**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) n^{2}R

(c) R/n^{2}

(d) nR

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

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

(a)

(b)

(c) v – u = f

(d) v + u = f

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

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

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 λ_{1} : λ_{2} emitted in the two cases is

(a) 7/5

(b) 27/20

(c) 27/5

(d) 20/7

7. In a common emitter transistor amplifier β = 60, R_{o} = 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

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 ms^{−}^{1}. What force is required to keep the gun in position?

(a) 10 N

(b) 5 N

(c) 15 N

(d) 30 N

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

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

11. Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I = I_{0} sin ωt, where I_{0} = 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

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) sin^{−}^{1} (λ/d)

(b) sin^{−}^{1} (λ/2d)

(c) sin^{−}^{1} (λ/3d)

(d) sin^{−}^{1} (λ/4d)

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)

14. The horizontal component of the earth’s magnetic field is 3.6 × 10^{−}^{5} tesla where the dip angle is 60°. The magnitude of the earth’s magnetic field is

(a) 2.8 × 10^{−}^{4} tesla

(b) 2.1 × 10^{−}^{4} tesla

(c) 7.2 × 10^{−}^{4}5tesla

(d) 3.6 × 10^{−}^{5} tesla

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 = 10^{−}^{2}

(a) 10^{−}^{1} N/m^{2}

(b) 10^{−}^{2} N/m^{2}

(c) 10^{−}^{3} N/m^{2}

(d) 10^{−}^{4} N/m^{2}

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

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) 10^{−}^{6}

(c) 10^{6}

(d) 100

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

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

20. The length of elastic string, obeying Hooke’s law is ℓ_{1} metres when the tension 4 N and ℓ_{2} metres when the tension is 5N. The length in metres when the tension is 9 N is-

(a) 5 ℓ_{1} – 4 ℓ_{2}

(b) 5 ℓ_{2} – 4 ℓ_{1}

(c) 9 ℓ_{1} – 8 ℓ_{2}

(d) 9 ℓ_{2} – 8 ℓ_{1}

21. A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I_{1} 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

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

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

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

(a)

(b)

(c) γR

(d)

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

26. The given electrical network is equivalent to :

(a) OR gate

(b) NOR gate

(c) NOT gate

(d) AND gate

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)

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

(a)

(b)

(c)

(d)

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

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

31. Ina photoelectric effect measurement, the stopping potential for a given metal is found to be V_{0} volt when radiation of wavelength λ_{0} is used. If radiation of wavelength 2λ_{0} is used with the same metal then the stopping potential (in volt) will be

(a) V_{0}/2

(b) 2 V_{0}

(c)

(d)

32. In the circuit shown the cells A and B have negligible resistances, For V_{A} = 12 V, R_{1} = 500 Ω and R = 100 Ω the galvanometer (G) shows no deflection. The value of V_{B} is:

(a) 4 V

(b) 2 V

(c) 12 V

(d) 6 V

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

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)

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°

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

37. In the given circuit the reading of voltmeter V_{1} and V_{2} are 300 volt each. The reading of the voltmeter V_{3} 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

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

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

(a) 0 A

(b) 10^{−}^{2} A

(c) 10^{−}^{1} A

(d) 10^{−}^{3} A

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/m^{2}. 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

**PART – II (CHEMISTRY)**

41. Ionisation energy of He^{+} is 19.6 × 10^{−}^{18} J atom^{−}^{1}. The energy of the first stationary state (n = 1) of Li^{2+} is

(a) 4.41 × 10^{−}^{16} J atom^{−}^{1}

(b) −4.41 × 10^{−}^{17} J atom^{−}^{1}

(c) −2.2 × 10^{−}^{15} J atom^{−}^{1}

(d) 8.8 × 10^{−}^{17} J atom^{−}^{1}

42. The chirality of the compound

(a) R

(b) S

(c) E

(d) Z

43. Which of the following compounds is formed when a mixture of K_{2}Cr_{2}O_{7} and NaCl is heated with conc. H_{2}SO_{4}?

