Punjab Agricultural University is going to start a new degree programme B.Tech. (Mechanical Engineering) from July 2019. The Department of Mechanical Engineering is an old and well established department that has been an integral part of the College of Agricultural Engineering & Technology since 1967. The department has excellent laboratories and well qualified faculty.

The Punjab Agricultural University offers excellent environment to the students for their all round development. The Punjab Agricultural University is a world renowned university that was modeled on the pattern of Land Grant Colleges in United States. The Ministry of Human Resource Development, Government of India has ranked PAU among the top 40 Universities (NIRF 2017). The University has produced distinguished alumni who, in recognition of their outstanding achievements, have brought laurels and won many prestigious awards at national and international level which include World Food Prize, Rafi Ahmed Kidwai Memorial Award, Shanti Swaroop Bhatnagar Award and Om Parkash Bhasin Award for Science & Technology apart from several other awards including the prestigious Padma Bhushan and Padma Shri.

The admission to this degree programme is based on JEE Mains through counselling by PTU, Kapurthala. There are total 40 seats in this programme. The students joining this degree programme will get to learn latest in Mechanical Engineering with major thrust on futuristic areas like Mechatronics, Automation & Robotics, Computer-Aided-Design & Analysis and Computer-Aided Manufacturing.

1. A wooden wedge of mass M and inclination angle (α) rest on a smooth floor. A block of mass m is kept on wedge. A force F is applied on the wedge as shown in the figure such that block remains stationary with respect to wedge. So, magnitude of force F is

(a) (M + m) g tan α

(b) g tan α

(c) mg cos α

(d) (M + m)g cosec α

Answer: (a)

2. A piece of ice slides down a rough inclined plane at 45° inclination in twice the time that it takes to slide down an identical but frictionless inclined plane. What is the coefficient of friction between ice and incline?

(a)

(b)

(c)

(d)

Answer: (c)

3. A body of mass 5 kg is suspended by a spring balance on an inclined plane as shown in figure.

So,, force applied on spring balance is

(a) 50 N

(b) 25 N

(c) 500 N

(d) 10 N

Answer: (b)

4. In the figure, blocks A and B of masses 2m and m are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses 2m and m just after the instant when the string is cut

(a) g, g

(b) g, g/2

(c) g/2, g

(d) g/2, g/2

Answer: (c)

5. If the formula, X =3YZ^{2}, X and Z have dimensions of capacitance and magnetic induction. The dimensions of Y in MKSQ system are

(a) [M^{−3}L^{−2}T^{4}Q^{4}]

(b) [ML^{2}T^{8}Q^{4}]

(c) [M^{−2}L^{−3}T^{2}Q^{4}]

(d) [M^{−2}L^{−2}TQ^{2}]

Answer: (a)

6. the figure shows a mass m on a frictionless surface. It is connected to rigid wall by the mean of a massless spring of its constant k. Initially, the spring is at its natural position. If a force of constant magnitude starts acting on the block towards. right, then the speed of the block when the deformation in spring is x, will be

(a)

(b)

(c)

(d)

Answer: (a)

7. Body of mass M is much heavier than the other body of mass m. The heavier body with speed u collides with the lighter body which was at rest initially elastically. The speed of lighter body after collision is

(a) 2v

(b) 3v

(c) v

(d) v/2

Answer: (a)

8. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc

(a) continuously decreases

(b) continuously increases

(c) first increases and then decrease

(d) remains unchanged

Answer: (c)

9. Three bodies having masses 5 kg,4 kg and 2 kg is moving at the speed of 5 m/s, 4 m/s and 2 m/s respectively along X-axis. The magnitude of velocity of centre of mass is

(a) 1.0 m/s

(b) 4 m/s

(c) 0.9 m/s

(d) 1.3 m/s

Answer: (b)

10. Two satellites A and B revolve round the same planet in coplanar circular orbits lying in the same plane. Their periods of revolutions are I h and 8 h, respectively. The radius of the orbit of d is 10^{4} The speed of B is relative to d. When they are closed in km/h is

(a) 3π × 10^{4}

(b) zero

(c) 2π × 10^{4}

(d) π × 10^{4}

Answer: (d)

11. A planet is revolving around the sun in a circular orbit with a radius r. The time period is T. If the force between the planet and star is proportion al to r^{−}^{3/2}, then the square of time period is proportional to

(a) r^{3/2}

(b) r^{2}

(c) r

(d) r^{5/2}

Answer: (d)

12. The weight of a body on the surface of the earth is 6l N. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

(a) 35 N

(b) 28 N

(c) 18 N

(d) 40 N

Answer: (b)

13. A block of rectangular size of mass m and area of cross-section ,4, floats in a liquid of density ρ. If we give a small vertical displacement from equilibrium, it undergoes SHM with time period T, then

(a) T^{2} ∝ 1/p

(b) T^{2} ∝ p

(c) T^{2} ∝ m^{−}^{1}

(d) T^{2} ∝ 1/A^{−2}

Answer: (a)

14. A steel rod 100 cm long is damped at into middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53 kHz. What is the speed of sound in sound is steel?

(a) 6.2 km/s

(b) 5.06 km/s

(c) 7.23 km/s

(d) 7.45 km/s

Answer: (b)

15. A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s,

(a) 12

(b) 8

(c) 6

(d) 4

Answer: (c)

16. An ideal gas of mass m in a state A. goes to another state B via three different processes as shown in figure. If Q_{1}, Q_{2 }and Q3 denote the heat absorbed by the gas along the three paths, then

(a) Q_{1} < Q_{2} < Q_{3}

(b) Q_{1}< Q_{2} = Q_{3}

(c) Q_{1} = Q_{2} > Q_{3}

(d) Q_{1} > Q_{2} > Q_{3}

Answer: (a)

17. A metal wire has a resistance of 15 Ω. If its length is increased to double by drawing it, then its new resistance, will be

(a) 70 Ω

(b) 140 Ω

(c) 105 Ω

(d) 35 Ω

Answer: (b)

18. A half ring of radius R has a charge of λ per unit length. The electric force on 1 C charged placed at the centre is

(a) zero

(b) kλ/R

(c) 2kλ/R

(d) kπλ/R

Answer: (c)

19. Positive charge Q is distributed uniformly over a circular ring of radius R. A point particle having a mass (m) and a negative charge -q is placed on its axis at a distance x from the centre. Assuming x < R, find the time period of oscillation of the particle, if it is released from there [neglect gravity].

(a)

(b)

(c)

(d) None of these

Answer: (a)

20. An infinite number of identical capacitors each of capacitance 1 μF are connected as shown in the figure. Then, the equivalent capacitance between ,4 and E is

(a) 1 μF

(b) 2 μF

(c)

(d) ∞

Answer: (b)

21. In the circuit in the figure, if no current flows through the galvanometer when the key K is closed, the bridge is balanced. The balancing condition for bridge is

(a)

(b)

(c)

(d)

Answer: (b)

22. In a series R-C circuit shown in figure, the applied voltage is l0 V and the voltage across capacitor is found to be 8V. Then, the voltage across R and the phase difference between current and the applied voltage will respectively be

(a) 6V, tan^{−}^{1}(4/3)

(b) 3V, tan^{−}^{1}(3/4)

(c) 6V, tan^{−}^{1}(5/3)

(d) None of these

Answer: (a)

23. A system S consists of two coils A and B, The coil A carries a steady current I. While the coil .B is suspended nearby as shown in figure. Now, if the system is heated, so as to raise the temperature of two coils steadily, then

(a) the two coils shows attraction

(b) the two coils shows repulsion

(c) there is no change in the position of the two coils

(d) induced current are not possible in coil B

Answer: (a)

24. A long straight wire, carrying current I is bent at its mid-point to form an angle of 45°. Induction of magnetic field (in tesla) at point P, distant R from point of bending is equal to

(a)

(b)

(c)

(d)

Answer: (a)

25. An element (where dx = 1 cm) is placed at the origin and carries a large current i = 10 A. What is the magnetic field on the Y-axis at a distance of 0.5 m?

(a)

(b)

(c)

(d)

Answer: (b)

26. The horizontal component of the earth’s magnetic field at any place is 0.36 × 10^{−}^{4} Wb/m^{2}. If the angle of dip at that place is 60°, then the value of vertical component of the earth’s magnetic field will be (in Wb/m^{2})

(a) 0.12 × 10^{−}^{4}

(b) 0.24 × 10^{−}^{4}

(c) 0.40 × 10^{−}^{4}

(d) 0.622 × 10^{−}^{4}

Answer: (d)

27. Consider the following figure, a uniform magnetic field of 0.2 T is directed along the positive X-axis. The magnetic flux through top surface of the figure.

(a) zero

(b) 0.8 m-Wb

(c) 1.0 m-Wb

(d) −1.8 m-Wb

Answer: (c)

28. An ideal coil of 10 H is connected in series with a resistance of 5Ω and a battery of 5 V. After 2 s, after the connection is made, the current flowing (in ampere) in the circuit is

(a) (1 – e)

(b) e

(c) e^{−}^{1}

(d) (1 – e^{−}^{1})

Answer: (d)

29. In the circuit, shown the galvanometer G of resistance 60 Ω is shunted by a resistance r = 0.02 Ω. The current through R is nearly 1A. The value of resistance R (in ohm) is nearly

(a) 1.00 Ω

(b) 5.00 Ω

(c) 11.0 Ω

(d) 6.0 Ω

Answer: (b)

30. In a circuit L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is

(a)

(b)

(c)

(d)

Answer: (c)

31. The graph between the energy log E of an electron and its de-Broglie wavelength log λ will be

(a)

(b)

(c)

(d)

Answer: (c)

32. The half-life of a radioactive substance is 20 min. The approximate time interval (t_{2} – t_{1}) between the time t_{2}, when 2/3 of it has decayed and time t_{2}, when 2/3 of it has decayed and time t_{1} when 1/3 of it had decayed is

(a) 14 min

(b) 20 min

(c) 28 min

(d) 7 min

Answer: (b)

33. In the figure, mass of a ball is 9/5 times mass of the rod. Length of rods is 1 m. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod.

(a) 1.4 s

(b) 2.45 s

(c) 3.25 s

(d) 5 s

Answer: (a)

34. The diode used at a constant potential drop of 0.5 V at al currents and maximum power rating of 100 mW. What resistance must be connected in series diode, so that current in circuit is maximum ?

(a) 200Ω

(b) 6.67Ω

(c) 5Ω

(d) 15Ω

Answer: (c)

35. An unpolarised beam of intensity 2a^{2} passes through a tin Polaroid. Assuming zero absorption in the Polaroid, the intensity of emergent plane plarised light is

(a) 2a^{2}

(b) a^{2}

(c) √2a^{2}

(d) a^{2}/2

Answer: (b)

36. A gas consisting of a rigid diatomic molecules was initially under standard condition. Then, gas was compressed adiabatically to one-fifth of its initial volume. What will be the mean kinetic energy of a rotating molecule in the final state ?

(a) 1.44 J

(b) 4.55 J

(c) 787.98 × 10^{−}^{23} J

(d) 757.3 × 10^{−}^{23} J

Answer: (c)

37. A diode detector is used to detect and amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pF in parallel with a load resistance 100 kΩ. Find the maximum modulated frequency which could be detected by it.

(a) 10.62 MHz

(b) 10.61 kHz

(c) 5.31 MHz

(d) 5.31 kHz

Answer: (b)

38. Red light of wavelength 5400 Å from a distance source falls on a slit 0.80 mm wide. Calculate the distance between first two dark bands on each side of central bright band in the diffraction pattern observed on a screen place 1.4 m from the slit.

(a) 1.89 mm

(b) 4 mm

(c) 1 mm

(d) 3 mm

Answer: (a)

39. A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 20 A flows through the smaller loop, then the flux linked with bigger drop is

(a) 9.1 × 10^{−}^{11} Wb

(b) 6 × 10^{−}^{11} Wb

(c) 3.3 × 10^{−}^{11} Wb

(d) 6.6 × 10^{−}^{9} Wb

Answer: (a)

40. In the adjoining circuit diagram, the readings of ammeter and voltmeter are 2 A and 120 V, respectively. If the value of R is 75 Ω, then the voltmeter resistance will be

(a) 100Ω

(b) 150Ω

(c) 300Ω

(d) 75Ω

Answer: (c)

Direction (Q. Nos. 41-60) Each of these questions contains two statements Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of codes (a), (b), (c) and (d) given below.

(a) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion

(b) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion

(c) Assertion is correct and Reason is incorrect

(d) Assertion is incorrect and Reason is correct

41. Assertion A body is momentarily at res at the instant, if it reverse the direction.

Reason A body cannot have acceleration, if its velocity is zero at a given instant of time.

Answer: (c)

42. Assertion The maximum height of projectile is always 25% of the maximum range.

Reason For maximum range, projectile should be projected at 90°

Answer: (c)

43. Assertion Angle of repose is equal to angle of limiting friction.

Reason When a body is just at the point of motion. the force of friction of this stage is called as limiting friction.

Answer: (a)

44. Assertion Two particles moving in the same direction do not lose all their energy in completely inelastic collision.

Reason Principle of conservation of momentum holds true for all kinds of collisions.

Answer: (a)

45. Assertion The angular momentum of system always remain constant.

Reason For a system,

Answer: (d)

46. Assertion A pendulum is falling freely its time period becomes zero.

Reason Freely falling body has the acceleration equal to g.

Answer: (d)

47. Assertion Smaller drop of water resist deformation forces better than the larger drops.

Reason Excess pressure inside drop is inversely proportional to its radius.

Answer: (a)

48. Assertion In isothermal process, whole of the heat energy supplied to the body is converted into internal energy.

Reason According to the first law of thermodynamics, ∆Q = ∆U + ∆W

Answer: (d)

49. Assertion Internal energy of an ideal gas does not depend on volume of gas.

Reason Internal energy depends only on temperature of gas.

Answer: (a)

50. Assertion To hear different beats difference of the frequencies of two sources should be less than 10.

Reason More the number of beats more in the confusion.

Answer: (c)

51. Assertion Mass of a body decreases slightly when it is negatively charged.

Reason Charging is due to transfer of electrons.

Answer: (d)

52. Assertion A dielectric slab is inserted between plates of an isolated charged capacitor which remain same.

Reason Charge on an isolated system is conserved.

Answer: (a)

53. Assertion Terminal voltage of a cell is greater than emf of cell during charging of the cell.

Reason The magnetic field interacts with a moving charge and not with a stationary charge.

Answer: (c)

54. Assertion A magnetic field interacts with a moving charge and not with a stationary charge.

Reason A moving charge produce a magnetic fied.

Answer: (a)

55. Assertion Bulb generally get fused when they are switched on or off.

Reason When we switch on or off, a circuit current changes in it rapidly.

Answer: (d)

56. Assertion A convex mirror always make a virtual image.

Reason The ray always diverge after reflection from the convex mirror.

Answer: (a)

57. Assertion If a glass slab is placed in front of one of the slits, then fringe with will decrease.

Reason Glass slab will produce an additional path difference.

Answer: (d)

58. Assertion If electrons in an atom were stationary, then they would fall into the nucleus.

Reason Electrostatic force of attraction acts between negatively charged electrons and positive nucleus.

60. Assertion Thickness of depletion layer is fixed inn all semiconductor devices.

Reason No free charge carriers are available in depletion layer.

