JEE Main Previous Year Papers Solved with Answer Key & PDF Download

JEE Main Previous Year Papers Solved with Answer Key & PDF Download

**JEE Main Online Computer Based Test (CBT) Examination Morning Held on 16-04-2018**

**Timing : 9 : 30 AM – 12 : 30 PM**

1. The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity The maximum percentage error in the value of A will be :

(1) 6.0%

(2) 7.5%

(3) 8.5%

(4) 6.5%

2. Let The magnitude of a coplanar vector such that is given by :

(1)

(2)

(3)

(4)

3. A body of mass m starts moving from rest along x-axis so that its velocity varies as where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :

(1)

(2) 8 m a^{4}t^{2}

(3) 4 m a^{4}t^{2}

(4)

4. Two particles of the same mass m are moving in circular orbits because of force, given by

The first particle is at a distance r=1, and the second, at r=4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to :

(1) 6 × 10^{−}^{2}

(2) 3 × 10^{−}^{3}

(3) 10^{−1}

(4) 6 × 10^{2}

5. An oscillator of mass M is at rest in its equilibrium position in a potential A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)

(1)

(2) 1/2

(3) 2/3

(4)

6. Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :

(1) Weight of the object, everywhere on the earth, will increase.

(2) Weight of the object, everywhere on the earth, will decrease.

(3) There will be no change in weight anywhere on the earth.

(4) Except at poles, weight of the object on the earth will decrease.

7. A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and zʹ axes will be :

(1) 1 : 3

(2) 1 : 4

(3) 1 : 5

(4) 1 : 2

8. The relative uncertainty in the period of a satellite orbiting around the earth is 10^{−2}. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

(1) 10^{−2}

(2) 2 × 10^{−2}

(3) 3 × 10^{−2}

(4) 6 × 10^{−2}

9. A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P_{2} be the pressure inside the inner bubble and P_{0}, the pressure outside the outer bubble. Radius of another bubble with pressure difference P_{2 }− P_{0} between its inside and outside would be :

(1) 12 cm

(2) 2.4 cm

(3) 6 cm

(4) 4.8 cm

10. One mole of an ideal monoatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

(1)

(2)

(3)

(4)

11. Two moles of helium are mixed with n moles of hydrogen. If for the mixture, then the value of n is :

(1) 1

(2) 3

(3) 2

(4) 3/2

12. A particle executes simple harmonic motion and is located at x=a, b and c at times t_{o}, 2t_{o} and 3t_{o} The frequency of the oscillation is :

(1)

(2)

(3)

(4)

13. Two sitar strings, A and B, playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease by 3 Hz. If the frequency of A is 425 Hz, the original frequency of B is :

(1) 430 Hz

(2) 420 Hz

(3) 428 Hz

(4) 422 Hz

14. Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between them is F. A third identical conducting sphere, C, is uncharged. Sphere C is first touched to A, then to B, and then removed. As a result, the force between A and B would be equal to :

(1) F

(2) 3F/4

(3) 3F/8

(4) F/2

15. A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500°C more than room temperature. What is the temperature coefficient of resistance of the heating element ?

(1) 0.5 × 10^{−}^{4} °C^{−}^{1}

(2) 5 × 10^{−}^{4} °C^{−}^{1}

(3) 1 × 10^{−}^{4} °C^{−}^{1}

(4) 2 × 10^{−}^{4} °C^{−}^{1}

16. A galvanometer with its coil resistance 25 Ω requires a current of 1 mA for its full deflection. In order to construct an ammeter to read up to a current of 2 A, the approximate value of the shunt resistance should be :

(1) 2.5 × 10^{−}^{3} Ω

(2) 1.25 × 10^{−}^{2} Ω

(3) 1.25 × 10^{−}^{3} Ω

(4) 2.5 × 10^{−}^{2} Ω

17. In the following circuit, the switch S is closed at t=0. The charge on the capacitor C_{1} as a function of time will be given by

(1) C_{1}E [1 − exp(−tR/C_{1})]

(2) C_{2}E [1 − exp(−t/RC_{2})]

(3) C_{eq}E [1 − exp(−t/RC_{eq})]

(4) C_{eq}E exp (−t/RC_{eq})

18. A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity ω, the maximum e.m.f. induced in the coil will be :

(1) 3 nBAω

(2)

(3) nBAω

(4)

19. A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity ω with respect to normal axis then the magnetic moment of the loop is :

(1) q ωr^{2}

(2)

(3)

(4)

20. A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5 A, and its efficiency is 90%, the output current would be :

(1) 50 A

(2) 45 A

(3) 25 A

(4) 20 A

21. A plane electromagnetic wave of wavelength λ has an intensity I. It is propagating along the positive Y-direction. The allowed expressions for the electric and magnetic fields are given by :

(1)

(2)

(3)

(4)

22. A ray of light is incident at an angle of 60° on one face of a prism of angle 30°. The emergent ray of light makes an angle of 30° with incident ray. The angle made by the emergent ray with second face of prism will be :

(1) 0°

(2) 90°

(3) 45°

(4) 30°

23. Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The angle between the polarizers A and C is θ. Then :

(1)

(2)

(3)

(4)

24. The de-Broglie wavelength (λ_{B}) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (λ_{G}) by :

(1) λ_{B} = 2λ_{G}

(2) λ_{B} = 3λ_{G}

(3) λ_{B} = λ_{G/2}

(4) λ_{B} = λ_{G/3}

25. Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths λ_{N}, λ_{A } The ratio is closest to :