(a) CrO_{2}Cl_{2}

(b) CrCl_{3}

(c) Cr_{2}(SO_{4})_{3}

(d) Na_{2}CrO_{4}

44. For the process H_{2}O(*l*) (1 bar, 373 K) → H_{2}O(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

45. Compound ‘A’ of molecular formula C_{4}H_{10}O 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

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

(a) 2, 4-dinitrophenylhydrazine

(b) aqueous solution of NaHSO_{3}

(c) benedict reagent

(d) I_{2} and Na_{2}CO_{3}

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

(a) Cu_{2}S + 2Cu_{2}O → 6Cu + SO_{2}

(b) Cu_{2}S → 2Cu +S

(c) Fe + Cu_{2}O → 2Cu + FeO

(d) 2Cu_{2}O → 4Cu + O_{2}

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) H_{2}(g) + Cl_{2}(g) ⇌ 2HCl(g)

(b) 2CO(g) + O_{2}(g) ⇌ 2CO_{2}(g)

(c) Fe + Cu_{2}O → 2Cu + FeO

(d) 2Cu_{2}O → 4Cu + O_{2}

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

50. Calculate enthalpy change for the change 85(g) → S_{8}(g), given that

H_{2}S_{2}(g) → 2H(g) + 2S(g), ∆H = 239.0 k cal mol^{−}^{1}

H_{2}S(g) → 2H(g) + S(g), ∆H = 175.0 k cal mol^{−}^{1}

(a) +512.0 k cal

(b) −512.0 k cal

(c) 508.0 k cal

(d) −508.0 k cal

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

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

(a) [Zn(en) (NH_{3})_{2}]^{2+}

(b) [Co(en)_{3}]^{3+}

(c) [Co(H_{2}O)_{4}(en)]^{3+}

(d) [Zn(en)_{2}]^{2+}

53. An element occurring in the bcc structure has 12.08 × 10^{23} unit cells. The total number of atoms of the element in these cells will be

(a) 24.16 × 10^{23}

(b) 36.18 × 10^{23}

(c) 6.04 × 10^{23}

(d) 12.08× 10^{23}

54. Te major product of the following reaction is

(a) a hemiacetal

(b) an acetal

(c) an ether

(d) an ester

55. Standard cell voltage for the cell Pb |Pb^{2+}|| Sn^{2+}| Sn is – 0.01 V. If the cell is to exhibit E_{cell} = 0, the value of [Sn^{2+}]/[Pb^{2+}] should be antilog of-

(a) +0.3

(b) 0.5

(c) 1.5

(d) −0.5

56. HBr reacts with CH_{2} = CH – OCH_{3} under anhydrous conditions at room temperature to give

(a) BrCH_{2} – CH_{2} – OCH_{3}

(b) H_{3}C – CHBr – OCH_{3}

(c) CH_{3}CHO and CH_{3}Br

(d) BrCH_{2}CHO and CH_{3}OH

57. Acetic anhydride reacts with diethyl ether in the presence of anhydrous AlCl_{3} to give:

(a) CH_{3}CH_{2}COOH

(b) CH_{3}CH_{2}COOH_{2}H_{5}

(c) CH_{3}COOCH_{3}

(d) CH_{3}COOC_{2}H_{5}

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 cm^{−}^{1}. The value of equivalent conductance of solution is-

(a) 400 mho cm^{2} g eq^{−}^{1}

(b) 295 mho cm^{2} g eq^{−}^{1}

(c) 419 mho cm^{2} g eq^{−}^{1}

(d) 425 mho cm^{2} g eq^{−}^{1}

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)

60. The radius of La^{3+} (Atomic number of La = 57) is 1.06Å. Which one of the following given values will be closest to the radius of Lu^{3+} (Atomic number of Lu = 71)?