Answer: (d)

Chemistry

61. In an adiabatic process, no transfer of heat takes place between system and surroundings. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following

(a) q = 0, ∆T ≠ 0, W = 0

(b) q ≠ 0, ∆T = 0, W = 0

(c) q = 0, ∆T = 0, W = 0

(d) q = 0, ∆T < 0, W = 0

Answer: (c)

62. Which of the following represents Wurtz-Fittig reaction?

65. Food preservatives prevent spoilage of food due to microbial growth. The most commonly used preservatives are

(a) C_{6}H_{5}COONa

(b) table salt, sugar

(c) vegetable oils and sodium benzoate

(d) All of the above

Answer: (d)

66. Among the following statements, the correct statement about the half-life period for a first order reaction is

(a) independent of concentration

(b) proportional to concentration

(c) inversely proportional to concentration

(d) inversely proportional to the square of the concentration

Answer: (a)

67. The electronic configuration of central metal atom/ion in [Co(CN)_{6}]^{3}^{−} is

(a)

(b)

(c)

(d)

Answer: (d)

68. A bromoalkane ‘X’ reacts with magnesium in dry ether to form compound ‘Y’. The reaction of ‘Y’ with methanol followed by hydrolysis yield an alcohol having molecular formula, C_{4}H_{10} The compound ‘X’ is

(a) bromomethane

(b) bromoethane

(c) 1-bromopropane

(d) 2-bromopropane

Answer: (c)

The spin only magnetic moment of [MnBr_{4}]^{2}^{−} is 5.9 BM. The geometry this complex ion is

(a) tetrahedral

(b) octahedral

(c) trigonal pyramidal

(d) square planar

Answer: (a)

70. At equilibrium, the concentration of

N_{2} = 3.0 × 10^{−}^{3} M

O_{2} = 4.2 × 10^{−}^{3} M

and NO = 2.8 × 10^{−}^{3} M

in a sealed vessel at 800 K and 1 atm pressure. What will be K_{p} for the given reaction?

N_{2}(g) + O_{2}(g) ⇌ 2NO(g)

(a) 0.328 atm

(b) 0.622 atm

(c) 0.483 atm

(d) 0.712 atm

Answer: (b)

71. Which of the following is an example of network solid?

(a) SO_{2}(solid)

(b) I_{2}

(c) Diamond

(d) H_{2}O(ice)

Answer: (c)

72. Affinity for hydrogen decreases in the group from fluorine to iodine. Which of the halogen acids should have highest bond dissociation enthalpy?

(a) HF

(b) HCl

(c) HBr

(d) HI

Answer: (a)

73. Which of the following compound has same oxidation state of the central metal atom in the cationic and anionic part?

(a) [Pt(NH_{3})_{4}][PtCl_{6}]

(b) [Pt(NH_{3})_{4}Cl_{2}] [PtCl_{4}]

(c) [Pt(Py)_{4}] [PtCl_{4}]

(d) K_{4}[Ni(CN)_{6}]

Answer: (c)

74. The rate constant for the first order decomposition of a certain reaction is described by the equation

The energy of activation for this reaction is

(a) 1.26 × 10^{4} cal mol^{−}^{1}

(b) 4.29 × 10^{4} cal mol^{−}^{1}

(c) 3.12 × 10^{4} cal mol^{−}^{1}

(d) 2.50 × 10^{4} cal mol^{−}^{1}

Answer: (d)

75. In which of the following arrangements, the order is not strictly according to the property written against it?

77. Which of the following oxyacid does not contain P−O−P bond?

(a) Isohypophosphoric acid

(b) Pyrophosphorus acid

(c) Diphosphoric acid

(d) Hypophosphoric acid

Answer: (d)

78. Nioibium crystallizes in body centred cubic structure. If density is 8.55 g cm^{−}^{3}, then the atomic radius of niobium is (atomic mass of niobium = 93 u)

(a) 163 pm

(b) 143 pm

(c) 182 Å

(d) 152 Å

Answer: (b)

79. The IUPAC name of the complex [Pt(NH_{3})_{3}Br(NO_{2})Cl]Cl is

(c) triamine bromidochloridonitro platinum (II) chloride

(d) triamine chloridobromidonitro platinum (II) chloride

Answer: (b)

80. When an excess and a very dilute aqueous solution of KI is added to very dilute aqueous solution of silver nitrate. The colloidal particles of silver iodide which are associated with the Helmholtz double layer in the form of

(a) Agl/Ag^{+} : I^{−}

(b) Agl/K^{+} : NO_{3}^{−}

(c) Agl/NO_{3}^{−} : Ag^{+}

(d) Agl/I^{−} : K^{+}

Answer: (a)

81. 8NH_{3} + 3Cl_{2} → X

(Excess)

NH_{3} + 3Cl_{2} → Y

(Excess)

What is X and Y in the above reaction ?

(a) X = 6NH_{4}Cl + N_{2}; Y = NCl_{3} + 3HCl

(b) X = NCl_{3} + 3HCl; Y = 6NH_{4}Cl + N_{2}

(c) X = NCl_{3} + N_{2}; Y = 6NH_{4}Cl + 3HCl

(d) X = 6NH_{4}Cl + 3HCl; Y = NCl_{3} + N_{2}

Answer: (a)

82. The ionic radii (Å) of C^{4}^{−} and O^{2−} respectively are 2.60 and 1.40. The ionic radius of the isoelectronic ion N^{3−} would be

(a) 1.31 Å

(b) 2.83 Å

(c) 1.71 Å

(d) 2.63 Å

Answer: (c)

83. Which of the following products will be obtained when copper metal is reacted with HNO_{3}?

(a) NO and N_{2}O_{5}

(b) NO and NO_{2}

(c) NO_{2} and N_{2}O_{5}

(d) HNO_{2} and N_{2}

Answer: (b)

84. A gas ‘X’ is used in filling balloons for meterological observations. It is also used in gas-cooled nuclear reactors. Here, the gas X is

(a) neon

(b) argon

(c) krypton

(d) helium

Answer: (d)

85. A solid has a structure in which W atoms are located at the corners of a cubic lattice. O atoms at the centre of edges and Na atom at centre of the cube. The formula for the compound is

(a) NaWO_{2}

(b) NaWO_{3}

(c) Na_{2}WO_{3}

(d) NaWO_{4}

Answer: (b)

86. Benzoic acid undergoes dimerisation in benzene solution. The van’t Hoff factor (i) is related to the degree of association ‘x’ of the acid as

(a) i = (1 – x)

(b) i = (1 + x)

(c) i = (1 – x/2)

(d) i = (1 + x/2)

Answer: (c)

87.

(a)

(b)

(c)

(d)

Answer: (c)

88. At 25°C, the molar conductance at infinite dilution for the strong electrolytes NaOH, NaCl and BaCl_{2} are 248 × 10^{−}^{4}, 126 × 10^{−}^{4} and 280 × 10^{−}^{4} Sm^{2}mol^{−}^{1} λ°_{m} Ba(OH)_{2} in Sm^{2}mol^{−1 }is

(a) 362 × 10^{−}^{4}

(b) 402× 10^{−}^{4}

(c) 524× 10^{−}^{4}

(d) 568 × 10^{−}^{4}

Answer: (c)

89.

In the above reaction sequence, X is

(a) cyclohexanone

(b) caprolactam

(c) hexamethylene di-isocyanate

(d) HO(CH_{2})_{6}NH_{2}

Answer: (b)

90. The correct order of spin only magnetic moment (in BM) for Mn^{2+}, Cr^{2+} and Ti^{2+} ions is

(a) Mn^{2+} > Ti^{2+} > Cr^{2+}

(b) Ti^{2+} > Cr^{2+} > Mn^{2+}

(c) Mn^{2+} > Cr^{2+} > Ti^{2+}

(d) Cr^{2+} > Ti^{2+} > Mn^{2+}

Answer: (c)

91. Which of the following compounds do not undergo aldol condensation ?

(a)

(b) CH_{3} – CHO

(c)

(d) CH_{3}CH_{2}CHO

Answer: (a)

92. A green yellow gas reacts with an alkali metal hydroxide to form a halite which can be used in fireworks and safety matches. The gas and halite are, respectively

(a) Br_{2}, KBrO_{3}

(b) Cl_{2}, KClO_{3}

(c) I_{2}, NalO_{3}

(d) Cl_{2}, NaClO_{3}

Answer: (b)

93. The correct order of decreasing stability of the following carbocation is

(a) II > I > III

(b) II > III > I

(c) III > I > II

(d) I > II > III

Answer: (a)

94. Hydrolysis of sucrose with dilute aqueous sulphuric acid yields

(a) 1 : 2 D-(+)-glucose; D-(−)-fructose

(b) 1 : 2 D-(−)-glucose; D-(+)-fructose

(c) 1 : 1 D-(−)-glucose; D-(+)-fructose

(d) 1 : 1 D-(+)-glucose; D-(−)-fructose

Answer: (d)

95. Among the following complex ions, the one which shows geometrical isomerism will be

(a) [Cr(H_{2}O)_{4}Cl_{2}]^{+}

(b) [Pt(NH_{3})_{3}Cl]

(c) [CO(NH_{3})_{6}]^{3+}

(d) [CO(CN)_{5}(NC)]^{3}^{−}

Answer: (a)

96. ∆H and ∆E for the reaction,

Fe_{2}O_{3} (s) + 3H_{3}(s) → 2Fe(s) + H_{0}O(l)

at constant temperature are related as

(a) ∆H = ∆E

(b) ∆H = ∆E + RT

(c) ∆H = ∆E + 3R

(d) ∆H = ∆E – 3RT

Answer: (d)

97. The correct IUPAC name of the given compound is

(a) 7-hydroxy cyclohex-5-en-1-one

(b) 3-hydroxy cyclohex-5-en-1-one

(c) 8-hydroxy cyclohex -3-en-1-one

(d) 5-hydroxy cyclohex-3-en-1-one

Answer: (d)

98. Among the following rules, the one which is applied in the given reaction is

I. CH_{3}CH = CHCH_{3} (major product)

II. CH_{2} = CHCH_{2}CH_{3} (minor product)

(a) Saytzeff’s rule

(b) Hofmann’s rule

(c) Markownikoff’s rule

(d) Kharasch effect

Answer: (a)

99. The solubility product of sparingly soluble salt AX_{2} is 3.2 × 10^{−}^{11}. Its solubility (in mol/L) is

(a) 5.6 × 10^{−}^{6}

(b) 3.1 × 10^{−}^{4}

(c) 2 × 10^{−}^{4}

(d) 4 × 10^{−}^{4}

Answer: (c)

100. The structure of IF_{7} is

(a) square pyramidal

(b) trigonal bipyramidal

(c) octahedral

(d) pentagonal bipyramidal

Answer: (d)

Chemistry

Direction (Q. Nos. 101-120) In the questions that following two statements (Assertion and Reason) are given. Statement II (R) is purported to be the explanation for statement I (A). Study both the statements carefully and then mark your answers, according to the codes given below.

(a) Both (A) and (R) are true and (R) is the correct explanation of (A).

(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).

(c) (A) is true but (R) is false.

(d) Both (A) and (R) are false.

101. Assertion (A) Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).

Reason (R) The conductivity of a solution having surfactant molecules decreases sharply at the CMC.

Answer: (b)

Assertion (A) The pH of acid rain is less than 5.6.

Reason (R) Carbon dioxide present in the atmosphere dissolves in rain water and becomes carbonic acid.

Answer: (b)

103. Assertion (A) Electron gain enthalpy becomes less negative as we go down a group.

Reason (R) Size of the atom increases on going down the group and the added electron would be farther away from the nucleus.

Answer: (a)

104. Assertion (A) Among the two O―H bonds in H_{2}O molecule, the energy required to break the first O―H bond and the other O―H bond is same.

Reason (R) This because the electronic environment around oxygen is the same even after breakage of one O―H bond.

Answer: (d)

105. Assertion (A) Nitration of benzene with nitric acid requires the use of concentrated sulphuric acid.

Reason (R) The mixture of concentrated sulphuric acid and concentrated nitric acid produces the electrophile, NO_{2}^{+}.

Answer: (a)

106. Assertion (A) Beryllium carbonate is kept in the atmosphere of carbon dioxide.

Reason (R) Beryllium carbonate is unstable and decomposes to give beryllium oxide and carbon dioxide.

Answer: (a)

107. Assertion (A) Separation of Zr and Hf is difficult.

Reason (R) Zr and Hf lie in the same group of the periodic table.

Answer: (b)

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128. Assertion (A) Toxic metal ions are removes by the chelating ligands.

Reason (R) Chelate complexes tend to be more stable.

Answer: (a)

109. Assertion (A) IUPAC name of the compound is

Reason (R) In IUPAC nomenclature, ether is regarded as hydrocarbon derivative in which a hydrogen atom is replaced by-OR or-Oar group [where, R = alkyl group and Ar = aryl group].

Answer: (a)

Assertion (A) The reaction

2NO + O_{2} → 2 NO_{2}

and 2CO + O_{2} → 2CO_{2}

proceeds at the same rate because they are similar.

Reason (R) Both the reactions have same activation energy.

Answer: (d)

111. Assertion (A) The boiling points of alkyl halides decreases in the order RI > RBr > RCl > RF.

Reason (R) The boiling points of alkyl chlorides, bromides and iodides are considerably higher than that of the hydrocarbon of comparable molecular mass

Answer: (b)

112. Assertion (A) N_{2} is less reactive than P_{4}/

Reason (R) Nitrogen has more electron gain enthalpy than phosphorus.

Answer: (c)

113. Assertion (A) The molecular mass of the polymers cannot be calculate using the boiling point or freezing point method.

Reason (R) The freezing point method is used for determining the molecular mass of small molecules.

Answer: (a)

114. Assertion (A) NaCl reacts with concentrated H_{2}SO_{4} to give colouless fumes with pungent smell. But on adding MnO_{2} the fume become greenish yellow.

Reason (R) MnO_{2} oxidises HCl to chlorine gas which is greenish yellow

Answer: (a)

115. Assertion (A) K_{p} can be equal to or less than or even greater than the value of K_{C}.

Reason (R) K_{p} = K_{C} (RT)^{∆}^{n}

Relation between K_{p} and K_{C} depends on the change in the number of moles of gaseous reactants and products.

Answer: (a)

116. Assertion (A) CH_{4} does not react with Cl_{2} in dark.

Reason (R) Chlorination of CH_{4} takes place in sunlight.

Answer: (a)

117. Assertion (A) CH_{3}OH and CH_{3}CH_{2}OH can be distinguished by haloform test.

Reason (R)Haloform test is given by 2° alcohol.

Answer: (b)

118. Assertion (A) For a Daniell cell Zn/Zn^{2+}||Cu^{2+}|Cu with E_{cell} = 1.1 V, the application of opposite potential greater than 1.1 V results into the flow of electrons from cathode to anode.

Reason (R) Zn is deposited at zinc electrode and Cu is dissolved at copper electrode.

Answer: (a)

119. Assertion (A) Most of the synthetic polymers are not biodegradable.

Reason (R) Polymerisation process induces toxic polymerisation.

Answer: (c)

120. Assertion (A) Graphite an example of tetragonal crystal system.

Reason (R) For a tetragonal system, a = b ≠ c and α = β = 90°, γ = 120°.

Answer: (d)

Biology

121. Biomagnification can be defined as

(a) Decomposition of organic waste in water by the action of microbes

(b) Breeding of crops that are rich in minerals and vitamins good proteins and healthier fats

(c) Increase in concentration of the toxicant at successive trophic levels

(d) Exploring the products of economic importance at molecular, genetic and species level diversity

Answer: (c)

122. Leaf tendrils are found in

(a) grapevine

(b) peas

(c) cucumber

(d) All of the above

Answer: (d)

123. Diagram of large intestine is given below. Identify the parts A, B, C, D, E and F.

124. Select the incorrect statement(s) from options given below with respect to dihybrid cross.

(I) Tightly linked genes on the same chromosome show higher recombinations.

(II) Genes far apart on the same chromosome show very few recombinations.