(1) 10^{−}^{6}

(2) 10

(3) 10^{−}^{10}

(4) 10^{−}^{1}

26. At some instant, a radioactive sample S_{1} having an activity 5 μCi has twice the number of nuclei as another sample S_{2} which has an activity of 10 μCi. The half lives of S_{1} and S_{2} are :

(1) 20 years and 5 years, respectively

(2) 20 years and 10 years, respectively

(3) 5 years and 20 years, respectively

(4) 10 years and 20 years, respectively

27. In the given circuit, the current through zener diode is :

(1) 5.5 mA

(2) 6.7 mA

(3) 2.5 mA

(4) 3.3 mA

28. A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be :

(1) 7 V

(2) 28 V

(3) 11.2 V

(4) 22.4 V

29. In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 kΩ are used. The figure of merit of the galvanometer is 60 μA/division. In the absence of shunt resistance, the galvanometer produces a deflection of θ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of θ/2, is closest to :

(1) 550 Ω

(2) 220Ω

(3) 55Ω

(4) 110Ω

30. The end correction of a resonance column is 1 cm. If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be :

(1) 28 cm

(2) 32 cm

(3) 36 cm

(4) 40 cm

31. An unknown chlorohydrocarbon has 3.55% of chlorine. If each molecule of the hydrocarbon has one chlorine atom only; chlorine atoms present in 1 g of chlorohydrocarbon are :

(Atomic wt. of Cl=35.5 u; Avogadro constant=6.023 × 10^{23} mol^{−1})

(1) 6.023 × 10^{20}

(2) 6.023 × 10^{9}

(3) 6.023 × 10^{21}

(4) 6.023 × 10^{23}

32. The gas phase reaction 2NO_{2}(g) → N_{2}O_{4}(g) is an exothermic reaction. The decomposition of N_{2}O_{4}, in equilibrium mixture of NO_{2}(g) and N_{2}O_{4}(g), can be increased by :

(1) lowering the temperature.

(2) increasing the pressure.

(3) addition of an inert gas at constant volume.

(4) addition of an inert gas at constant pressure.

33. Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl=35.5 u)

(1) 1.46

(2) 0.46

(3) 1.64

(4) 0.64

34. When 9.65 ampere current was passed for 1.0 hour into nitrobenzene in acidic medium, the amount of p-aminophenol produced is :

(1) 9.81 g

(2) 10.9 g

(3) 98.1 g

(4) 109.0 g

35. For which of the following processes, ΔS is negative ?

(1) H_{2}(g) → 2H(g)

(2) N_{2}(g, 1 atm) → N_{2}(g, 5 atm)

(3) C(diamond) → C(graphite)

(4) N_{2}(g, 273 K) → N_{2}(g, 300 K)

36. Which one of the following is not a property of physical adsorption ?

(1) Higher the pressure, more the adsorption

(2) Lower the temperature, more the adsorption

(3) Greater the surface area, more the adsorption

(4) Unilayer adsorption occurs

37. If 50% of a reaction occurs in 100 second and 75% of the reaction occurs in 200 second, the order of this reaction is :

(1) Zero

(2) 1

(3) 2

(4) 3

38. Which of the following statements is false ?

(1) Photon has momentum as well as wavelength.

(2) Splitting of spectral lines in electrical field is called Stark effect.

(3) Rydberg constant has unit of energy.

(4) Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases.

39. At 320 K, a gas A2 is 20% dissociated to A(g). The standard free energy change at 320 K and 1 atm in J mol^{−1} is approximately : (R=8.314 JK^{−1} mol^{−1}; ln 2=0.693; ln 3=1.098)

(1) 4763

(2) 2068

(3) 1844

(4) 4281

40. The mass of a non-volatile, non-electrolyte solute (molar mass=50 g mol^{−1}) needed to be dissolved in 114 g octane to reduce its vapour pressure to 75%, is :

(1) 37.5 g

(2) 75 g

(3) 150 g

(4) 50 g

41. The **incorrect** statement is :

(1) Cu^{2+} salts give red coloured borax bead test in reducing flame.

(2) Cu^{2+} and Ni^{2+} ions give black precipitate with H2S in presence of HCl solution.

(3) Ferricion gives blood red colour with potassium thiocyanate.

(4) Cu^{2+} ion gives chocolage coloured precipitate with potassium ferrocyanide solution.

42. The incorrect geometry is represented by :

(1) BF_{3} – trigonal planar

(2) H_{2}O – bent

(3) NF_{3} – trigonal planar

(4) AsF_{5} – trigonal bipyramidal

43. In Wilkinson’s catalyst, the hybridization of central metal ion and its shape are respectively :

(1) sp^{3}d, trigonal bipyramidal

(2) sp^{3}, tetrahedral

(3) dsp^{2}, square planar

(4) d^{2}sp^{3}, octahedral

44. Among the oxides of nitrogen : N_{2}O_{3}, N_{2}O_{4} and N_{2}O_{5} ; the molecule(s) having nitrogen-nitrogen bond is/are :

(1) Only N_{2}O_{5}

(2) N_{2}O_{3} and N_{2}O_{5}

(3) N_{2}O_{4} and N_{2}O_{5}

(4) N_{2}O_{3} and N_{2}O_{4}

45. Which of the following complexes will show geometrical isomerism ?

(1) aquachlorobis(ethylenediamine) cobalt(II) chloride

(2) pentaaquachlorochromium(III) chloride

(3) potassium amminetrichloroplatinate (II)

(4) potassium tris(oxalato)chromate(III)