(a) 1.40 Å

(b) 1.06 Å

(c) 0.85 Å

(d) 1.60 Å

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) X_{4}Y_{3}

(b) X_{2}Y_{3}

(c) X_{2}Y

(d) X_{3}Y_{4}

62. An organic compound (C_{3}H_{9}N) (A), when treated with nitrous acid, gave an alcohol and N_{2} gas was evolved. (A) on warming with CHCl_{3} and caustic potash gave (C) which on reduction gave isopropylmethylamine. Predict the structure of (A).

(a)

(b) CH_{3}CH_{2} – NH – CH_{3}

(c)

(d) CH_{3}CH_{2}CH_{2} – NH_{2}

63. For the reaction 2N_{2}O_{5} → 4NO_{2} + O_{2}, rate and rate constant are 1.02 × 10^{−}^{4} mol lit^{−}^{1} sec^{−}^{1} and 3.4 × 10^{−}^{5} sec^{−}^{1} respectively then concentration of N_{2}O_{5} at that time will be

(a) 1.732 M

(b) 3 M

(c) 3.4 × 10^{5}M

(d) 1.02 × 10^{−}^{4} M

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

(a) Ni(CO)_{4}

(b) [NiCl_{4}]^{2}^{−}

(c) Ni(PPh_{3})_{4}

(d) [Ni(CN)_{4}]^{2}^{−}

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 × 10^{−}^{3}

0.1 0.2 0.02 2.01× 10^{−}^{3}

0.1 1.8 0.18 6.03 × 10^{−}^{3}

0.2 0.1 0.08 6.464 × 10^{−}^{2}

(a) −1, 1, 3/2

(b) −1, 1, 1/2

(c) 1, 3/2, −1

(d) 1, −1, 3/2

66. In the silver plating of copper, K[Ag(CN)_{2}] is used instead of AgNO_{3}. 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

67. Nitrosoamines (R_{2}N – N = 0) are soluble in water. On heating them with concentrated H_{2}SO_{4}, they give secondary amines. This reaction is called

(a) Perkin reaction

(b) Sandmeyer’s reaction

(c) Fitting reaction

(d) Liebermann nitroso reaction

68. The energies E_{1 }and E_{2} of two radiations are 25 eV and 50 eV, respectively. The relation between their wavelengths i.e., λ_{1} and λ_{2} will be

(a) λ_{1} = λ_{2}

(b) λ_{1} = 2λ_{2}

(c) λ_{1} = 4λ_{2}

(d)

69. In the reaction:

(a) SiC

(b) H_{2}SO_{4}

(c) KMnO_{4}

(d) Fe + HCl

70. Nucleotide in DNA are linked by-

(a) hydrogen bond

(b) 3’-5’ phosphodiester bond

(c) glycosidic bond

(d) peptide bond

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

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

(a) 910 K

(b) 1110 K

(c) 510 K

(d) 710 K

73. The following carbohydrate is

(a) a ketohexose

(b) an aldohexose

(c) an α-furnaose

(d) an α-pyranose

74. Given that the equilibrium constant for the reaction 2SO_{2}(g) + O_{2}(g) ⇌ 2SO_{3}(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 × 10^{−}^{3}

(b) 3.6 × 10^{−}^{3}

(c) 6.0 × 10^{−}^{2}

(d) 1.3 × 10^{−}^{5}

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

76. In case of nitrogen, NCl_{3} is possible but not NCl_{5} while in case of phosphorus, PCl_{3} as well as PCl_{5} 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.