(III) Genes loosely linked on the same chromosome show similar recombinations.

(a) I and II

(b) III and II

(c) I and III

(d) All of these

Answer: (d)

125. Match the stages of meiosis in column I to their characteristic features in column II and select the correct option using the codes given

Answer: (d)

126. Read the following statements

(I) Species diversity decreases as we move away from the quator towards the poles.

(II) Stellar’s sea cow and passenger pigeon got extinct due to overexploitation by man.

(III) Lantana and Eichhornia are invasive weed in India.

(IV) The historic convention on biological diversity was held in 1992.

Choose the option containing correct statements.

(a) I and II

(b) I, II and IV

(c) I, III and IV

(d) II, III and IV

Answer: (d)

127. Characteristics of cancer are

(a) All viruses are oncogenic

(b) All tumours are cancers

(c) Cancerous cells show properly of contact inhibtion

(d) Cancer cells show metastasis

Answer: (d)

128. Select the incorrect match.

(I) Sedimentary nutrient cycle-Nitrogen cycle

(II) Pioneer species-Lichens

(III) Secondary succession-Burned forests

(IV) Pyramid of biomass in sea – Upright

(a) I and IV

(b) I and III

(c) II and III

(d) II and IV

Answer: (a)

129. Apical dominance is caused by

(a) auxin

(b) ethylene

(c) gibberellin

(d) cytokinin

Answer: (a)

130. Consider the following four measures (I-IV) that could be taken to successfully grow chickpea in an area where bacterial blight is common.

(I) Spray with Bordeaux mixture.

(II) Control of the insect vector of the disease pathogen.

(III) Use of disease-free seeds only.

(IV) Use of varieties resistant to the disease.

Which of the above measures can control the diseases?

(a) I, II and IV

(b) I, III and IV

(c) II, III and IV

(d) I, II and III

Answer: (b)

131. Match the organisms given in Column I to their functions given in Column II and choose the correct option.

Answer: (a)

132. A plant has a butterfly-shaped flower with one standard, two wing like and two keel petals. To which family, this plant belongs?

(a) Malvaceae

(b) Papilionaceae

(c) Rubiaceae

(d) Compositate

Answer: (b)

133. Identify the permanent tissues shown in the following figures.

(a) A-Collenchyma, B-Parenchyma, C-Sclerenchyma

(b) A-Sclerenchyma, B-Collenchyma, C-Parenchyma

(c) A-Collenchyma, B-Sclerenchyma, C-Parenchyma

(d) A-Parenchya, B-Collenchyma, C-Sclerenchyma

Answer: (d)

134. Find the correct statements from the following

(I) Gene therapy is a genetic engineering technique used to treat diseases at molecular level.

(II) Calcitonin is medically useful recombinant product in the treatment of infertility.

(III) Bt toxin is a biodegradable insecticide obtained from Bacillus thuringiensis.

(a) Only I

(b) Only II

(c) I and III

(d) I and II

Answer: (c)

135. A mutant plant is unable to produce materials or precursors that form Casparian strip. This plan would be

(a) unable to transport water from roots to the leaves

(b) able to exert greater root pressure than the normal plant

(c) unable to transport food from leaves to roots

(d) unable to control amount of water and solute it absorbs

Answer: (c)

136. Cell A has osmotic pressure of −20 bars and pressure potential of 5 bars, whereas cell B has osmotic pressure of −18 bars and pressure potential of 2 bars.

The direction of flow of water will be

(a) from cell B to cell A

(b) fro cell A to B

(c) no flow of water

(d) in both the directions

Answer: (a)

137. If a recombinant DNA bearing gene for ampicillin resistance is transferred into E.coli cells and the host cells are spread on agar plates containing ampicillin, then

(a) both transformed and untransformed recipient cells will die

(b) both transformed and untransformed recipient cells will grow

(c) transformed recipient cells will grow and untransformed recipient cells will die

(d) transformed recipient cells will die and untransformed recipient cells will grow

Answer: (c)

138. Adults of Wuchereria bancrofti attack

(a) excretory system

(b) digestive system

(c) lymphatic system

(d) nervous system

Answer: (c)

139. Which of the following pathways occurs through cell wall?

(a) Apoplast pathway

(b) Vascular pathway

(c) Symplast pathway

(d) Non-vacuolar pathway

Answer: (a)

140. Which of the following plants are used to treat bone fractures?

(a) Digitalin purpea

(b) Hevea brasiliensis

(c) Cissus quadrangularis

(d) Lowsomia inemis

Answer: (c)

141. C_{4} pathway is advantageous over C_{3} pathway in plants, because it

(a) occurs in relatively low CO_{2} concentration

(b) uses more amount of water

(c) occurs in relatively low O_{2} concentration

(d) is less efficient in energy utilization

Answer: (a)

142. Production of human protein in bacteria by genetic engineering is possible because

(a) the human chromosomes can replicate in the bacterial cell

(b) the mechanism of gene regulation is identical in humans and bacteria

(c) bacterial cells can carry out RNA splicing reactions

(d) the genetic code is universal

Answer: (d)

143. Choose the correct statements with reference to organic evolution.

(I) Flippers of whale and wings of bat exhibit analogy.

(II) Wings of butterfly and wings of bird exhibit homology.

(III) Organs with dissimilar structure are called analogous organs.

(IV) Organs with similar structure and origin are called homologous organs.

(a) I and IV

(b) I and III

(c) III and IV

(d) II and IV

Answer: (c)

144. Triticale is the first man-made cereal crop. Mention the type of hybridization through which it produced.

(a) Intervarietal hyrbidisation

(b) Interspecific hybridisation

(c) Intergeneric hybridisation

(d) Intavarietal hybridisation

Answer: (c)

145. Azolla is used as a biofertiliser because it

(a) has association of mycorrhiza

(b) multiplies at faster rate to produce massive biomass

(c) has association of nitrogen-fixing Rhizobium

(d) has association of nitrogen-fixing cyanobacteria

Answer: (d)

146. Person ‘A’ cannot step out of his house. He has to spend his entire life in sterile isolation otherwise, he would quickly contract a fatal infection. This person has almost no effective immune system. This disease is also called as baby in a bubble syndrome. Identify the disease, this person ‘A’ is suffering from

(a) Cystic fibrosis

(b) Diabetes

(c) AIDS

(d) SCID

Answer: (d)

147. The peppered moth (Biston betularia), the black-coloured form becomes dominant over the light-coloured form of month in England during industrial revolution. This is an example of

(a) appearance of the darker-coloured individuals due to very poor sunlight

(b) protective mimicry

(c) inheritance of darker colour character acquired due to the darker environment

(d) natural selection whereby the darker forms were selected

Answer: (d)

148. A normal woman whose father was colourblind, marries a normal man. What kinds of children can be expected and in what proportion?

(a) All daughters normal, 50% of sons colourblind

(b) All daughters normal, all sons colourblind

(c) 50% daughters colourblind, all sons normal

(d) All daughters colourblind, all sons normal

Answer: (a)

149. From the graph of population growth, select the correct option having correct value of ‘r’ and bar graph.

Answer: (d)

What is true about the isolated small tribal populations?

(a) Wrestlers who develop strong body muscles in their lifetime pass this character on their progeny

(b) There is no change in population size as they have a large gene pool

(c) There is a decline in population as boys marry girls only from their own tribe

(d) Hereditary diseases like colour blindness do not spread in the isolated population

Answer: (c)

151. Codons of glycine are

(a) CCU, CCC, CCA, CCG

(b) CGU, CGC, CGA, CGG

(c) GGU, GGC, GGA, GGG

(d) ACU, ACC, ACA, ACG

Answer: (c)

152. Which one of the following organisms do not evolve oxygen during photosynthesis?

(a) Blue-green algae

(b) Red algae

(c) Photosynthetic bacteria

(d) C_{4} plants

Answer: (c)

153. Which of the following biomolecules is common to respiration-mediated breakdown of fats, carbohydrates and proteins?

(a) Glucose-6-phosphate

(b) Pyruvic acid

(c) Fructose-1, 6 biophosphate

(d) Acetyl Co-A

Answer: (d)

154. Match Column I (Antibiotic) with Column II (Source) and choose the correct option from the codes given below.

Answer: (b)

155. Arrange in correct order according to the given figures.

(a) A-Imbricate, B-Quincuncial, C – Valvate, D-Twisted, E – Vexillary

156. cry II Ab and cry I Ab produce toxins that control

(a) cotton bollworms and corn borer, respectively

(b) corn borer and cotton bollworms, respectively

(c) tobacco budworms and nematodes, respectively

(d) nematodes and tobacco budworms, respectively

Answer: (a)

157. Match the following columns.

Answer: (c)

158. Which one of the following conditions correctly describes the manner of determining the sex?

(a) Homozygous sex chromosomes (ZZ) determine female sex in birds

(b) XO type of sex chromosomes determine male sex in grasshopper

(c) XO condition in humans as found in Turner’s syndrome determines female sex

(d) Homozygous sex chromosomes (XX) produce males in Drosophila

Answer: (b)

159. Read the following statements

(I) Colostrum is recommended for the new borns because it is rich in antigens.

(II) Chikungunya is caused by a Gram negative bacterium.

(III) Tissue culture has proved useful in obtaining virus-free plants

(IV) Beer is manufactured by distillation of fermented grapes.

How many of the statement(s) is/are correct

(a) Two

(b) One

(c) Three

(d) Four

Answer: (b)

160. A scion is grafted to a stock. The quality of fruits produced will be determined by the genotype of

(a) stock

(b) scion

(c) Both (a) and (b)

(d) Neither (a) nor ( b)

Answer: (b)

Direction (Q. Nos. 161-180) In each of the following questions a statement of assertion is given followed by the corresponding statement of reason. Of the statements, mark the correct answer as

(a) Both A and R are true and R is the correct explanation of A

(b) Both A and R are true, but R is not the correct explanation of A

(c) A is true, but R is false

(d) A and R are false

161. Assertion Nitrogen-fixing bacteria of legume root nodules survive in oxygen depleted cells.

Reason Leghaemoglobin completely removes oxygen from nodule cells.

Reason Cyanide combines with copper of cytochroe oxide and prevents oxygen to combine with it.

Answer: (b)

163. Assertion In females, parturition is the act of giving birth to a baby.

Reason Signals for parturition originate from a fully developed foetus.

Answer: (b)

164. Assertion Meiotic division occurs in reproductive cells.

Reason Synapsis occurs during zygotene of meiosis.

Answer: (b)

165. Assertion Peptide and polypeptide hormones directly pass across the lipid bilayer of plasma membrane.

Reason Oxytocin hormone can pass across the plasma membrane.

Answer: (d)

166. Assertion In apomixis, the plants of new genetic sequence are produced.

Reason In apomixis, two organisms of same genetic sequence meet.

Answer: (d)

167. Assertion The quiescent centre acts as a reservoir of relatively resistance cells, which constitute a permanent source of active initials.

Reason The cells of the inactive region of quiescent centre become active, when the previous active initials get damaged.

Answer: (a)

168. Assertion Two turns of Kreb’s cycle occur per glucose molecule used.

Reason Each turn of Kreb’s cycle produces 3 NADH_{2} and 1 ATP molecule.

Answer: (b)

169. Assertion Alcoholics may show deficiency symptoms of Wernicke’s and Korsakoff’s syndromes.

Reason Alcohol acts as depressant.

Answer: (b)

170. Assertion BOD is an indicator of pollution in water.

Reason High BOD is observed in highly polluted water.

Answer: (a)

171. Assertion Pork should be properly cooked to avoid Taenia

Reason Pork of pig contains hexacanth and cystiercus larvae.

Answer: (c)

172. Assertion Magnesium is important in photosynthesis and carbohydrate metabolism.

Reason Mg^{2+} is involved in the synthesis of nucleic acids.

Answer: (b)

173. Assertion Phenylketonuria is recessive hereditary disease caused by body’s failure to oxidize can amino acid phenylalanine to tyrosine, because of defective enzyme.

Reason It is characterized by in the presence of phenylalanine acid in urine.

Answer: (b)

174. Assertion Caryopsis fruits differ from typical achenes with respect to the fusion of pericarp with the seed-caot (testa)

Reason Caryopsis fruits commonly occur in the members of family-Poaceae.

Answer: (b)

175. Assertion The collenchymas is a thick-walled living tissue.

Reason The collenchymas is thickened due to deposition of pectin.

Answer: (a)

176. Assertion In mitosis, two identical cells are produced from a single cell and karyokinesis is followed by cytokinesis.

Reason Cytokinesis is of two types, i.e. by cell-furrow method and cell-plate method.

Answer: (b)

177. Assertion Non-cyclic photophosphorylation occurs in the stroma of chloroplasts.

Reason There is discontinuous flow of electrons in this process.

Answer: (d)

178. Assertion Taeniasolium and Dugesia belong to Patyhelminthes.

Reason Platyhelminthes are coelomates.

Answer: (c)

179. Assertion The non-allelic genes for red hair and prickles are usually inherited together.

Reason The genes for red hair and prickles are located on the same chromosome in close association.

Answer: (a)

180. Assertion Photomodulation of flowr is phytochrome regulated process.

Reason Active form of phytochrome (Pfr) directly induces floral inducation in shoot buds.

Answer: (c)

General Knowledge

181. Identify this famous personality?

(a) Vladimir Putin

(b) Donald Trump

(c) George W Bush

(d) Barack Obama

Answer: (b)

182. The Parliament of Japan is known as

(a) Assembly

(b) Key

(c) Senate

(d) Diet

Answer: (d)

183. Name the person given in the figure.

(a) Ban-Ki-Moon

(b) Kim Jong-Un

(c) Haan Myeong-Sook

(d) Win Mying

Answer: (b)

184. Pruning is an essential part in cultivation of

(a) rubber

(b) tobacco

(c) coffee

(d) tea

Answer: (d)

185. An Ordinary Bill passed by the State Assembly can be delayed by the Legislative Council for a maximum period of

(a) 1 month

(b) 6 months

(c) 3 months

(d) 4 months

Answer: (c)

186. Which of the following hills are found where the Eastern ghats and the Western ghats

(a) Anaimalai Hills

(b) Cardamom Hills

(c) Nilgiri Hills

(d) Shevoroy Hills

Answer: (c)

187. The transition zone between two ecosystems is called

(a) biome

(b) biotope

(c) ecotone

(d) sere

Answer: (c)

188. The non-permanent members of the Security Council are elected for

(a) one year

(b) two years

(c) three years

(d) six months

Answer: (b)

189. The Fundamental Right which has been described by Dr. B R Ambedkar as ‘The heart and soul of the Constitution’ is the right to

(a) Equality

(b) Property

(c) Freedom of Religion

(d) Constitutional Remedies

Answer: (a)

190. One of the leaders who founded the Swaraj Party was

(a) Mahatma Gandhi

(b) B G Tilak

(c) K Kamaraj

(d) Chittaranjan Das

Answer: (d)

191. The policy of price control in markets was launched by

(a) Sher Shah

(b) Ashoka

(c) Akbar

(d) Alauddin Khalji

Answer: (d)

192. The place which has the longest day and the shortest night on 22nd December, is

(a) Chennai

(b) Madrid

(c) Melbourne

(d) Moscow

Answer: (c)

193. From which sports ‘Gary Player’ is associated with?

(a) Cricket

(b) Golf

(c) Hockey

(d) Table Tennis

Answer: (b)

194. Rashid khan has become the youngest captain in international cricket history. He belong to which country?

(a) Nepal

(b) Bangladesh

(c) Afghanistan

(d) Sri Lanka

Answer: (c)

195. Who among the following is/are the recipient of Rajiv Gandhi Khel Ratna Award 2017?

(a) Virat Kohli

(b) Devendra Jhajharia

(c) Saradara Singh

(d) Both (b) and (c)

Answer: (d)

196. Which of the following acts gave representation to the Indians for the first time in legislation ?

(a) Indian Councils Act, 1909

(b) Indian Councils Act, 1919

(c) Government of India Act, 1919

(d) Government of India Act, 1935

Answer: (a)

197. How many members of the Rajya Sabha retire from the house every 2 years?

(a) 1/6 of the total members

(b) 1/3 of the total members

(c) 1/12 of the total members

(d) 5/6 of the total members

Answer: (b)

198. The depiction of the stories of the previous lives of Gautam Buddha was firstly done in the art of

(a) Sarnath Pillar of Ashoka

(b) Bharat Stupa

(c) Ajanta Caves

(d) Ellora Caves

Answer: (d)

199. The earliest Surat factories were established by the

(a) Portuguese

(b) Dutch

(c) English

(d) French

Answer: (c)

200. In which year Gandhiji established Sabarmati Asharm in Gujarat?

1. A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60° with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is

(1) 2v/√3

(2)

(3) v/2

(4) v

Answer: (3)

2. In the figure shown, a circuit contains two identical resistors with resistance R = 5 Ω and an inductance with L = 2 mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed?