46. In a complexometric titration of metal ion with ligand M(Metal ion)+L(Ligand) → C(Complex) end point is estimated spectrophotometrically (through light absorption). If ‘M’ and ‘C’ do not absorb light and only ‘L’ absorbs, then the titration plot between absorbed light (A) versus volume of ligand ‘L’ (V) would look like :

(1)

(2)

(3)

(4)

47. In the extraction of copper from its sulphide ore, metal is finally obtained by the oxidation of cuprous sulphide with :

(1) Fe_{2}O_{3}

(2) Cu_{2}O

(3) SO_{2}

(4) CO

48. Which of the following conversions involves change in both shape and hybridisation ?

(1) NH_{3} → NH_{4}^{+}

(2) CH_{4} → C_{2}H_{6}

(3) H_{2}O → H_{3}O^{+}

(4) BF_{3} → BF_{4}^{−}

49. A group 13 element ‘X’ reacts with chlorine gas to produce a compound XCl_{3} . XCl_{3} is electron deficient and easily reacts with NH3 to form Cl_{3}X ← NH_{3} adduct; however, XCl_{3} does not dimerize. X is :

(1) B

(2) Al

(3) Ga

(4) In

50. When XO_{2} is fused with an alkali metal hydroxide in presence of an oxidizing agent such as KNO_{3} ; a dark green product is formed which disproportionates in acidic solution to afford a dark purple solution. X is :

(1) Ti

(2) V

(3) Cr

(4) Mn

51. The major product of the following reaction is :

(1)

(2)

(3)

(4)

52. For standardizing NaOH solution, which of the following is used as a primary standard ?

(1) Ferrous Ammonium Sulfate

(2) dil. HCl

(3) Oxalic acid

(4) Sodium tetraborate

53. The most polar compound among the following is :

(1)

(2)

(3)

(4)

54. The correct match between items of **List – I** and **List – II** is :

(1) (A)-(R), (B)-(S), (C)-(P), (D)-(Q)

(2) (A)-(S), (B)-(R), (C)-(P), (D)-(Q)

(3) (A)-(S), (B)-(R), (C)-(Q), (D)-(P)

(4) (A)-(R), (B)-(S), (C)-(Q), (D)-(P)

55. Among the following, the incorrect statement is :

(1) Maltose and lactose has 1, 4-glycosidic linkage.

(2) Sucrose and amylose has 1, 2-glycosidic linkage.

(3) Cellulose and amylose has 1, 4-glycosidic linkage.

(4) Lactose contains β-D-galactose and β-D-glucose.

56. Which of the following compounds will most readily be dehydrated to give alkene under acidic condition ?

(1) 1-Pentanol

(2) 4-Hydroxypentan-2-one

(3) 3-Hydroxypentan-2-one

(4) 2-Hydroxycyclopentanone

57. Products A and B formed in the following reactions are respectively :

(1)

(2)

(3)

(4)

58. The major product B formed in the following reaction sequence is :

(1)

(2)

(3)

(4)

59. The major product of the following reaction is :

(1)

(2)

(3)

(4)

60. The major product of the following reaction is :

(1)

(2)

(3)

(4)

61. Let N denote the set of all natural numbers. Define two binary relations on N as R_{1}={(x, y) ϵ N × N : 2x + y = 10} and R_{2}={(x, y) ϵ N × N : x + 2y = 10}. Then :

(1) Range of R_{1} is {2, 4, 8}.

(2) Range of R_{2} is {1, 2, 3, 4}.

(3) Both R_{1} and R_{2} are symmetric relations.

(4) Both R_{1} and R_{2} are transitive relations.

62. Let p, q and r be real numbers (p ≠ q, r ≠ 0), such that the roots of the equation are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

(1)

(2) p^{2} + q^{2}

(3) 2(p^{2} + q^{2})

(4) p^{2} + q^{2} + r^{2}

63. The least positive integer n for which is

(1) 2

(2) 3

(3) 5

(4) 6

64. Let and B = A^{20}. Then the sum of the elements of the first column of B is :

(1) 210

(2) 211

(3) 231

(4) 251

65. The number of values of k for which the system of linear equations,

(k + 2)x + 10y = k

kx + (k + 3)y = k – 1

has no solution, is :

(1) 1

(2) 2

(3) 3

(4) infinitely many

66. The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is :

(1) 24

(2) 30

(3) 36

(4) 48

67. The coefficient of x^{2} in the expansion of the product (2− x^{2}) ⋅ ((1 + 2x + 3x^{2})6+ (1 − 4x^{2})6) is :

(1) 107

(2) 106

(3) 108

(4) 155

68. Let (x_{i} ≠ 2 for i = 1, 2, . . . , n) be in A.P. such that x_{1} = 4 and x_{21} = 20. If n is the least positive integer for which x_{n} > 50, then is equal to :

(1) 1/8

(2) 3

(3) 13/8

(4) 13/4

69. The sum of the first 20 terms of the series is :

(1)

(2)

(3)

(4)

70.