77. For the reaction :

2BaO_{2}(s) ⇌ 2BaO(s) + O_{2}(g);

∆H = +ve. In equilibrium condition, pressure of O_{2} is dependent on

(a) mass of BaO_{2}

(b) mass of BaO

(c) temperature of equilibrium

(d) mass of BaO_{2} and BaO both

78. In the series of reaction

X and Y are respectively

(a) C_{6}H_{5} – N = N – C_{6}H_{5}, C_{6}H_{5}N_{2}^{⨁}Cl^{⊝}

(b) C_{6}H_{5}N_{2}^{⨁}Cl^{−}, C_{6}H_{5} – N = N – C_{6}H_{5}

(c) C_{6}H_{5}N_{2}^{⨁}Cl^{−}, C_{6}H_{5}NO_{2}

(d) C_{6}H_{5}NO_{2}, C_{6}H_{6}

79. In XeF_{2}, XeF_{4}, XeF_{6} 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

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.

**PART-III (MATHEMATICS)**

81. If 12 cot^{2}θ – 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

82. Amplitude of is:

(a) π/6

(b) π/4

(c) π/3

(d) π/2

83. The value of is

(a) 1

(b) −2

(c) 2

(d) 0

84. The connective in the statement :

“ 2 + 7 > 9 or 2 + 7 < 9” is

(a) and

(b) or

(c) >

(d) <

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

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.

87. The focus of the curve y^{2} + 4x – 6y + 13 = 0 is

(a) (2, 3)

(b) (–2, 3)

(c) (2, –3)

(d) (–2, –3)

88. If the parabola y^{2} = 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

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

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

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]

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

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

(a) 4x^{2} – 3y^{2} + 36 = 0

(b) 4x^{2} – 3y^{2} + 12 = 0

(c) 4x^{2} – 3y^{2} – 36 = 0

(d) 4x^{2} + 3y^{2} – 25 = 0

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

95. If then the value of B is

(a) 3

(b) 4

(c) 6

(d) 8

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

(a)

(b)

(c)

(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)

98. The principal value of

(a) −5π/3

(b) 5π/3

(c) −π/3

(d) 4π/3

99. If then x is

(a) −1/2

(b) 1/2

(c) 1

(d) −1

100. If then which statement is true?

(a) AA^{T} = I

(b) BB^{T} = I

(c) AB ≠ BA

(d) (AB)^{T} = I

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

f(x) = e^{x} sin x, x ∈ [0, π] is

(a) π/6

(b) π/4

(c) π/2

(d) 3π/4

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

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

104. The value of the determinant is

(a) 2

(b) 4

(c) 6

(d) 8

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

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

(a) 0

(b) 1

(c) 3

(d) 5

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

(a) 3

(b) 5

(c) 7

(d) 9

108. The radius of the sphere

x^{2} + y^{2} + z^{2} = 49, 2x + 3y – z – 5√14 = 0 is

(a) √6

(b) 2√6

(c) 4√6

(d) 6√6

109. One of the values of is

(a)

(b) −i

(c) i

(d) −√3 + i

110. The value of does the line y = x + λ touches the ellipse 9x^{2} + 16y^{2} = 144 is/are

(a) ±2√2

(b) 2 ± √3

(c) ±5

(d) 5 ± √2

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

(a) 2x^{2} + 5xy + 2y^{2} + 4x + 5y + 2 = 0

(b) 2x^{2} + 5xy + 2y^{2} + 4x + 5y − 2 = 0

(c) 2x^{2} + 5xy + 2y^{2} = 0

(d) None of these

112. The two curves x^{3} – 3xy^{2} + 2 = 0 and 3x^{2}y – y^{3} – 2 = 0 intersect at an angle of

(a) π/4

(b) π/3

(c) π/2

(d) π/6

113. If at x = 1, the function x^{−}^{4} – 62x^{2} + 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

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

(a) 0

(b) 1

(c) 2

(d) None of these

115. The correct evaluation of is

(a) 8π/3

(b) 2π/3

(c) 4π/3

(d) 3π/8

116. The order and degree of the differential equation whose solution is y = cx + c^{2} – 3c^{3/2} + 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

117. The solution of is

(a)

(b)

(c)

(d)

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

119. If then

(a)

(b)

(c)

(d)

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

**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

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

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

**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.

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

**Latest Govt Job & Exam Updates:**