(1) 7.5 A

(2) 3 A

(3) 6 A

(4) 5.5 A

Answer: (3)

3. The galvanometer deflection, when key K1 is closed but K_{2} is open, equal θ_{0} (see figure). On closing K_{2} also and adjusting R 2 to 5 Ω, the deflection in galvanometer becomes θ_{0}/5. The resistance of the galvanometer is, then given by [Neglect the internal resistance of battery]

(1) 22 Ω

(2) 25 Ω

(3) 5 Ω

(4) 12 Ω

Answer: (1)

4. The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 μm diameter of a wire is

(1) 200

(2) 50

(3) 100

(4) 500

Answer: (1)

5. A travelling harmonic wave is represented by the equation y(x, t) = 10^{–3} sin (50t + 2x), where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?

(1) The wave is propagating along the negative x-axis with speed 25 ms^{–1}.

(2) The wave is propagating along the positive x-axis with speed 100 ms^{–1}.

(3) The wave is propagating along the negative x-axis with speed 100 ms^{–1}.

(4) The wave is propagating along the positive x-axis with speed 25 ms^{–1}.

Answer: (1)

6. A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass ‘m’ at x = 0, if the mass per unit length of the rod is A + Bx^{2}, is given by

Answer: (3)

7. There is a uniform spherically symmetric surface charge density at a distance R_{0} from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is

Answer: (4)

8. A proton and an α-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii r_{p} : r_{α} of the circular paths described by them will be

(1) 1 : 3

(2) 1 : 2

(3) 1 : √3

(4) 1 : √2

Answer: (4)

9. For the given cyclic process CAB as shown for a gas, the work done is

(1) 30 J

(2) 10 J

(3) 5 J

(4) 1 J

Answer: (2)

10. In a meter bridge, the wire of length 1 m has a nonuniform cross-section such that, the variation dR/dl of its resistance R with length l is . Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?

(1) 0.2 m

(2) 0.35 m

(3) 0.25 m

(4) 0.3 m

Answer: (3)

11. The output of the given logic circuit is

(1)

(2)

(3)

(4)

Answer: (2)

12. As shown in the figure, two infinitely long, identical wires are bent by 90° and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4 cm, and the magnitude of the magnetic field at O is 10^{–4} T, and the two wires carry equal currents (see figure), the magnitude of the currents in each wire and the direction of the magnetic field at O will be (μ_{0} = 4π × 10^{–7} NA^{–2})

(1) 40 A, perpendicular into the page

(2) 20 A, perpendicular into the page

(3) 40 A, perpendicular out of the page

(4) 20 A, perpendicular out of the page

Answer: (2)

13. An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5 Ω. The value of R, to give an potential difference of 5 mV across 10 cm of potentiometer wire, is

(1) 480 Ω

(2) 490 Ω

(3) 495 Ω

(4) 395 Ω

Answer: (4)

14. A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K_{1} and that of the outer cylinder is K_{2} . Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

(1)

(2)

(3) K_{1} + K_{2}

(4)

Answer: (2)

15. A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction, and (ii) in the opposite directions is

(1) 25/11

(2) 5/2

(3) 11/5

(4) 3/2

Answer: (3)

16. Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P_{1} and P_{2} respectively, then

(1) P_{1} = 9 W, P_{2} = 16 W

(2) P_{1} = 4 W, P_{2} = 16 W

(3) P_{1} = 16 W, P_{2} = 9 W

(4) P_{1} = 16 W, P_{2} = 4 W

Answer: (4)

17. A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

(1) 0.5

(2) 0.4

(3) 0.6

(4) 0.3

Answer: (3)

18. Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre ‘O’ and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is

(1)

(2)

(3)

(4)

Answer: (4)

19. A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ_{0}. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ_{1} . Then M is given by

(1)

(2)

(3)

(4)

Answer: (1)

20. Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is

(1) 14 cm

(2) 12 cm

(3) 16 cm

(4) 18 cm

Answer: (3)

21. A particle A of mass ‘m’ and charge ‘q’ is accelerated by a potential difference of 50 V. Another particle B of mass ‘4 m’ and charge ‘q’ is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths λ_{A}/λ_{B} is close to

(1) 0.07

(2) 14.14

(3) 4.47

(4) 10.00

Answer: (2)

22. The position vector of the centre of mass of an asymmetric unifom bar of negligible area of cross-section as shown in figure is

Answer: (3)

23. An ideal gas occupies a volume of 2 m^{3} at a pressure of 3 × 106 Pa. The energy of the gas is

(1) 10^{8} J

(2) 9 × 10^{6} J

(3) 6 × 10^{4} J

(4) 3 × 10^{2} J

Answer: (2)

24. A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be

(1) Such that it escapes to infinity

(2) In a circular orbit of a different radius

(3) In an elliptical orbit

(4) In the same circular orbit of radius R

Answer: (3)

25. A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror is

(1) d/2

(2) 3d

(3) 2d

(4) d

Answer: (2)

26. A particle of mass m moves in a circular orbit in a central potential field If Bohr’s quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as

(1) r_{n} ∝ n, E_{n} ∝ n

(2) r_{n} ∝ √n, E_{n} ∝ n

(3) r_{n} ∝ √n, E_{n} ∝ 1/n

(4) r_{n} ∝ n^{2}, E_{n} ∝ 1/n

Answer: (2)

27. A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propogating in the glass medium will be

(1) 6 V/m

(2) 10 V/m

(3) 24 V/m

(4) 30 V/m

Answer: (3)

28. What is the position and nature of image formed by lens combination shown in figure? (f _{1}, f _{2} are focal lengths)

(1) 20/3 cm from point B at right; real

(2) 70 cm from point B at right; real

(3) 40 cm from point B at right; real

(4) 70 cm from point B at left; virtual

Answer: (2)

29. In the figure shown, after the switch ‘S’ is turned from position ‘A’ to position ‘B’, the energy dissipated in the circuit in terms of capacitance ‘C’ and total charge ‘Q’ is

Answer: (1)

30. Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure

(1)

(2)

(3)

(4)

Answer: (3)

CHEMISTRY

1. Water samples with BOD values of 4 ppm and 18 ppm, respectively, are

(1) Clean and Highly polluted

(2) Clean and Clean

(3) Highly polluted and Clean

(4) Highly polluted and Highly polluted

Answer: (1)

2. Given

Gas H_{2 }CH_{4 }CO_{2 }SO_{2}

Critical 33 190 304 630

Temperature/K

On the basis of data given above, predict which of the following gases shows least adsorption on a definite amount of charcoal?

(1) SO_{2}

(2) CO_{2}

(3) CH_{4}

(4) H_{2}

Answer: (4)

3. The metal d-orbitals that are directly facing the ligands in K_{3}[Co(CN)_{6}] are

(1) d_{xy}, d_{xz} and d_{yz}

(2)

(3)

(4)

Answer: (3)

4. A metal on combustion in excess air forms X. X upon hydrolysis with water yields H_{2}O_{2} and O_{2} along with another product. The metal is

(1) Rb

(2) Li

(3) Mg

(4) Na

Answer: (1)

5. The correct order for acid strength of compounds

CH ≡ CH, CH_{3} – C ≡ CH and CH_{2} = CH_{2} is as follows :

(1) CH_{3} – C ≡ CH > CH ≡ CH > CH_{2} = CH_{2}

(2) CH_{3} – C ≡ CH > CH_{2} = CH_{2} > HC ≡ CH

(3) CH ≡ CH > CH_{2} = CH_{2} > CH_{3} – C ≡ CH

(4) HC ≡ CH > CH_{3} – C ≡ CH > CH_{2} = CH_{2}

Answer: (4)

6. The hardness of a water sample (in terms of equivalents of CaCO3) containing 10–3 M CaSO4 is (molar mass of CaSO_{4} = 136 g mol^{–1})

(1) 10 ppm

(2) 100 ppm

(3) 90 ppm

(4) 50 ppm

Answer: (2)

7. In the following reaction

Adehyde Alcohol

HCHO BuOH

CH_{3}CHO MeOH

The best combination is

(1) HCHO and MeOH

(2) HCHO and ^{t}BuOH

(3) CH_{3}CHO and ^{t}BuOH

(4) CH_{3}CHO and MeOH

Answer: (1)

8. Poly-β-hydroxybutyrate-co- β -hydroxyvalerate (PHBV) is a copolymer of ___.

(1) 3-hydroxybutanoic acid and 4-hydroxypentanoic acid

(2) 3-hydroxybutanoic acid and 2-hydroxypentanoic acid

(3) 2-hydroxybutanoic acid and 3-hydroxypentanoic acid

(4) 3-hydroxybutanoic acid and 3-hydroxypentanoic acid

Answer: (4)

9. The molecule that has minimum/no role in the formation of photochemical smog, is

(1) NO

(2) CH_{2} = O

(3) O_{3}

(4) N_{2}

Answer: (2)

10. The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is

(1) (A) < (B) < (C) < (D)

(2) (B) < (A) < (C) < (D)

(3) (B) < (A) < (D) < (C)

(4) (A) < (C) < (D) < (B)

Answer: (2)

11. cannot be prepared by

(1) PhCOCH_{2}CH_{3} + CH_{3}MgX

(2) CH_{3}CH_{2}COCH_{3} + PhMgX

(3) HCHO + PhCH(CH_{3})CH_{2}MgX

(4) PhCOCH_{3} + CH_{3}CH_{2}MgX

Answer: (3)

12. Two solids dissociate as follows

The total pressure when both the solids dissociate simultaneously is

(1) x^{2} + y^{2} atm

(2) (x + y) atm

(3)

(4)

Answer: (4)

13. The standard electrode potential E^{⊝} and its temperature coefficient (dE^{⊝}/dT) for a cell are 2 V and −5 × 10^{−}^{4} VK^{−}^{1} at 300 K respectively. The cell reaction is

Zn(s) + Cu^{2+}(aq) → Zn^{2+}(aq) + Cu(S)

The standard reaction enthalpy (∆_{r}H^{⊝}) at 300 K in kJ mol^{−}^{1} is,

[Use R = 8 JK^{−}^{1} mol^{−}^{1} and F = 96,000 C mol^{−}^{1}]

(1) 206.4

(2) −384.0

(3) −412.8

(4) 192.0

Answer: (3)

14. Decomposition of X exhibits a rate constant of 0.05 μg/year. How many years are required for the decomposition of 5 μg of X into 2.5 μg?

(1) 40

(2) 20

(3) 50

(4) 25

Answer: (3)

15. In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out of

(1) Carbon

(2) Copper

(3) Platinum

(4) Pure aluminium

Answer: (1)

16. What is the work function of the metal if the light of wavelength 4000 Å generates photoelectrons of velocity 6 × 10^{5} ms^{–1} from it?

(Mass of electron = 9 × 10^{–31} kg

Velocity of light = 3 × 10^{8} ms^{–1}

Planck’s constant = 6.626 × 10^{–34} Js

Charge of electron = 1.6 × 10^{–19} JeV^{–1})

(1) 4.0 eV

(2) 2.1 eV

(3) 3.1 eV

(4) 0.9 eV

Answer: (2)

17. Among the following four aromatic compounds, which one will have the lowest melting point?

(1)

(2)

(3)

(4)

Answer: (1)

18. In the following reactions, products A and B are

Answer: (2)

19. The pair of metal ions that can give a spin only magnetic moment of 3.9 BM for the complex [M(H_{2}O)_{6}]Cl_{2}, is

(1) V^{2+} and Co^{2+}

(2) Co^{2+} and Fe^{2+}

(3) V^{2+} and Fe^{2+}

(4) Cr^{2+} and Mn^{2+}

Answer: (1)

20. In a chemical reaction, the initial concentration of B was 1.5 times of the concentration of A, but the equilibrium concentrations of A and B were found to be equal. The equilibrium constant (K) for the aforesaid chemical reaction is

(1) 1

(2) 16

(3) 4

(4) 1/4

Answer: (3)

21. The major product of the following reaction

(1)

(2)

(3)

(4)

Answer: (2)

22. For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?

(1)

(2)

(3)

(4)

Answer: (4)

23. The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressure of the gases for equal number of moles are

(1) P_{A} = 2P_{B}

(2) P_{A} = 3P_{B}

(3) 3P_{A} = 2P_{B}

(4) 2P_{A} = 3P_{B}

Answer: (4)

24. Among the following compounds most basic amino acid is

(1) Serine

(2) Lysine

(3) Histidine

(4) Asparagine

Answer: (2)

25. Mn_{2}(CO)_{10} is an organometallic compound due to the presence of

(1) Mn – C bond

(2) Mn – Mn bond

(3) Mn – O bond

(4) C – O bond

Answer: (1)

26. The major product of the following reaction is

(1)

(2)

(3)

(4)

Answer: (4)

27. Iodine reacts with concentrated HNO_{3} to yield Y along with other products. The oxidation state of iodine in Y, is

(1) 7

(2) 1

(3) 5

(4) 3

Answer: (3)

28. The element with Z = 120 (not yet discovered) will be an/a

(1) Inner-transition metal

(2) Transition metal

(3) Alkaline earth metal

(4) Alkali metal

Answer: (3)

29. Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is

(1) 2A

(2) 3A

(3) A

(4) 4A

Answer: (2)

30. 50 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is

(1) 10 g

(2) 40 g

(3) 20 g

(4) 80 g

Answer: (*)

MATHEMATICS

1. The maximum value of for any real value of θ is

(1) √34

(2) √19

(3) √79/2

(4) √31

Answer: (2)

2. A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of is

(1) 1 : 4(16)^{1/3}

(2) 1 : 2(6)^{1/3}

(3) 2(36)^{1/3} : 1

(4) 4(36)^{1/3} : 1

Answer: (4)

3. Let f and g be continuous functions on [0, a] such that f(x) = f(a – x) and g(x) + g(a – x) = 4, then is equal to

(1)

(2)

(3)

(4)

Answer: (4)

4. An ordered pair (α, β) for which the system of linear equations

(1 + α) x + β y + z = 2

αx + (1 + β)y + z = 3

αx + βy + 2z = 2

has a unique solution, is

(1) (1, –3)

(2) (2, 4)

(3) (–3, 1)

(4) (–4, 2)

Answer: (2)

5. The perpendicular distance from the origin to the plane containing the two lines, and is

(1) 11√6

(2) 6√11

(3) 11

(4) 11/√6

Answer: (4)