(1) 1/3

(2) −1/3

(3) −1/6

(4) 1/6

71. If the function f defined as is continuous at x = 0, then the ordered pair (k, f(0)) is equal to :

(1) (3, 2)

(2) (3, 1)

(3) (2, 1)

(4) (1/3, 2)

72. If then is equal to :

(1) y/x

(2) x/y

(3) −y/x

(4) −x/y

73. Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f (x)=2x^{3} − 9x^{2} + 12x + 5 in the interval [0, 3]. Then M−m is equal to :

(1) 5

(2) 9

(3) 4

(4) 1

74. If (C is a constant of integration), then the ordered pair (K, A) is equal to :

(1) (2, 1)

(2) (−2, 3)

(3) (2, 3)

(4) (−2, 1)

75. If then :

(1) fʹʹʹ(x) + fʹʹ(x) = sin x

(2) fʹʹʹ(x) + fʹʹ(x) – fʹ(x) = cos x

(3) fʹʹʹ(x) + fʹ(x) = cos x – 2x sin x

(4) fʹʹʹ(x) – fʹʹ(x) = cos x – 2x sin x

76. If the area of the region bounded by the curves, y = x^{2}, y = 1/x and the lines y = 0 and x = t (t > 1) is 1 sq. unit, then it is equal to :

(1) e^{3/2}

(2) 4/3

(3) 3/2

(4) e^{2/3}

77. The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point (0, 3) is :

(1) xy yʹʹ + x(yʹ)^{2} – y yʹ = 0

(2) x + y yʹʹ = 0

(3) xy yʹ + y^{2} – 9 = 0

(4) xy yʹ – y^{2} + 9 = 0

78. The locus of the point of intersection of the lines, and (k is any non-zero real parameter), is :

(1) an ellipse whose eccentricity is 1/√3.

(2) an ellipse with length of its major axis 8√2.

(3) a hyperbola whose eccentricity is √3.

(4) a hyperbola with length of its transverse axis 8√2.

79. If a circle C, whose radius is 3, touches externally the circle, x^{2} + y^{2 }+ 2x − 4y – 4 = 0 at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

(1) 2√5

(2) 3√2

(3) √5

(4) 2√3

80. Let P be a point on the parabola, x^{2} = 4y. If the distance of P from the centre of the circle, x^{2} + y^{2} + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P, is :

(1) x + 4y – 2 = 0

(2) x – y + 3 = 0

(3) x + y + 1 = 0

(4) x + 2y = 0

81. If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 3/2 units, then its eccentricity is :

(1) 1/2

(2) 1/3

(3) 2/3

(4) 1/9

82. The sum of the intercepts on the coordinate axes of the plane passing through the point (−2, −2, 2) and containing the line joining the points (1, −1, 2) and (1, 1, 1), is :

(1) 4

(2) −4

(3) −8

(4) 12

83. If the angle between the lines, is then p is equal to :

(1) 7/2

(2) 2/7

(3) −7/4

(4) −4/7

84. Let and a vector be such that Then equals :

(1) 11/3

(2) 11/√3

(3)

(4)

85. The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

(1) 0

(2) 1

(3) 2

(4) 4

86. Let A, B and C be three events, which are pair-wise independent and denotes the complement of an event E. If P(A ∩ B ∩ C) = 0 and P(C) > 0, then is equal to :

(1)

(2)

(3)

(4)

87. Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is 1/12, then the number of children in each family is :

(1) 3

(2) 4

(3) 5

(4) 6

88. If an angle A of a ΔABC satisfies 5 cosA+3=0, then the roots of the quadratic equation, 9x^{2} + 27x + 20=0 are :

(1) sec A, cot A

(2) sin A, sec A

(3) sec A, tan A

(4) tan A, cos A

89. A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angle of depression of the car to change from 30° to 45° ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is :

(1)

(2)

(3)

(4)

90. If p→(∼p∨∼q) is false, then the truth values of p and q are respectively :

(1) F, F

(2) T, F

(3) F, T

(4) T, T

**JEE Main Online Computer Based Test (CBT) Examination Afternoon Held on 15-04-2018,**

**PHYSICS**

1. The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length ?

(1) G h^{2} c^{3}

(2) G^{2} h c

(3) G^{1/2} h^{2} c

(4)

2. A man in a car at location Q on a straight highway is moving with speed υ. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?

(1) d

(2) d/√2

(3) d/2

(4) d/√3

3. A body of mass 2 kg slides down with an acceleration of 3 m/s^{2} on a rough inclined plane having a slope of 30°. The external force required to take the same body up the plane with the same acceleration will be : (g=10 m/s^{2})

(1) 14 N

(2) 20 N

(3) 6 N

(4) 4 N

4. A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90° with respect to each other. The mass of unknown particle is :

(1) m/2

(2) m

(3) m/√3

(4) 2 m

5. A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : (g=10 m/s^{2})

(1) 0.5

(2) 0.3

(3) 0.7

(4) 0.6

6. A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2υ and υ respectively. The masses stick to the bar after collision at a distance respectively from the centre of the abr. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be :

(1)

(2)

(3)

(4)

7. A thin rod MN, free to rotate in the vertical plane about the fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle α with the horizontal, will be proportional to : (see figure)

(1)

(2) sin α

(3)

(4) cos α

8. As shown in the figure, forces of 10^{5} N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :

(1) 0.25 cm

(2) 0.37 cm

(3) 0.75 cm

(4) 1.00 cm

9. When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5r/4. Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :

(1) 11.2 m

(2) 8.7 m

(3) 9.5 m

(4) 10.5 m

10. Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two engines A and B are represented by η_{A} and η_{B}, respectively, then what is the value of

(1) 12/7

(2) 7/12

(3) 12/5

(4) 5/12

11. The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms^{−}^{1} : [k_{B} = 1.4 × 10^{−}^{23} J/K; m_{He} = 7 × 10^{−}^{27} kg]

(1) 1.3 × 10^{4}

(2) 1.3 × 10^{3}

(3) 1.3× 10^{5}

(4) 1.3 × 10^{2}

12. Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.

x(t) = A sin (at + δ)

y(t) = B sin (bt)

Identify the **correct **match below.

