   Mis-chu-vies

Answer: (a)

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