6. Consider three boxes, each containing 10 balls labelled 1, 2, …,10. Suppose one ball is randomly drawn from each of the boxes. Denote by n_{i}, the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n_{1}< n_{2}< n_{3}is

(1) 240

(2) 120

(3) 164

(4) 82

Answer: (2)

7. In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

(1) 150/6^{5}

(2) 225/6^{5}

(3) 175/6^{5}

(4) 200/6^{5}

Answer: (3)

8. If a variable line, 3x + 4y – λ = 0 is such that the two circles x^{2} + y^{2} – 2x – 2y + 1 = 0 and x^{2} + y^{2} – 18x – 2y + 78 = 0 are on its opposite sides, then the setof all values of λ is the interval

(1) (2, 17)

(2) (12, 21)

(3) (13, 23)

(4) (23, 31)

Answer: (2)

9. Let and Q = [q_{ij}] two 3 × 3 matrices such that Q – P^{5} = l_{3} . Then is equal to

(1) 10

(2) 135

(3) 9

(4) 15

Answer: (1)

10. The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is

(1) 36

(2) 32

(3) 24

(4) 28

Answer: (4)

11. A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is

(1) cos^{−}^{1} (19/35)

(2) cos^{−}^{1} (9/35)

(3) cos^{−}^{1} (17/31)

(4) cos^{−}^{1} (7/31)

Answer: (1)

12. If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is

(1) 31

(2) 30

(3) 50

(4) 51

Answer: (1)

13. Let y = y(x) be the solution of the differential equation, If 2y(2) =log_{e} 4 – 1, then y(e) is equal to

(1) e^{2}/4

(2) −e/2

(3) −e^{2}/2

(4) e/4

Answer: (4)

14. is

(1) 8√2

(2) 4

(3) 4√2

(4) 8

Answer: (4)

15. The area (in sq. units) of the region bounded by the parabola, y = x^{2} + 2 and the lines, y = x + 1, x = 0 and x = 3, is

(1) 15/2

(2) 21/2

(3) 15/4

(4) 17/4

Answer: (1)

16. Let P(4, –4) and Q(9, 6) be two points on the parabola, y^{2} = 4x and let X be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of ∆PXQ is maximum. Then this maximum area (in sq. units) is

(1) 75/2

(2) 125/4

(3) 625/4

(4) 125/2

Answer: (2)

17. Let C_{1}and C_{2} be the centres of the circles x^{2} + y^{2} – 2x – 2y – 2 = 0 and x^{2} + y^{2} – 6x – 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC_{1}QC_{2}is

(1) 4

(2) 9

(3) 6

(4) 8

Answer: (1)

18. The sum of the distinct real values of μ, for which the vectors, are co-planar, is

(1) 2

(2) 1

(3) −1

(4) 0

Answer: (3)

19. If λ be the ratio of the roots of the quadratic equation in x, 3m^{2}x^{2} + m(m – 4)x + 2 = 0, then the least value of m for which is

(1) 4 – 2√3

(2) 4 – 3√2

(3) 2 – √3

(4) −2 + √2

Answer: (2)

20. Considering only the principal values of inverse functions, the set

(1) Is a singleton

(2) Contains two elements

(3) Contains more than two elements

(4) Is an empty set

Answer: (1)

21. If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals

(1) −35/3

(2) −5

(3) 5

(4) 35/3

Answer: (3)

22. If is a purely imaginary number and |z| = 2, then a value of α is

(1) √2

(2) 2

(3) 1/2

(4) 1

Answer: (2)

23. The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x^{2} such that the rectangle lies inside the parabola, is

(1) 32

(2) 36

(3) 20√2

(4) 18√3

Answer: (1)

24. If the vertices of a hyperbola be at (–2, 0) and (2, 0) and one of its foci be at (–3, 0), then which one of the following points does not lie on this hyperbola?

(1) (4, √15)

(2) (6, 5√2)

(3) (2√6, 5)

(4) (−6, 2√10)

Answer: (2)

25. For x > 1, if (2x)^{2y} = 4e^{2x – 2y}, then is equal to

(1) log_{e} 2x

(2) x log_{e} 2x

(3)

(4)

Answer: (4)

26. Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is

(1) 2^{100} – 1

(2) 2^{50} + 1

(3) 2^{50}(2^{50} – 1)

(4) 2^{50} – 1

Answer: (3)

27. Let S be the set of all points in (–π, π) at which the function, f(x) = min {sinx, cosx} is not differentiable. Then S is a subset of which of the following?

(1)

(2)

(3)

(4)

Answer: (1)

28. The integral ∫ cos(log _{e} x) dx is equal to (where C is a constant of integration)

(1)

(2)

(3)

(4)

Answer: (2)

29. Let . If then A is equal to

(1) 303

(2) 156

(3) 301

(4) 283

Answer: (1)

30. The Boolean expression ((p ⋀ q) ⋁ (p ⋁ ~ q)) ( ~ p ⋀ ~ q) is equivalent to

In the figure, given that V_{BB} supply can vary from 0 to 5.0 V, V_{CC} = 5V, β_{dc}= 200, R_{B} = 100 KΩ, R_{C} = 1 KΩ and V_{BE}= 1.0V. The minimum base

current and the input voltage at which the transistor

will go to saturation, will be respectively:

(1) 25 μ A and 3.5 V

(2) 20 μ A and 2.8 V

(3) 25 μ A and 2.8 V

(4) 20 μ A and 3.5 V

Answer: (1)

2. A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is I_{1}, and hat below the piston isI_{2}, such that I_{1}> I_{2}. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m will be given by :

(R is universal gas constant and g is the acceleration due to gravity)

(1)

(2)

(3)

(4)

Answer: (1)

3. A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × 10^{–4} A passes through it, its needle(pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of:

(1) 6250 ohm

(2) 250 ohm

(3) 200 ohm

(4) 6200 ohm

Answer: (3)

4. In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μ All values in the circuit are in μF.

(1)

(2)

(3)

(4)

Answer: (1)

5. The mean intensity of radiation on the surface of the Sun is about 10^{8} W/m^{2}. The rms value of the corresponding magnetic field is closet to:

(1) 10^{2\}T

(2) 10^{−}^{4} T

(3) 1 T

(4) 10^{−}^{2} T

Answer: (2)

6. In a radioactive decay chain, the initial nucleus is At the end there are 6 α-particles and particles which are emitted. If the end nucleus is A and Z are given by :

(1) A = 200; Z = 81

(2) A = 202; Z = 80

(3) A = 208; Z = 80

(4) A = 208; Z = 82

Answer: (4)

7. The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is ‘I(x)’. Which one of the graphs represents the variation of I(x) with x correctly?

(1)

(2)

(3)

(4)

Answer: (3)

8. A simple harmonic motion is represented by :

The amplitude and time period of the motion are:

(1)

(2)

(3)

(4)

Answer: (1)

9. In the given circuit diagram, the currents, I_{1} = −3 A, I_{4} = 0.8 A and I_{5} = 0.4 A, are flowing as shown. The currents I_{2}, I_{3} and I_{6}, respectively, are :

(1) 1.1 A, 0.4 A, 0.4 A

(2) 1.1 A, – 0.4 A, 0.4 A

(3) 0.4 A, 1.1 A, 0.4 A

(4) –0.4 A, 0.4 A, 1.1 A

Answer: (1)

10. When a certain photosensistive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photo current is –V_{0}/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is –V_{0} . The threshold frequency for photoeletric emission is:

(1) 3v/2

(2)

(3) 5v/3

(4) 2 v

Answer: (1)

11. A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle’s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now th load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8.

The new value of increase in length of the steel wire is:

(1) 4.0 mm

(2) zero

(3) 5.0 mm

(4) 3.0 mm

Answer: (4)

12. A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is a height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be:

(Take g = 10 m/s^{2})

(1) 2 kg-m^{2}/s

(2) 3 kg-m^{2}/s

(3) 8 kg-m^{2}/s

(4) 6 kg-m^{2}/s

Answer: (4)

13. Formation of real image using a biconvex lens is shown below:

If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

(1) Erect real image

(2) No change

(3) Image disappears

(4) Magnified image

Answer: (3)

14. A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms^{–1}, at right angles to the horizontal component of the earth’s magnetic field, of 0.3×10^{–4} Wb/m^{2}. The value of the induced emf in wire is:

(1) 1.1 × 10^{−}^{3} V

(2) 0.3 × 10^{−}^{3} V

(3) 2.5 × 10^{−}^{3} V

(4) 1.5 × 10^{−}^{3} V

Answer: (1)

15. An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is:

(1) 1.5 m

(2) 3.5 m

(3) 4 m

(4) 2 m

Answer: (3)

16. To double the covering range of a TV transmission tower, its height should be multiplied by:

(1) √2

(2) 2

(3) 1/√2

(4) 4

Answer: (4)

17. A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is:

[Take g = 10 m/s^{2}]

(1) 1/2

(2) √3/2

(3) √3/4

(4) 2/3

Answer: (2)

18. A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by:

(1)

(2)

(3)

(4)

Answer: (*)

19. A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:

(1) 1.2

(2) 0.1

(3) 0.4

(4) 2.0

Answer: (4)

20. A plano-convex lens (focal length f_{2} , refractive index μ_{2}, radius of curvature R) fits exactly into a planoconcave lens(focal length f_{1} , refractive index μ _{1} radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

(1) f_{1} – f_{2}

(2)

(3)

(4) f_{1} + f_{2}

Answer: (2)

21. In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to

(1) 1700 nm

(2) 2020 nm

(3) 250 nm

(4) 220 nm

Answer: ()

22. Two satellites, A and B, have masses m and 2 m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2 R around the earth. The ratio of their kinetic energies, T_{A}/T_{B} is

(1) 1

(2) 1/2

(3) 2

(4)

Answer: (1)

23. An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 × 10^{–8} If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

(1) 2 × 10^{−}^{7} s

(2) 3 × 10^{−}^{6} s

(3) 0.5 × 10^{−}^{8} s

(4) 4 × 10^{−}^{8} s

Answer: (4)

24.

In the above circuit, R_{2} = 20 Ω, and R_{1} = 10 Ω. Current in L-R_{1} path is I_{1} and in C-R_{2} path it is I_{2}. The voltage of A.C. source is given by

V = 200√2 sin(100 t) volts. The phase difference between I_{1}and I_{2} is

(1) 0°

(2) 60°

(3) 30°

(4) 90°

Answer: ()

25. A paramagnetic material has 10^{28} atoms/m^{3}. Its magnetic susceptibility at temperature 350 K is 2.8 × 10^{–4}. Its susceptibility at 300 K is

(1) 3.726 × 10^{−}^{4}

(2) 3.672 × 10^{−}^{4}

(3) 2.672 × 10^{−}^{4}

(4) 3.267 × 10^{−}^{4}

Answer: (4)

26. Let I, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of 1/rcv in SI units will be

(1) [A^{−}^{1}]

(2) [LA^{−2}]

(3) [LT^{2}]

(4) [LTA]

Answer: (1)

27. The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure

What is the value of current at t = 4 s?

(1) 2 μA

(2) zero

(3) 3 μA

(4) 1.5 μA

Answer: (2)

28. A parallel plate capacitor with plates of area 1 m^{2 }each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is:

(1) 8.85 × 10^{−}^{10} C

(2) 9.85 × 10^{−}^{10} C

(3) 6.85 × 10^{−}^{10} C

(4) 7.85 × 10^{−}^{10} C

Answer: (1)

29. Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure

The relative velocity

(1)

(2)

(3)

(4)

Answer: ()

30. A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to

(1) 322 ms^{−}^{1}

(2) 341 ms^{−}^{1}

(3) 328 ms^{−}^{1}

(4) 335 ms^{−}^{1}

Answer: (3)

CHEMISTRY

1. An open vessel at 27°C is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is

(1) 750°C

(2) 750 K

(3) 500°C

(4) 500 K

Answer: (4)

2. Given

Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?

(1) x = y – z

(2) x = y + z

(3) y = 2z – x

(4) z = x + y

Answer: (2)

3. The increasing order of the reactivity of the following with LiAlH_{4} is

(1) (A) < (B) < (C) < (D)

(2) (B) < (A) < (D) < (C)

(3) (A) < (B) < (D) < (C)

(4) (B) < (A) < (C) < (D)

Answer: (3)

4. Among the following, the false statement is

(1) Tyndall effect can be used to distinguish between a colloidal solution and a true solution.

(2) Latex is a colloidal solution of rubber particles which are positively charged

(3) Lyophilic sol can be coagulated by adding an electrolyte.

(4) It is possible to cause artificial rain by throwing electrified sand carrying charge opposite to the one on clouds from an aeroplane.

Answer: (2)

5. The major product of the following reaction is

Answer: (4)

6. The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 BM. The suitable ligand for this complex is

(1) CO

(2) Ethylenediamine

(3) NCS^{−}

(4) CN^{−}

Answer: (3)

7. The major product of the following reaction is

(1)

(2)

(3)

(4)

Answer: (2)

8. If K_{sp} of Ag_{2}CO_{3} is 8 × 10^{−}^{12}, the molar solubility of Ag_{2}CO_{3} in 0.1 M AgNO_{3} is

(1) 8 × 10^{−}^{11} M

(2) 8 × 10^{−}^{12} M

(3) 8 × 10^{−}^{13} M

(4) 8 × 10^{−}^{10} M

Answer: (4)

9. for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S cm^{2}mol^{–1}, respectively. If the conductivity of 0.001 M HA is 5 × 10^{–5} S cm^{–1}, degree of dissociation of HA is

(1) 0.25

(2) 0.125

(3) 0.50

(4) 0.75

Answer: (2)

10. The major product of the following reaction is

Answer: ()

11. The aldehydes which will not form Grignard product with one equivalent Grignard reagent are

(1) (B), (C)

(2) (B), (D)

(3) (B), (C), (D)

(4) (C), (D)

Answer: (2)

12. For a reaction, consider the plot of In k versus 1/T given in the figure. If the rate constant of this reaction at 400 K is 10^{–5} s^{–1}, then the rate constant at 500 K is

(1) 4 × 10^{–4} s^{–1}

(2) 10^{–6} s^{–1}

(3) 2 × 10^{–4} s^{–1}

(4) 10^{–4} s^{–1}

Answer: (4)

13. The major product of the following reaction is

Answer: (4)

14. The compound that is NOT a common component of photochemical smog is:

(1)

(2) CH_{2} = CHCHO

(3) CF_{2}Cl_{2}

(4) O_{3}

Answer: (3)

15. The major product in the following conversion is

Answer: (3)

16. The major product of the following reaction is

Answer: (3)

17. Molecules of benzoic acid (C6H5 COOH) dimerise in benzene. ‘w’ g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is

(Given that K_{f} =5 K kg mol^{−}^{1}, Molar mass of benzoic acid = 122 g mol^{−}^{1})

(1) 1.5 g

(2) 2.4 g

(3) 1.8 g

(4) 1.0 g

Answer: (2)

18. Chlorine on reaction with hot and concentrated sodium hydroxide gives

(1) Cl ^{–} and ClO^{–}

(2) Cl^{–} and ClO_{2}^{–}

(3) ClO_{3}^{–} and ClO_{2}^{–}

(4) Cl^{–} and ClO_{3}^{–}

Answer: (4)

19. The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are

I. They activate many enzymes

II. They participate in the oxidation of glucose to produce ATP

III. Along with sodium ions, they are responsible for the transmission of nerve signals

(1) I and III only

(2) I, II and III

(3) III only

(4) I and II only

Answer: (2)

20. If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5 πa_{0} (a_{0} is Bohr radius), then the value of n/z is

(1) 0.40

(2) 1.50

(3) 0.75

(4) 1.0

Answer: (3)