**Parameters Curve**

(1) A ≠ B, a = b ; δ = 0 Parabola

(2) A = B, a = b ; δ = π/2 Line

(3) A ≠ B, a = b ; δ = π/2 Ellipse

(4) A = B, a = 2b ; δ = π/2 Circle

13. 5 beats/second are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :

(1) 195 Hz

(2) 150 Hz

(3) 300 Hz

(4) 251 Hz

14. A solid ball of radius R has a charge density ρ given by ρ = ρ_{0}(1 – r/R) for 0 ≤ r ≤ The electric field outside the ball is :

(1)

(2)

(3)

(4)

15. A parallel plate capacitor with area 200 cm^{2} and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is 25×10^{−6} N, the value of V is approximately :

(1) 250 V

(2) 100 V

(3) 300 V

(4) 150 V

16. A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is ρ, how long will the charges take to travel a distance d ?

(1)

(2)

(3)

(4)

17. A capacitor C_{1}=1.0 μF is charged up to a voltage V=60 V by connecting it to battery B through switch (1). Now C_{1} is disconnected from battery and connected to a circuit consisting of two uncharged capacitors C_{2}=3.0 μF and C_{3}=6.0 μF through switch (2), as shown in the figure. The sum of final charges on C_{2} and C_{3} is :

(1) 40 μC

(2) 36 μC

(3) 20 μC

(4) 54 μC

18. A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5×10^{−2} The magnetic field at the centre of the triangle will be :

(1) 2 ×10^{−5} Wb/m^{2}

(2) Zero

(3) 8 ×10^{−5} Wb/m^{2}

(4) 4 ×10^{−5} Wb/m^{2}

19. At the centre of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity ω about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time t of its start of rotation.

(1)

(2)

(3)

(4)

20.

A copper rod of mass m slides under gravity on two smooth parallel rails, with

separation l and set at an angle of θ with the horizontal. At the bottom, rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is :

(1)

(2)

(3)

(4)

21. A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t_{1} it is found that the electric field is zero at a spatial point z_{1}. The next zero that occurs in its neighbourhood is at z_{2}. The frequency of the electromagnetic wave is :

(1)

(2)

(3)

(4)

22. A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is 2 cm. The focal lengths of the component lenses are :

(1) 10 cm, 12 cm

(2) 12 cm, 14 cm

(3) 16 cm, 18 cm

(4) 18 cm, 20 cm

23. A plane polarized light is incident on a polariser with its pass axis making angle θ with x-axis, as shown in the figure. At four different values of θ, θ=8°, 38°, 188° and 218°, the observed intensities are same. What is the angle between the direction of polarization and x-axis ?

(1) 98°

(2) 128°

(3) 203°

(4) 45°

24. If the de Broglie wavelengths associated with a proton and an α-particle are equal, then the ratio of velocities of the proton and the α-particle will be :

(1) 4 : 1

(2) 2 : 1

(3) 1 : 2

(4) 1 : 4

25. Muon (μ^{−}) is a negatively charged (|q| = |e|) particle with a mass m_{μ}=200 m_{e}, where m_{e} is the mass of the electron and e is the electronic charge. If μ^{−} is bound to a proton to form a hydrogen like atom, identify the correct statements.

(A) Radius of the muonic orbit is 200 times smaller than that of the electron.

(B) The speed of the μ^{−} in the nth orbit is 1/200 times that of the electron in the nth orbit.

(C) The ionization energy of muonic atom is 200 times more than that of an hydrogen atom.

(D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.

(1) (A), (B), (D)

(2) (A), (C), (D)

(3) (B), (D)

(4) (C), (D)

26. An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

(1) 8 : 27

(2) 4 : 9

(3) 3 : 2

(4) 2 : 3

27. Truth table for the following digital circuit will be :

(1)

(2)

(3)

(4)

28. The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49 μH and a capacitance of 2.5 nF. It is modulated by an audio signal of 12 kHz. The frequency range occupied by the side bands is :

(1) 13482 kHz − 13494 kHz

(2) 442 kHz − 466 kHz

(3) 63 kHz − 75 kHz

(4) 18 kHz − 30 kHz

29. A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

(1) Doubled

(2) Halved

(3) Unchanged

(4) Increased 8 times

30. A body takes 10 minutes to cool from 60°C to 50° The temperature of surroundings is constant at 25°C. Then, the temperature of the body after next 10 minutes will be approximately :

(1) 47°C

(2) 41°C

(3) 45°C

(4) 43°C

31. For per gram of reactant, the maximum quantity of N_{2} gas is produced in which of the following thermal decomposition reactions ?

(Given : Atomic wt. – Cr = 52 u, Ba = 137 u)

(1) (NH_{4})_{2}Cr_{2}O_{7}(s) → N_{2}(g)+4H_{2}O(g) +Cr_{2}O_{3}(s)

(2) 2NH_{4}NO_{3}(s) → 2 N_{2}(g)+4H_{2}O(g) +O_{2}(g)

(3) Ba(N_{3})_{2}(s) → Ba(s)+3N_{2}(g)

(4) 2NH_{3}(g) → N_{2}(g)+3H_{2}(g)

32. All of the following share the same crystal structure except :

(1) LiCl

(2) NaCl

(3) RbCl

(4) CsCl

33. The de-Broglie’s wavelength of electron present in first Bohr orbit of ‘H’ atom is :

(1) 0529 Å

(2) 2π × 0.529 Å

(3)

(4) 4 × 0.529 Å

34. ∆_{f}G° at 500 K for substance ‘S’ in liquid state and gaseous state are +100.7 kcal mol^{−1} and +103 kcal mol−1, respectively. Vapour pressure of liquid ‘S’ at 500 K is approximately equal to :

(R – 2 cal K^{−}^{1} mol^{−}^{1})

(1) 0.1 atm

(2) 1 atm

(3) 10 atm

(4) 100 atm

35. Given

(i) 2Fe_{2}O_{3}(s) → 4Fe(s)+3O_{2}(g) ∆_{r}G° = +1487.0 kJ mol^{−}^{1}

(ii) 2CO(g) + O_{2}(g) → 2CO_{2}(g); ∆_{r}G° = −514.4 kJ mol^{−}^{1}

Free energy change, ∆_{r}G° for the reaction 2Fe_{2}O_{3}(s) + 6CO(g) → 4Fe(s) + 6CO_{2}(g) will be :

(1) −112.4 kJ mol^{−1}

(2) −56.2 kJ mol^{−1}

(3) −168.2 kJ mol^{−1}

(4) −208.0 kJ mol^{−1}

36. Two 5 molal solutions are prepared by dissolving a non-electrolyte non-volatile solute separately in the solvents X and Y. The molecular weights of the solvents are M_{X} and M_{Y}, respectively where The relative lowering of vapour pressure of the solution in X is “m” times that of the solution in Y. Given that the number of moles of solute is very small in comparison to that of solvent, the value of “m” is :

(1) 4/3

(2) 3/4

(3) 1/2

(4) 1/4

37. Following four solutions are prepared by mixing different volumes of NaOH and HCl of different concentrations, pH of which one of them will be equal to 1 ?

(1)

(2)

(3)

(4)

38. At a certain temperature in a 5 L vessel, 2 moles of carbon monoxide and 3 moles of chlorine were allowed to reach equilibrium according to the reaction,

CO + Cl_{2} ⇌ COCl_{2}

At equilibrium, if one mole of CO is present then equilibrium constant (K_{c}) for the reaction is :

(1) 2

(2) 2.5

(3) 3

(4) 4

39. If x gram of gas is adsorbed by m gram of adsorbent at pressure P, the plot of versus log P is linear. The slope of the plot is :

(n and k are constants and n > 1)

(1) 2 k

(2) log k

(3) n

(4) 1/n

40. For a first order reaction, A → P, t_{1/2} (half-life) is 10 days. The time required for 1/4th conversion of A (in days) is :

(ln 2 = 0.693, ln 3 = 1.1)

(1) 5

(2) 3.2

(3) 4.1

(4) 2.5

41. Which of the following best describes the diagram below of a molecular orbital ?

(1) A non-bonding orbital

(2) An antibonding σ orbital

(3) A bonding π orbital

(4) An antibonding π orbital

42. Biochemical Oxygen Demand (BOD) value can be a measure of water pollution caused by the organic matter. Which of the following statements is correct ?

(1) Aerobic bacteria decrease the BOD value.

(2) Anaerobic bacteria increase the BOD value.

(3) Clean water has BOD value higher than 10 ppm.

(4) Polluted water has BOD value higher than 10 ppm.

43. In KO_{2}, the nature of oxygen species and the oxidation state of oxygen atom are, respectively :

(1) Oxide and −2

(2) Superoxide and −1/2

(3) Peroxide and −1/2

(4) Superoxide and −1

44. The number of P−O bonds in P_{4}O_{6} is :

(1) 6

(2) 9

(3) 12

(4) 18

45. Lithium aluminium hydride reacts with silicon tetrachloride to form :

(1) LiCl, AlH_{3} and SiH_{4}

(2) LiCl, AlCl_{3} and SiH_{4}

(3) LiH, AlCl_{3} and SiCl_{2}

(4) LiH, AlH_{3} and SiH_{4}

46. The correct order of spin-only magnetic moments among the following is :

(Atomic number : Mn=25, Co=27, Ni=28, Zn=30)

(1) [ZnCl_{4}]^{2−} > [NiCl_{4}]^{2−} > [CoCl_{4}]^{2−} > [MnCl_{4}]^{2−}

(2) [CoCl_{4}]^{2−} > [MnCl_{4}]^{2−} > [NiCl_{4}]^{2−} > [ZnCl_{4}]^{2−}

(3) [NiCl_{4}]^{2−} > [CoCl_{4}]^{2−} > [MnCl_{4}]^{2−} > [ZnCl_{4}]^{2−}

(4) [MnCl_{4}]^{2−} > [CoCl_{4}]^{2−} > [NiCl_{4}]^{2−} > [ZnCl_{4}]^{2−}

47. The correct order of electron affinity is :

(1) F > Cl > O

(2) F > O > Cl

(3) Cl > F > O

(4) O > F > Cl

48. In XeO_{3}F_{2}, the number of bond pair(s), π-bond(s) and lone pair(s) on Xe atom respectively are :

(1) 5, 2, 0

(2) 4, 2, 2

(3) 5, 3, 0

(4) 4, 4, 0

49. In the leaching method, bauxite ore is digested with a concentrated solution of NaOH that produces ‘X’. When CO_{2} gas is passed through the aqueous solution of ‘X’, a hydrated compound ‘Y’ is precipitated. ‘X’ and ‘Y’ respectively are :

(1) NaAlO_{2} and Al_{2}(CO_{3})_{3}⋅ x H_{2}O

(2) Al(OH)_{3} and Al_{2}O_{3}⋅ x H_{2}O

(3) Na[Al(OH)_{4}] and Al_{2}O_{3}⋅ x H_{2}O

(4) Na[Al(OH)_{4}] and Al_{2}(CO_{3})_{3}⋅ x H_{2}O

50. The total number of possible isomers for square-planar [Pt(Cl)(NO_{2})(NO_{3})(SCN)]^{2−} is :

(1) 8

(2) 12

(3) 16

(4) 24

51. Two compounds I and II are eluted by column chromatography (adsorption of I > II). Which one of following is a correct statement ?