21. The volume strength of 1M H_{2}O_{2} is

(Molar mass of H_{2}O_{2} = 34 g mol^{−}^{1})

(1) 11.35

(2) 22.4

(3) 5.6

(4) 16.8

Answer: (1)

22. The correct order of atomic radii is

(1) Ce > Eu > Ho > N

(2) N > Ce > Eu > Ho

(3) Eu > Ce > Ho > N

(4) Ho > N > Eu > Ce

Answer: (3)

23. The element that does NOT show catenation is

(1) Sn

(2) Ge

(3) Pb

(4) Si

Answer: (3)

24. The two monomers for the synthesis of nylon 6, 6 are

26. The upper stratosphere consisting of the ozone layer protects us from the sun’s radiation that falls in the wavelength region of

(1) 200 – 315 nm

(2) 600 – 750 nm

(3) 400 – 500 nm

(4) 0.8 – 1.5 nm

Answer: (1)

27. The combination of plots which does not represent isothermal expansion of an ideal gas is

(1) (A) and (C) (2)

(A) and (D)

(3) (B) and (C)

(4) (B) and (D)

Answer: (4)

28. 8 g of NaOH is dissolved in 18 g of H_{2} Mole fraction of NaOH in solution and molality (in mol kg^{–1}) of the solution respectively are

(1) 0.2, 22.20

(2) 0.167, 22.20

(3) 0.167, 11.11

(4) 0.2, 11.11

Answer: (3)

29. The element that shows greater ability of form pπ – pπ multipole bonds, is

(1) Sn

(2) Si

(3) Ge

(4) C

Answer: (4)

30. The correct structure of histidine in a strongly acidic solution (pH = 2) is

(1)

(2)

(3)

(4)

Answer: (4)

MATHEMATICS

1. In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither of NCC nor for NSS is

(1) 5/6

(2) 1/3

(3) 1/6

(4) 2/3

Answer: (3)

2. Let be three unit vectors, out of which vectors are non-parallel. If α and β are the angles which vector makes with vectors respectively and the |α – β| is equal to

(1) 90°

(2) 45°

(3) 30°

(4) 60°

Answer: (3)

3. If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30° and the angle of depression of reflection of the cloud in the lake from P be 60°, then the height of the cloud (in meters) from the surface of the lake is

(1) 45

(2) 50

(3) 42

(4) 60

Answer: (2)

4. The tangent to the curve y = x^{2} – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point

(1) (1/4, 7/2)

(2) (1/8, −7)

(3) (7/2, 1/4)

(4) (−1/8, 7)

Answer: (2)

5. If ; then for all det (A) lies in the interval:

(1) (1, 5/2]

(2) (0, 3/2]

(3) [5/2, 4)

(4) (3/2, 3]

Answer: (4)

6. In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is

(1)

(2) 0

(3)

(4)

Answer: (2)

7. If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as then the curve also passes through the point

(1) (−1, 2)

(2) (√3, 0)

(3) (3, 0)

(4) (−√2, 1)

Answer: (2)

8. If sin^{4}α + 4 cos^{4}β + 2 = 4√2 sin α cos β; α, β ∈[0, π], then cos(α + β) – cos(α – β) is equal to

(1) √2

(2) −√2

(3) −1

(4) 0

Answer: (2)

9. The integral is equal to

(1)

(2)

(3)

(4)

Answer: (1)

10. Let S and Sʹ be the foci of an ellipse and B be any one of the extremities of its minor axis. If ∆SʹBS is a right angled triangle with right angle at B and area (∆SʹBS) = 8 sq. units, then the length of a latus rectum of the ellipse is

(1) 4√2

(2) 4

(3) 2√2

(4) 2

Answer: (2)

11. Let f be a differentiable function such that f (1) = 2 and f ʹ(x) = f(x) for all x ∈ If h(x) = f(f (x)), then hʹ (1) is equal to

(1) 2e

(2) 2e^{2}

(3) 4e

(4) 4e^{2}

Answer: (3)

12. If the function f given by f (x) = x^{3} – 3 (a – 2)x^{2} + 3ax + 7, for some a ∈ R is increasing in (0, 1] and decreasing n [1, 5), then a root of the equation, is:

(1) −7

(2) 5

(3) 6

(4) 7

Answer: (4)

13. There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is

(1) 9

(2) 7

(3) 11

(4) 12

Answer: (4)

14. Let Z be the set of integers.

If and

B = {x ∈ Z : −3 < 2x – 1 < 9}, then the number of subsets of the set A × B is

(1) 2^{15}

(2) 2^{12}

(3) 2^{18}

(4) 2^{10}

Answer: (1)

15. The expression ~(~p → q) is logically equivalent to

(1) p ⋀ q

(2) p ⋀ ~ q

(3) ~ p ⋀ ~ q

(4) ~ p ⋀ ~ q

Answer: (3)

16. The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is

(1) 5

(2) 7

(3) 3

(4) 1

Answer: (2)

17. Let S be the set of all real values of λ such that a plane passing through the points (−λ^{2}, 1, 1), (1, −λ^{2}, 1) and (1, 1, −λ^{2}) also passes through the point (–1, –1, 1). Then S is equal to

(1) {1, −1}

(2) {√3}

(3) {√3, −√3}

(4) {3, −3}

Answer: (3)

18. If an angle between the line, and the plane, x – 2y – kz = 3 is then a value of k is

(1)

(2)

(3) −5/3

(4) −3/5

Answer: (2)

19. Let z_{1} and z_{2} be two complex numbers satisfying |z_{1}| = 9 and |z_{2} – 3 – 4i | = 4. Then the minimum value of |z_{1} – z_{2}| is

(1) 0

(2) √2

(3) 1

(4) 2

Answer: (1)

20. The number of integral values of m for which the quadratic expression, (1 + 2m)x^{2} – 2(1 + 3m)x + 4(1 + m), x ∈ R, is always positive, is:

(1) 8

(2) 3

(3) 6

(4) 7

Answer: (4)

21. If ^{n}C_{4}, ^{n}C_{5} and ^{n}C_{6} are in A.P., then n can be :

(1) 12

(2) 9

(3) 14

(4) 11

Answer: (3)

22. If a circle of radius R pases through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is:

(1) (x^{2} + y^{2})^{2} = 4Rx^{2}y^{2}

(2) (x^{2} + y^{2})^{2} = 4R2x^{2}y^{2}

(3) (x^{2} + y^{2})^{3} = 4R2x^{2}y^{2}

(4) (x^{2} + y^{2})(x + y) = R^{2}xy

Answer: (3)

23. is equal to:

(1) π/4

(2) tan^{−}^{1}(3)

(3) tan^{−}^{1} (2)

(4) π/2

Answer: (3)

24. The integral is equal to (where C is a constant of integration)

(1)

(2)

(3)

(4)

Answer: (3)

25. The equation of a tangent to the parabola, x^{2} = 8y, which makes an angle θ with the positive direction of x-axis, is:

(1) x = y cot θ – 2tan θ

(2) y = x tan θ + 2cot θ

(3) x = y cot θ + 2tan θ

(4) y = x tan θ – 2cot θ

Answer: (3)

26. If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is:

(1) 3x – 4y + 25 = 0

(2) 4x – 3y + 24 = 0

(3) x – y + 7 = 0

(4) 4x + 3y = 0

Answer: (2)

27. is equal to :

(1)

(2)

(3)

(4)

Answer: (1)

28. If the sum of the first 15 terms of the series is equal to 225 k, then k is equal to :

(1) 108

(2) 27

(3) 9

(4) 54

Answer: (2)

29. The total number of irrational terms in the binomial expansion of (7^{1/5} – 3^{1/10})^{60} is :

(1) 48

(2) 49

(3) 54

(4) 55

Answer: (3)

30. The set of all values of λ for which the system of linear equations

1. An amplitude modulated signal is given by V(t) = 10 [1 + 0.3cos (2.2 × 10^{4}t)] sin(5.5 × 10^{5}t). Here t is in seconds. The sideband frequencies (in kHz) are, [Given π =22/7]

(1) 1785 and 1715

(2) 178.5 and 171.5

(3) 89.25 and 85.75

(4) 892.5 and 857.5

Answer: (3)

2. In the circuit shown,

the switch S_{1} is closed at time t = 0 and the switch S_{2} is kept open. At some later time(t_{0}), the switch S_{1} is opened and S_{2} is closed. The behaviour of the

current I as a function of time ‘t ’ is given by

(1)

(2)

(3)

(4)

Answer: (3)

3. The force of interaction between two atoms is given by where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is

(1) M^{0}L^{2}T^{−}^{4}

(2) M^{2}LT^{−}^{4}

(3) MLT^{−}^{2}

(4) M^{2}L^{2}T^{−}^{2}

Answer: (2)

4. The given graph shows variation (with distance r from centre) of

(1) Potential of a uniformly charged spherical shell

(2) Electric field of a uniformly charged sphere

(3) Electric field of uniformly charged spherical shell

(4) Potential of a uniformly charged sphere

Answer: (1)

5. A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60° around the centre of the circle?

(1) 10 m/s

(2) Zero

(3) 10√3 m/s

(4) 10√2 m/s

Answer: (1)

6. A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980 Å. The radius of the atom in the excited state, in terms of Bohr radius a_{0}, will be

(hc = 12500 eV-Å)

(1) 4a_{0}

(2) 9a_{0}

(3) 25a_{0}

(4) 16a_{0}

Answer: (4)

7. Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be

(1) 60 W

(2) 30 W

(3) 120 W

(4) 240 W

Answer: (4)

8. Three charges Q, +q and +q are placed at the vertices of a right-angle isosceles triangles as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is

(1)

(2) +q

(3) −2q

(4)

Answer: (1)

9. In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R = 400 Ω, the bridge is balanced. On interchanging P and Q, the value of R, for balance, is 405 Ω. The value of X is close to

(1) 404.5 ohm

(2) 401.5 ohm

(3) 402.5 ohm

(4) 403.5 ohm

Answer: (3)

10. There are two long co-axial solenoids of same length l. The inner and outer coils have radii r_{1} and r_{2} and number of turns per unit length n_{1} and n_{2}, respectively. The ratio of mutual inductance to the self inductance of the inner-coil is

(1)

(2)

(3)

(4)

Answer: (2)

11. The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if D_{m} is the angle of minimum deviation?

(1)

(2)

(3)

(4)

Answer: (1)

12. A particle undergoing simple harmonic motion has time dependent displacement given by The ratio of kinetic to potential energy of this particle at t = 210 s will be

(1) 1

(2) 3

(3) 2

(4) 1/9

Answer: (*)

13. In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 × 10^{–19} C, Mass of the electron = 9.1 × 10^{–31} kg]

(1) 7.5 × 10^{−}^{3} m

(2) 7.5 m

(3) 7.5 × 10^{−}^{2} m

(4) 7.5 × 10^{−}^{4} m

Answer: (2)

14. An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are the midpoints of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I_{0}. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then

(1)

(2)

(3)

(4)

Answer: (2)

15. A body is projected at t = 0 with a velocity 10 ms^{–1} at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms^{–2}, the value of R is

(1) 5.1 m

(2) 2.5 m

(3) 2.8 m

(4) 10.3 m

Answer: (3)

16. Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450t – 9x) where distance and time are measured in SI units. The tension in the string is

(1) 10 N

(2) 7.5 N

(3) 5 N

(4) 12.5 N

Answer: (4)

17. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is

(1) 4RT

(2) 12RT

(3) 15RT

(4) 20 RT

Answer: (3)

18. In the figure shown below, the charge on the left plate of the 10 μF capacitor is –30 μ The charge on the right plate of the 6 μF capacitor is

(1) +18 μC

(2) −12 μC

(3) +12 μC

(4) −18 μC

Answer: (1)

19. An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be

(1) 0.92 × 10^{–3} m/s away from the lens

(2) 2.26 × 10^{–3} m/s away from the lens

(3) 1.16 × 10^{–3} m/s towards the lens

(4) 3.22 × 10^{–3} m/s towards the lens

Answer: (3)

20. A slab is subjected to two forces of same magnitude F as shown in the figure. Force is in XY-plane while force F_{1} acts along z-axis at the point moment of these forces about point O will be

(1)

(2)

(3)

(4)

Answer: (1)

21. An electromagnetic wave of intensity 50 Wm^{–2} enters in a medium of refractive index ‘n’ without any loss. The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by

(1)

(2)

(3)

(4)

Answer: (2)

22. A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be

(1)

(2)

(3)

(4)

Answer: (1)

23. The resistance of the metre bridge AB in given figure is 4 Ω. With a cell of emf ε = 0.5 V and rheostat resistance Rh = 2 Ω the null point is obtained at some point J. When the cell is replaced by another one of emf ε = ε_{2} the same null point J is found for Rh = 6 Ω.The emf ε_{2} is

(1) 0.6 V

(2) 0.5 V

(3) 0.3 V

(4) 0.4 V

Answer: (3)

24. A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 10^{6} N/m. The body sticks to the platform and the spring’s maximum compression is found to be x. Given that g = 10 ms^{–2}, the value of x will be close to

(1) 80 cm

(2) 8 cm

(3) 4 cm

(4) 40 cm

Answer: (*)

25. In a Young’s double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is 1/8th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to

(1) 0.74

(2) 0.94

(3) 0.80

(4) 0.85

Answer: (4)

26. A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

(1)

(2)

(3)

(4)

Answer: (2)

27. In the given circuit the current through Zener Diode is close to

(1) 6.7 mA

(2) 0.0 mA

(3) 4.0 mA

(4) 6.0 mA

Answer: (2)

28. A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TV^{x} = constant, then x is

(1) 2/5

(2) 2/3

(3) 5/3

(4) 3/5

Answer: (1)

29. Ice at –20°C is added to 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount off ice added to the water was close to (Specific heat of water = 4.2 J/g/°C Specific heat of Ice = 2.1 J/g/°C Heat of fusion of water at 0°C = 334 J/g)

(1) 100 g

(2) 40 g

(3) 50 g

(4) 60 g

Answer: (2)

30. If the deBroglie wavelength of an electron is equal to 10^{–3} times the wavelength of a photon of frequency 6 × 10^{14} Hz, then the speed of electron is equal to :

(Speed of light = 3 × 10^{8} m/s

Planck’s constant = 6.63 × 10^{–34} J-s

Mass of electron = 9.1 × 10^{–31} kg)

(1) 1.7 × 10^{6} m/s

(2) 1.45 × 10^{6} m/s

(3) 1.8 × 10^{6} m/s

(4) 1.1 × 10^{6} m/s

Answer: (2)

CHEMISTRY

1. Match the ores (column A) with the metals (column B):

2. The concentration of dissolved oxygen (DO) in cold water can go upto:

(1) 14 ppm

(2) 16 ppm

(3) 10 ppm

(4) 8 ppm

Answer: (3)

3. The freezing point of a diluted milk sample is found to be –0.2°C, while it should have been –0.5°C for pure milk. How much water has been added to pure milk to make the diluted sample?