(1) I moves faster and has higher R_{f} value than II

(2) II moves faster and has higher R_{f} value than I

(3) I moves slower and has higher R_{f} value than II

(4) II moves slower and has higher R_{f} value than I

52. Which of the following statements is not true ?

(1) Step growth polymerisation requires a bifunctional monomer.

(2) Nylon 6 is an example of step growth polymerisation.

(3) Chain growth polymerization includes both homopolymerisation and copolymerisation.

(4) Chain growth polymerization involves homopolymerisation only.

53. When 2-butyne is treated with H_{2}/ Lindlar’s catalyst, compound X is produced as the major product and when treated with Na/liq. NH_{3} it produces Y as the major product. Which of the following statements is correct ?

(1) X will have higher dipole moment and higher boiling point than Y.

(2) Y will have higher dipole moment and higher boiling point than X.

(3) X will have lower dipole moment and lower boiling point than Y.

(4) Y will have higher dipole moment and lower boiling point than X.

54. The increasing order of the acidity of the following carboxylic acids is :

(1) I < III < II < IV

(2) IV < II < III < I

(3) II < IV < III < I

(4) III < II < IV < I

55. The major product formed in the following reaction is :

(1)

(2)

(3)

(4)

56. On treatment of the following compound with a strong acid, the most susceptible site for bond cleavage is :

(1) C1 – O2

(2) O2 – C3

(3) C4 – O5

(4) O5 – C6

57. The increasing order of diazotisation of the following compounds is :

(1) (a) < (b) < (c) < (d)

(2) (a) < (d) < (b) < (c)

(3) (a) < (d) < (c) < (b)

(4) (d) < (c) < (b) < (a)

58. The dipeptide, Gln-Gly, on treatment with CH_{3}COCl followed by aqueous work up gives :

(1)

(2)

(3)

(4)

59. The total number of optically active compounds formed in the following reaction is :

(1) Two

(2) Four

(3) Six

(4) Zero

60. The major product formed in the following reaction is :

(1)

(2)

(3)

(4)

61. Let f : A → B be a function defined as where A = R – {2} and B R – {1}. Then f is :

(1) invertible and

(2) invertible and

(3) invertible and

(4) not invertible

62. If f (x) is a quadratic expression such that f (1)+f (2)=0, and −1 is a root of f (x)=0, then the other root of f (x)=0 is :

(1) −5/8

(2) −8/5

(3) 5/8

(4) 8/5

63. If |z – 3 + 2i| ≤ 4 then the difference between the greatest value and the least value of |z| is :

(1) 2√13

(2) 8

(3) 4 + √13

(4) √13

64. Suppose A is any 3×3 non-singular matrix and (A − 3I) (A − 5I) = O, where I = I_{3} and O = O_{3}. If αA + βA^{−1 }= 4I, then α + β is equal to :

(1) 8

(2) 7

(3) 13

(4) 12

65. If the system of linear equations

x + ay + z = 3

x + 2y + 2z = 6

x + 5y + 3z = b

has no solution, then :

(1) a=−1, b=9

(2) a=−1, b ≠ 9

(3) a ≠−1, b=9

(4) a=1, b ≠ 9

66. The number of four letter words that can be formed using the letters of the word **BARRACK** is :

(1) 120

(2) 144

(3) 264

(4) 270

67. The coefficient of x^{10} in the expansion of (1+x)^{2}(1+x^{2})^{3}(1+x^{3})^{4} is equal to :

(1) 52

(2) 56

(3) 50

(4) 44

68. If a, b, c are in A.P. and a^{2}, b^{2}, c^{2} are in G.P. such that a < b < c and then the value of a is :

(1)

(2)

(3)

(4)

69. Let and B_{n} = 1 – A_{n}. Then, the least odd natural number p, so that B_{n} > A_{n}, for all n ≥ p, is :

(1) 9

(2) 7

(3) 11

(4) 5

70.

(1) 1/4

(2) 1

(3) 1/2

(4) −1/2

71. Let

The value of k for which f is continuous at x = 2 is :

(1) 1

(2) e

(3) e^{−}^{1}

(4) e^{−}^{2}

72. If equals :

(1) −√3 log_{e} √3

(2) √3 log_{e} √3

(3) −√3 log_{e} 3

(4) √3 log_{e} 3

73. Let f (x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2.

If then f(−1) is equal to :

(1) 9/2

(2) 5/2

(3) 3/2

(4) 1/2

74. If

(where C is a constant of integration), then the ordered pair (A, B) is equal to :

(1) (2, 1)

(2) (−2, −1)

(3) (−2, 1)

(4) (2, −1)

75. The value of integral is :

(1)

(2)

(3)

(4)

76. If

(1) I_{2} > I_{3} > I_{1}

(2) I_{2} > I_{1} > I_{3}

(3) I_{3} > I_{2} > I_{1}

(4) I_{3} > I_{1} > I_{2}

77. The curve satisfying the differential equation, (x^{2 }− y^{2})dx+2xydy=0 and passing through the point (1, 1) is :

(1) a circle of radius one.