(1) 3 cups of water and 2 cups of pure milk

(2) 1 cup of water and 2 cups of pure milk

(3) 2 cups of water to 3 cups of pure milk

(4) 1 cup of water to 3 cups of pure milk

Answer: (1)

4. The correct match between item (I) and item (II) is:

Item – I Item – II

(A) Norethindrone (P) Anti-biotic

(B) Ofloxacin (Q) Anti-fertility

(C) Equanil (R) Hypertension

(S) Analgesics

(1) (A) → (R) ; (B) → (P) ; (C) → (R)

(2) (A) → (R) ; (B) → (P) ; (C) → (S)

(3) (A) → (Q) ; (B) → (P) ; (C) → (R)

(d) (A) → (Q) ; (B) → (R) ; (C) → (S)

Answer: (3)

5. The major product of the following reaction is

Answer: (2)

6. The major product of the following reaction is:

(2)

(3)

(4)

Answer: (1)

7. The chloride that CANNOT get hydrolysed is:

(1) PbCl_{4}

(2) CCl_{4}

(3) SnCl_{4}

(4) SiCl_{4}

Answer: (2)

8. If a reaction follows the Arrhenius equation, the plot Ink vs gives straight line with a gradient (–y) unit. The energy required to activate the reactant is:

(1) yR unit

(2) y/R unit

(3) −y unit

(4) y unit

Answer: (4)

9. The major product of the following reaction is

(1)

(2)

(3)

(4)

Answer: (3)

10. The major product of the following reaction is:

Answer: (4)

11. A solid having density of 9 × 10^{3} kg m^{–3} forms face centred cubic crystals of edge length 200√2 pm. What is the molar mass of the solid?

13. The correct order of the atomic radii of C, Cs, Al, and S is

(1) S < C < Al < Cs

(2) C < S < Cs < Al

(3) S < C < Cs < Al

(4) C < S < Al < Cs

Answer: (4)

14. For the cell Zn(s)|Zn^{2+}(aq)||M^{x+}(aq)| M(s), different half cells and their standard electrode potentials are given below

If which cathode will give a maximum value of

E°_{cell} per electron transferred?

(1) Fe^{2+}/Fe

(2) Ag^{+}/Ag

(3) Fe^{3+}/Fe^{2+}

(4) Au^{3+}/Au

Answer: (4)

15. Consider the reaction

N_{2}(g) + 3H_{2}(g) ⇌ 2NH_{3} (g)

The equilibrium constant of the above reaction is K_{P}. If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that at equilibrium)

(1)

(2)

(3)

(4)

Answer: (4)

16. For the chemical reaction X ⇌ Y, the standard reaction Gibbs energy depends on temperature T (in K) as

The major component of the reaction mixture at T is

(1) Y if T = 280 K

(2) X if T = 315 K

(3) X if T = 300 K

(4) X if T = 350 K

Answer: (2)

17. An organic compound is estimated through Dumas method and was found to evolve 6 moles of CO_{2}, 4 moles of H_{2}O and 1 mole of nitrogen gas. The formula of the compound is

(1) C_{6}H_{8}N

(2) C_{12}H_{8}N

(3) C_{6}H_{8}N

(4) C_{12}H_{8}N_{2}

Answer: (1)

18. Match the metals (column I) with the coordination compound(s)/enzyme(s) (column II)

19. Two blocks of the same metal having same mass and at temperature T_{1} and T_{2}, respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, ∆S, for this process is

(1)

(2)

(3)

(4)

Answer: (2)

20. The correct statements among (a) to (d) regarding H_{2} as a fuel are

(a) It produces less pollutants than petrol.

(b) A cylinder of compressed dihydrogen weighs ~ 30 times more than a petrol tank producing the same amount of energy.

(c) Dihydrogen is stored in tanks of metal alloys like NaNi_{5}.

(d) On combustion, values of energy released per gram of liquid dihydrogen and LPG are 50 and 142 kJ, respectively.

(1) (b) and (d) only

(2) (a) and (c) only

(3) (b), (c) and (d) only

(4) (a), (b) and (c) only

Answer: (4)

21. The element that usually does NOT show variable oxidation states is

(1) Cu

(2) Ti

(3) V

(4) Sc

Answer: (4)

22. Among the following compounds, which one is found in RNA?

Answer: (4)

23. The polymer obtained from the following reactions is

Answer: (1)

24. NaH is an example of

(1) Metallic hydride

(2) Electron –rich hydride

(3) Molecular hydride

(4) Saline hydride

Answer: (4)

25. The amphoteric hydroxide is

(1) Mg(OH)_{2}

(2) Be(OH)_{2}

(3) Sr(OH)_{2}

(4) Ca(OH)_{2}

Answer: (2)

26. Which compound(s) out of following is/are not aromatic?

(1) (B), (C) and (D)

(2) (A) and (C)

(3) (C) and (D)

(4) (B)

Answer: (1)

27. Peroxyacetyl nitrate (PAN), an eye irritant is produced by

(1) Classical smog

(2) Acid rain

(3) Organic waste

(4) Photochemical smog

Answer: (4)

28. A 10 mg effervescent tablet containing sodium bicarbonate and oxalic acid releases 0.25 ml of CO_{2} at T = 298.15 K and p = 1 bar. If molar volume of CO_{2} is 25.0 L under such condition, what is the percentage of sodium bicarbonate in each tablet?

[Molar mass of NaHCO_{3} = 84 g mol^{–1}]

(1) 33.6

(2) 8.4

(3) 0.84

(4) 16.8

Answer: (2)

29. Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this purpose?

[RH= 1 × 10^{5} cm, h = 6.6 × 10^{–34} Js, c = 3 × 10^{8} ms^{–1}]

(1) Balmer, ∞ → 2

(2) Lyman, ∞ → 1

(3) Paschen, 5 → 3

(4) Paschen, ∞ → 3

Answer: (4)

30. An example of solid sol is.

(1) Butter

(2) Hair cream

(3) Paint

(4) Gem stones

Answer: (4)

MATHEMATICS

1. Let and g(x) = | f(x)|+f(|x|). Then, in the interval (–2, 2), g is

(1) not differentiable at two points

(2) not differentiable at one point

(3) not continuous

(4) differentiable at all points

Answer: (2)

2. The plane containing the line and also containing its projection on the plane 2x + 3y – z = 5, contains which one of the following points?

(1) (0, –2, 2)

(2) (2, 2, 0)

(3) (–2, 2, 2)

(4) (2, 0, –2)

Answer: (4)

3. Let f : R → R be defined by Then the range of f is

(1) R – [−1/2, 1/2]

(2) [−1/2, 1/2]

(3) [–1, 1) – {0}

(4) R – [–1, 1]

Answer: (2)

4. The outcome of each of 30 items was observed; 10 items gave an outcome each, 10 items gave outcome 1/2 each and the remaining 10 items gave outcome . If the variance of this outcome data is 4/3 then |d| equals.

(1) √2

(2) √5/2

(3) 2/3

(4) 2

Answer: (1)

5. Let and be coplanar vectors. Then the none-zero vector is:

(1)

(2)

(3)

(4)

Answer: (4)

6. The area (in sq. units) of the region bounded by the curve x^{2} = 4y and the straight line x = 4y – 2 is

(1) 7/8

(2) 5/4

(3) 9/8

(4) 3/4

Answer: (3)

7. Let a_{1}, a_{2}, …, a_{10} be a G.P. If equals

(1) 5^{3}

(2) 5^{4}

(3) 2(5^{2})

(4) 4(5^{2})

Answer: (2)

8. If the system of linear equations

2x + 2y + 3z = a

3x – y + 5z = b

x – 3y + 2z = c

where a, b, c are non-zero real numbers, has more than one solution, then

(1) b – c + a = 0

(2) b + c – a = 0

(3) a + b + c = 0

(4) b – c – a = 0

Answer: (4)

9. The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is

(1) √5/4

(2) √5/2

(3) 4√5

(4) 2√5

Answer: (2)

10 Let [x] denote the greatest integer less than or equal to x. Then

(1) equals 0

(2) equals π + 1

(3) equals π

(4) does not exist

Answer: (4)

11. Let If AA^{T} = I_{3}, then |p| is:

(1) 1/√3

(2) 1/√6

(3) 1/√5

(4) 1/√2

Answer: (4)

12. Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is:

(1) 1

(2) √2

(3) 2√2

(4) 2

Answer: (4)

13. The value of r for which ^{20}C_{r}^{20}C_{0} + ^{20}C_{r – 1}^{20}C_{1} + ^{20}C_{r – 2 }^{20}C_{2}+ … + ^{20}C_{0}^{20}C_{r} is maximum, is :

(1) 10

(2) 20

(3) 15

(4) 11

Answer: (2)

14. If x log_{e} (log_{e} x) – x^{2} + y^{2} = 4 (y > 0), then dy/dx at x = e is equal to :

(1)

(2)

(3)

(4)

Answer: (1)

15. If for a suitable chosen integer m and a function A(x), where C is a constant of integration, then (A(x))^{m} equals:

(1) −1/3x^{3}

(2) 1/27x^{6}

(3) 1/9x^{4}

(4) −1/27x^{9}

Answer: (4)

16. Two integers are selected at random from the set {1, 2, …, 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

(1) 3/5

(2) 7/10

(3) 1/2

(4) 2/5

Answer: (4)

17. Equation of a common tangent to the parabola y^{2} = 4x and the hyperbola xy = 2 is:

(1) 4x + 2y + 1 = 0

(2) x + 2y + 4 = 0

(3) x – 2y + 4 = 0

(4) x + y + 1 = 0

Answer: (2)

18. If tangents are drawn to the ellipse x^{2} + 2y^{2} = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve:

(1)

(2)

(3)

(4)

Answer: (4)

19. A square is inscribed in the circle x^{2} + y^{2} – 6x + 8y – 103 = 0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is:

(1) 6

(2) √41

(3) 13

(4) √137

Answer: (2)

20. In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x^{2} – c^{2} = y, where c is the length of the third side of the triangle, then the circum radius of the triangle is:

(1) c/√3

(2)

(3) c/3

(4) y/√3

Answer: (1)

21. Let where x and y are real numbers, the y – x equals

(1) −85

(2) −91

(3) 85

(4) 91

Answer: (4)

22. If q is false and p ⋀ q ↔ r is true, then which one of the following statements is a tautology?

(1) p ⋁ r

(2) (p ⋀ r) → (p ⋁ r)

(3) (p ⋁ r) → (p ⋀ r)

(4) p ⋀ r

Answer: (2)

23. If y(x) is the solution of the differential equation then

(1) y(x) is decreasing in (1/2, 1)

(2)

(3) y(log_{e} 2) = log_{e} 4

(4) y(x) is decreasing in (0, 1)

Answer: (1)

24. The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle π/4 with the plane y – z + 5 = 0 are

(1) 2√3, 1, −1

(2) 2, √2, −√2

(3) 2, −1, 1

(4) √2, 1, −1

Answer: (2, 4)

25. The maximum value of the function f(x) = 3x^{3} – 18x^{2} + 27x – 40 on the set S = {x ∈ R: x^{2} + 30 ≤ 11x} is

(1) 122

(2) −122

(3) 222

(4) −222

Answer: (1)

26. Let for k = 1, 2, 3, …. Then for all x ∈ R, the value of f_{4}(x) – f_{6}(x) is equal to

(1) −1/12

(2) 1/12

(3) 5/12

(4) 1/4

Answer: (2)

27. The sum of the real values of x for which the middle term in the binomial expansion of equals 5670 is

(1) 4

(2) 8

(3) 0

(4) 6

Answer: (3)

28. The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is 27/19. Then the common ratio of this series is

(1) 1/3

(2) 2/9

(3) 2/3

(4) 4/9

Answer: (3)

29. The value of the integral (where [x] denotes the greatest integer less than or equal to x) is

(1) sin 4

(2) 4 – sin 4

(3) 0

(4) 4

Answer: (3)

30. If one real root of the quadratic equation 81x^{2} + kx + 256 = 0 is cube of the other root, then a value of k is

1. A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 × 10^{–6} J/T when a magnetic intensity of 60 × 10^{3} A/m is applied. Its magnetic susceptibility is

(1) 3.3 × 10^{−}^{2}

(2) 2.3 × 10^{−}^{2}

(3) 3.3 × 10^{−}^{4}

(4) 4.3 × 10^{−}^{2}

Answer: (3)

2. An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10–29 Cm. What is the potential energy of the electric dipole?

(1) –9 × 10^{–20} J

(2) –10 × 10^{–29} J

(3) –7 × 10^{–27} J

(4) –20 × 10^{–18} J

Answer: (3)

3. A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is

(1)

(2)

(3)

(4)

Answer: (2)

4. A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 JK^{–1 }and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg^{–1}K^{–1} and 400 Jkg^{–1}K^{–1}]

(1) 25%

(2) 20%

(3) 30%

(4) 15%

Answer: (2)

5. The region between y = 0 and y = d contains a magnetic field A particle of mass m and charge q enters the region with a velocity if the acceleration of the charged particle at the point of its emergence at the other side is

(1)

(2)

(3)

(4)

Answer: (Bonus)

6. A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :

(1) 16 rad/s^{2}

(2) 20 rad/s^{2}

(3) 12 rad/s^{2}

(4) 10 rad/s^{2}

Answer: (1)

7. A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10^{–2} The relative change in the angular frequency of the pendulum is best given by

(1) 10^{−}^{3} rad/s

(2) 10^{−1} rad/s

(3) 10^{−5} rad/s

(4) 1 rad/s

Answer: (1)

8. If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young’s modulus will be

(1) V^{−}^{2}A^{2}F^{−}^{2}

(2) V^{−}^{2}A^{2}F^{2}

(3) V^{−}^{4}A^{2}F

(4) V^{−}^{4}A^{−}^{2}F

Answer: (3)

9. When 100 g of a liquid A at 100°C is added to 50 g of a liquid B at temperature 75°C, the temperature of the mixture becomes 90°C. The temperature of the mixture, if 100 g of liquid A at 100°C is added to 50 g of liquid B at 50°C, will be

(1) 85°C

(2) 80°C

(3) 70°C

(4) 60°C

Answer: (2)

10. A 27 mW laser beam has a cross-sectional area of 10 mm^{2}. The magnitude of the maximum electric field in this electromagnetic wave is given by:

[Given permittivity of space ∈_{0} = 9 × 10^{−}^{12} SI units, Speed of light c = 3 × 10^{8} m/s]

(1) 1.4 kV/m

(2) 1 kV/m

(3) 2 kV/m

(4) 0.7 kV/m

Answer: (1)

11. The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be:

(1)

(2)

(3)

(4)

Answer: (4)

12. In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is λ. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

(1)

(2)

(3)

(4)

Answer: (3)

13. In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to :

(1) 1.0 V

(2) 2.0 V

(3) 1.5 V

(4) 0.5 V

Answer: (1)

14. Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180°C and B upto T°C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value f T is:

(1) 270°C

(2) 230°C

(3) 250°C

(4) 200°C

Answer: (2)

15. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process, the temperature of the gas is increased by ∆ The amount of heat absorbed by gas is (R is gas constant):

(1)

(2)

(3)

(4)

Answer: (2)

16. A galvanometer having a resistance of 20 Ω and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

(1) 100 Ω

(2) 125 Ω

(3) 80 Ω

(4) 120 Ω

Answer: (3)

17. A thermometer graduated according to a linear scale reads a value x_{0} when in contact with boiling water, and x_{0} /3 when in contact with ice. What is the temperature of an object in °C, if this thermometer in the contact with the object reads x_{0} /2?

(1) 40

(2) 60

(3) 35

(4) 25

Answer: (4)

18. In the circuit shown, the potential difference between A and B is:

(1) 6 V

(2) 3 V

(3) 2 V

(4) 1 V

Answer: (3)

19. An amplitude modulated signal is plotted below:

Which one of the following best describes the above signal?

(1) (9 + sin(2π × 10^{4}t))sin(2.5π × 10^{5}t) V

(2) (9 + sin(4π × 10^{4}t))sin(5π × 10^{5}t) V

(3) (1 + 9sin(2π × 10^{4}t))sin(2.5π × 10^{5}t) V

(4) (9 + sin(2.5π × 10^{5}t))sin(2π × 10^{4}t) V

Answer: (1)

20. In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 Ω resistor is connected in series with R_{1}, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R_{1} + 10) Ω such that the null point shifts back to its initial position is:

(1) 60 Ω

(2) 30 Ω

(3) 40 Ω

(4) 20 Ω

Answer: (1)

21. A particle of mass m and charge q is in an electric and magnetic field given by

The charged particle is shifted from the origin to the point P(x = 1 ; y = 1) along a straight path. The magnitude of the total work done is:

(1) (0.15)q

(2) (5q)

(3) (0.35)q

(4) (2.5)q

Answer: (2)

22. Seven capacitors, each of capacitance 2 μF, are to be connected in a configuration to obtain an effective capacitance of (6/13) μ Which of the combinations, shown in figures below, will achieve the desired value?

(1)

(2)

(3)

(4)

Answer: (1)

23. A pendulum is executing simple harmonic motion and its maximum kinetic energy is K_{1}. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K_{2}. Then

(1) K_{2} = 2K_{1}

(2) K_{2} = K_{1}/4

(3) K_{2} = K_{1}

(4) K_{2} = K_{1}/2

Answer: (1)

24. A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is √3, then the angle of incidence is:

(1) 90°

(2) 30°

(3) 45°

(4) 60°

Answer: (4)

25. In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of 19.44 μm and a width of 4.05 μ The number of bright fringes between the first and the second diffraction minima is

(1) 05

(2) 09

(3) 10

(4) 04

Answer: (4)

26. A particle moves from the point at t = 0, with an initial velocity It is acted upon by a constant force which produces a constant acceleration What is the distance of the particle form the origin at time 2 s

(1) 20√2 m

(2) 15 m

(3) 10√2 m

(4) 5 m

Answer: (1)

27. The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians):

(1) π/8

(2) π/6

(3) π/3

(4) π/4

Answer: (2)

28. A circular disc D_{1} of mass M and radius R has two identical discs D_{2} and D_{3} of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OOʹ, passing through the centre of D_{1} as shown in the figure, will be:

(1) 3MR^{2}

(2)

(3) MR^{2}

(4)

Answer: (1)

29. The circuit shown below contains two ideal diodes, each with a forward resistance of 50Ω. If the battery voltage is 6 V, the current through the 100 Ω resistance (in amperes) is:

(1) 0.036

(2) 0.020

(3) 0.030

(4) 0.027

Answer: (2)

30. A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:

(1) Increases by a factor of 3

(2) Decreases by a factor of 9√3

(3) Decreases by a factor of 9

(4) Increases by a factor of 27

Answer: (1)

CHEMISTRY

1. Given the equilibrium constant :

K_{C} of the reaction :

Cu(s) + 2Ag^{+} (aq) → Cu^{2+} (aq) + 2Ag(s) is 10 × 10^{15}, calculate the E^{0}_{cell} of this reaction at 298 K

(1) 0.4736 mV

(2) 0.4736 V

(3) 0.04736 V

(4) 0.04736 mV

Answer: (2)

2. Among the colloids cheese (C), milk (M) and smoke (S), the correct combination of the dispersed phase and dispersion medium, respectively is :

(1) C : solid in liquid; M : liquid in liquid; S : gas in solid

(2) C : liquid in solid; M : liquid in solid; S : solid in gas

(3) C : liquid in solid; M : liquid in liquid; S : solid in gas

(4) C : solid in liquid; M : solid in liquid; S : solid in gas

Answer: (3)

3. The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by ‘a’)

(1) 0.027 a

(2) 0.047 a

(3) 0.067 a

(4) 0.134 a

Answer: (3)

4. The reaction 2X → B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final concentration of 0.2 M will be :

(1) 12.0 h

(2) 7.2 h

(3) 9.0 h

(4) 18.0 h

Answer: (4)

5. In the following compound,

the favourable site/s protonation is/are :

(1) (a)

(2) (b), (c) and (d)

(3) (a) and (d)

(4) (a) and (e)

Answer: (2)

6. The major product obtained in the following conversion is :

(1)

(2)

(3)

(4)

Answer: ()

7. K_{2 }HgI_{4 }is 40% ionised in aqueous solution. The value of its van’t Hoff factor (i) is :

(1) 1.6

(2) 2.0

(3) 2.2

(4) 1.8

Answer: (4)

8. Match the following items in column I with the corresponding items in column II.

9. The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (ν) of the incident radiation as, [ν_{0}is threshold frequency]:

(1)

(2)

(3)

(4)

Answer: (3)

10. The correct option with respect to the Pauling electronegativity values of the elements is:

(1) Si < Al

(2) P > S

(3) Te > Se

(4) Ga < Ge

Answer: (4)

11. The correct match between Item I and Item II is:

Item I Item II

(A) Ester test (P) Tyr

(B) Carbylamine test (Q) AsP

(C) Phthalein dye test (R) Ser

(S) Lys

(1) (A) → (Q); (B) → (S); (C) → (P)

(2) (A) → (R); (B) → (Q); (C) → (P)

(3) (A) → (Q); (B) → (S); (C) → (R)

(4) (A) → (R); (B) → (S); (C) → (Q)

Answer: (1)

12. The correct match between Item I and Item II is:

Item I

(A) Allosteric effect

(B) Competitive

(C) Receptor

(D) Poison

Item II

(P) Molecule binding to the active site of enzyme

(Q) Molecule crucial for inhibitor communication in the body

(R) Molecule binding to a site other than the active site of enzyme

(S) Molecule binding to the enzyme covalently

(1) (A) → (P); (B) → (R); (C) → (S); (D) → (Q)

(2) (A) → (R); (B) → (P); (C) → (Q); (D) → (S)

(3) (A) → (P); (B) → (R); (C) → (Q); (D) → (S)

(4) (A) → (R); (B) → (C); (C) → (D); (D) → (Q)

Answer: (2)

13. Which of the following compounds will produce a precipitate with AgNO_{3} ?

(1)

(2)

(3)

(4)

Answer: (4)

14. The number of bridging CO ligand(s) and Co-Co bond(s) in Co_{2}(CO)_{8}, respectively are:

(1) 2 and 1

(2) 0 and 2

(3) 2 and 0

(4) 4 and 0

Answer: (1)

15. The major product obtained in the following reaction is:

(1)

(2)

(3)

(4)

Answer: (1)

16.

In the above sequence of reactions, A and D, respectively, are :

(1) KI and K_{2}MnO_{4}

(2) KIO_{3} and MnO_{2}

(3) MnO_{2} and KIO_{3}

(4) KI and KMnO_{4}

Answer: (3)

17. The major product of the following reaction is :

(1)

(2)

(3)

(4)

Answer: (1)

18. Taj Mahal is being slowly disfigured and discoloured. This is primarily due to :

(1) Acid rain

(2) Water pollution

(3) Global warming

(4) Soil pollution

Answer: (1)

19. The relative stability of +1 oxidation state of group 13 elements follows the order :

(1) Tl < In < Ga < Al

(2) Al < Ga < Tl < In

(3) Al < Ga < In < Tl

(4) Ga < Al < In < Tl

Answer: (3)

20. The homopolymer formed from 4-hydroxy-butanoic acids is :

(1)

(2)

(3)

(4)

Answer: (1)

21. The reaction that does NOT define calcination is:

Answer: (4)

22. Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution?

(1)

(2)

(3)

(4)

Answer: (1 and 2)

23. The hydride that is NOT electron deficient is

(1) SiH_{4}

(2) GaH_{3}

(3) B_{2}H_{6}

(4) AlH_{3}

Answer: (1)

24. For the equilibrium

2H_{2}O ⇌ H_{3}O^{+} + OH^{−}, the value of ∆G° at 298 K is approximately

(1) −80 kJ mol^{−}^{1}

(2) −100 kJ mol^{−}^{1}

(3) 80 kJ mol^{−}^{1}

(4) 100 kJ mol^{−}^{1}

Answer: (3)

25. The coordination number of Th in K_{4}[Th(C_{2}O_{4})_{4}(OH_{2})_{2}] is

(C_{2}O_{4}^{2}^{−} = Oxalato)

(1) 10

(2) 6

(3) 14

(4) 8

Answer: (1)

26. A compound ‘X’ on treatment with Br_{2}/NaOH, provided C_{3}H_{9}N, which gives positive carbylamines test. Compound ‘X’ is

(1) CH_{3}CH_{2}CH_{2}CONH_{2}

(2) CH_{3}COCH_{2}NHCH_{3}

(3) CH_{3}CH_{2}COCH_{2}NH_{2}

(4) CH_{3}CON(CH_{3})_{2}

Answer: (1)

27. The higher concentration of which gas in air can cause stiffness of flower buds?

(1) SO_{2}

(2) CO

(3) CO_{2}

(4) NO_{2}

Answer: (1)

28. The reaction

MgO(s) + C(s) → Mg(s) + CO(g), for, which ∆_{r}H° = +491.1 kJ mol^{−1} and ∆_{s}H° = 198.0 JK^{−1} mol^{−1}, is not feasible at 298 K. Temperature above which reaction will be feasible is

(1) 2040.5 K

(2) 1890.0 K

(3) 2480.3 K

(4) 2380.5 K

Answer: (3)

29. 25 ml of the given HCl solution requires 30 mL of 0.1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution

(1) 25 mL

(2) 12.5 mL

(3) 50 mL

(4) 75 mL

Answer: (1)

30. The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by

∆_{r}G° A – BT

Where A and B are non-zero constants. Which of the following is true about this reaction?

(1) Exothermic if B < 0

(2) Endothermic if A > 0

(3) Endothermic if A < 0 and B > 0

(4) Exothermic if A > 0 and B < 0

Answer: (2)

MATHEMATICS

1. Let A and B be two invertible matrices of order 3 × 3. If det(ABA^{T}) = 8 and det(AB^{–1}) = 8, then det(BA^{–1}B^{T}) is equal to :

(1) 1

(2) 16

(3) 1/16

(4) 1/4

Answer: (3)

2. A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :

(1) A hyperbola

(2) A parabola

(3) An ellipse

(4) A straight line

Answer: (2)

3. Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression is

(1) 1/2

(2)

(3) 1

(4) 1/4

Answer: (4)

4. If (a + b + c) (x + a + b + c)^{2}, x ≠ 0 and a + b + c ≠ 0, then x is equal to :

(1) 2(a + b+ c)

(2) −(a + b +c)

(3) abc

(4) −2(a + b +c)

Answer: (4)

5. Let a function f : (0, ∞) → (0, ∞) be defined by Then f is :

(1) Injective only

(2) Both injective as well as surjective

(3) Not injective but it is surjective

(4) Neither injective nor surjective

Answer: (*)

6. If where C is a constant of integration, then f(x) is equal to :

(1)

(2)

(3)

(4)

Answer: (2)

7. If the area of the triangle whose one vertex is at the vertex of the parabola, y^{2} + 4(x – a^{2}) = 0 and the other two vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of ‘a’ is :

(1) 5√5

(2) (10)^{2/3}

(3) 5(2^{13})

(4) 5

Answer: (4)

8. Let z be a complex number such that |z| + z = 3 + i (where i = √−1).

Then |z| is equal to :

(1) √41/4

(2) 5/4

(3) 5/3

(4) √34/3

Answer: (3)

9. Let where a, b and d are non-zero constants. Then :

(1) f is an increasing function of x

(2) f is a decreasing function of x

(3) f is neither increasing nor decreasing function of x

(4) fʹ is not a continuous function of x

Answer: (1)

10. Contrapositive of the statement

“If two numbers are not equal, then their squares are not equal.” is :

(1) If the squares of two numbers are equal, then the numbers are equal

(2) If the squares of two numbers are not equal, then the numbers are equal

(3) If the squares of two numbers are equal, then the numbers are not equal

(4) If the squares of two numbers are not equal, then the numbers are not equal

Answer: (1)

11. If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is :

(1) 5x + 3y – 11 = 0

(2) 3x + 5y – 13 = 0

(3) 3x – 5y + 7 = 0

(4) 5x – 3y + 1 = 0

Answer: (4)

12. is equal to :

(1) 2

(2) 4

(3) 1

(4) 0

Answer: (3)

13. Two lines and intersect at the point R. The reflection of R in the xy-plane has coordinates :

(1) (–2, 4, 7)

(2) (2, 4, 7)

(3) (2, –4, –7)

(4) (2, –4, 7)

Answer: (3)

14. Let (x + 10)^{50} + (x – 10)^{50} = a_{0} + a_{1}x + a_{2}x^{2} + … + a_{50}x^{50}. for all x ∈ R; then a_{2}/a_{0} is equal to

(1) 12.25

(2) 12.75

(3) 12.00

(4) 12.50

Answer: (1)

15. Given for ∆ABC with usual notation. If then the ordered triplet (α, β, γ) has a value :

(1) (3, 4, 5)

(2) (7, 19, 25)

(3) (19, 7, 25)

(4) (5, 12, 13)

Answer: (2)

16. If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :

(1) 2 : 1

(2) 1 : 3

(3) 4 : 1

(4) 3 : 1

Answer: (4)

17. The number of function f from {1, 2, 3, …,20} onto {1, 2, 3, …, 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :

(1) 5^{6} × 15

(2) 6^{5} × (15)!

(3) 5! × 6!

(4) (15)! × 6!

Answer: (4)

18. The integral equals :

(1)

(2)

(3)

(4)

Answer: (1)

19. Let α and β the roots of the quadratic equation x^{2} sin θ – x(sin θ cos θ +1) + cos θ = 0 (0 < θ > 45°), and α < β. Then is equal to :

(1)

(2)

(3)

(4)

Answer: (2)

20. A bag contains 30 white ball and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then is equal to :

(1) 3√2

(2) 4√3

(3) 4√3/3

(4) 4

Answer: (2)

21. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :

(1) 2

(2) 13/8

(3) 13/6

(4) 13/12

Answer: (4)

22. Let S_{n} = 1 + q + q^{2} + … + q^{n} and where q is a real number and q ≠

23. Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

(1) (4√3, 2√3)

(2) (4√3, 2√2)

(3) (4√2, 2√2)

(4) (4√2, 2√3)

Answer: (2)

24. Let S = {1, 2, …., 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is “nice” is

(1) 7/2^{20}

(2) 6/2^{20}

(3) 4/2^{20}

(4) 5/2^{20}

Answer: (4)

25. If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2α – 3β is equal to

(1) 5

(2) 12

(3) 17

(4) 7

Answer: (4)

26. All x satisfying the inequality (cot^{–1}x)^{2} – 7 (cot^{–1}x) + 10 > 0, lie in the interval

(1) (cot 2, ∞)

(2) (cot 5, cot 4)

(3) (−∞, cot 5) ∪ (cot 4, cot 2)

(4) (−∞, cot 5) ∪ (cot 2, ∞)

Answer: (1)

27. Let respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is 3/√2, then the sum of all possible values of β is

(1) 3

(2) 1

(3) 4

(4) 2

Answer: (2)

28. The solution of the differential equation, when Y(1) = 1, is

(1)

(2)

(3)

(4)

Answer: (3)

29. Let K be the set of all real values of x where the function

f(x) = sin |x| – |x| + 2(x – π) is not differentiable. Then the set K is equal to

(1) {π}

(2) ϕ (an empty set)

(3) {0}

(4) {0, π}

Answer: (2)

30. The area (in sq. units) in the first quadrant bounded by the parabola, y = x^{2} + 1, the tangent to it at the point (2, 5) and the coordinate axes is

1. To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ, the torque, applied by the machine on the mop is

(1)

(2)

(3)

(4)

Answer: (4)

2. Two electric dipoles, A, B with respective dipole moments are placed on the x-axis with a separation R, as shown in the figure

The distance from A at which both of them produce the same potential is

(1)

(2)

(3)

(4)

Answer: (2)

3. To get output ‘1’ at R, for the given logic gate circuit the input values must be