(2) a hyperbola.

(3) an ellipse.

(4) a circle of radius two.

78. The sides of a rhombus ABCD are parallel to the lines, x−y+2=0 and 7x−y+3=0. If the diagonals of the rhombus intersect at P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the ordinate of A is :

(1) 5/2

(2) 7/4

(3) 2

(4) 7/2

79. The foot of the perpendicular drawn from the origin, on the line, 3x+y=λ(λ ≠ 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is :

(1) 1 : 3

(2) 3 : 1

(3) 1 : 9

(4) 9 : 1

80. The tangent to the circle C_{1} : x^{2}+y^{2 }− 2x−1=0 at the point (2, 1) cuts off a chord of length 4 from a circle C_{2} whose centre is (3, −2). The radius of C_{2} is :

(1) 2

(2) √2

(3) 3

(4) √6

81. Tangents drawn from the point (−8, 0) to the parabola y^{2} = 8x touch the parabola at P and Q. If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :

(1) 4x^{2} + 9y^{2} = 121

(2) 9x^{2} + 4y^{2} = 169

(3) 4x^{2} – 9y^{2} = 121

(4) 9x^{2} – 4y^{2} = 169

82. A normal to the hyperbola, 4x^{2} − 9y^{2} = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram OABP (O being the origin) is formed, then the locus of P is :

(1) 4x^{2} + 9y^{2} = 121

(2) 9x^{2} + 4y^{2} = 169

(3) 4x^{2} – 9y^{2} = 121

(4) 9x^{2} – 4y^{2} = 169

83. An angle between the lines whose direction cosines are given by the equations, *l* + 3m + 5n = 0 and 5*l*m −2mn + 6n*l *= 0, is :

(1) cos^{−}^{1} (1/3)

(2) cos^{−}^{1} (1/4)

(3) cos^{−}^{1} (1/6)

(4) cos^{−}^{1} (1/8)

84. A plane bisects the line segment joining the points (1, 2, 3) and (−3, 4, 5) at right angles. Then this plane also passes through the point :

(1) (−3, 2, 1)

(2) (3, 2, 1)

(3) (−1, 2, 3)

(4) (1, 2, −3)

85. If the position vectors of the vertices A, B and C of a ∆ABC are respectively and then the position vector of the point, where the bisector of ∠A meets BC is :

(1)

(2)

(3)

(4)

86. A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ‘p’ is :

(1) 1/5

(2) 1/3

(3) 2/5

(4) 1/4

87. If the mean of the data : 7, 8, 9, 7, 8, 7, λ, 8 is 8, then the variance of this data is :

(1) 7/8

(2) 1

(3) 9/8

(4) 2

88. The number of solutions of sin 3x=cos 2x, in the interval (π/2, π) is :

(1) 1

(2) 2

(3) 3

(4) 4

89. A tower T_{1} of height 60 m is located exactly opposite to a tower T_{2} of height 80 m on a straight road. From the top of T_{1}, if the angle of depression of the foot of T_{2} is twice the angle of elevation of the top of T_{2}, then the width (in m) of the road between the feet of the towers T_{1} and T_{2} is :

(1) 10√2

(2) 10√3

(3) 20√3

(4) 20√2

90. Consider the following two statements :

**Statement p :**

The value of sin 120° can be derived by taking θ = 240° in the equation

**Statement q :**

The angles A, B, C and D of any quadrilateral ABCD satisfy the equation

Then the truth values of p and q are respectively :

(1) F, T

(2) T, F

(3) T, T

(4) F, F

**JEE Main Online Computer Based Test (CBT) Examination Held on 15-04-2018**

**PHYSICS**

1. In a common emitter configuration with suitable bias, it is given that R_{L} is the load resistance and R_{BE} is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by :

β is current gain, I_{B}, I_{C} and I_{E} are respectively base, collector and emitter currents.

(1)

(2)

(3)

(4)

2. A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, whose densities are ρ_{1} and ρ_{2} (ρ_{1} > ρ_{2}), fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is :

(1)

(2)

(3)

(4)

3.

In a meter bridge, as shown in the figure, it is given that resistance Y = 12.5 Ω and that the balance is obtained at a distance 39.5 cm from end A (by Jockey J). After interchanging the resistances X and , a new balance point is found at a distance *l*_{2} from end A. What are the values of X and *l*_{2}?

(1) 19.15 Ω and 39.5 cm

(2) 8.16 Ω and 60.5 cm

(3) 19.15 Ω and 60.5 cm

(4) 8.16 Ω and 39.5 cm

4. An automobile, travelling 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding) :

(1) 160 m

(2) 75 m

(3) 150 m

(4) 100 m

5. A given object takes n times more time to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth 45° The coefficient of kinetic friction between the object and the incline is :

(1)

(2)

(3)

(4)

6. A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at x = 0, with an amplitude A. An electric field E is applied along the x-direction. Which of the following statements is **correct**?

(1) The new equilibrium position is at a distance

(2) The total energy of the system is

(3) The total energy of the system is

(4) The new equilibrium position is at a distance

7. The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is :

(1)

(2) α

(3)

(4)

8. A monochromatic beam of light has a frequency and is propagating along the direction It is polarized along thedirection. The acceptable form for the magnetic field is :

(1)

(2)

(3)

(4)

9. The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is :

(1) 109 eV

(2) 34 eV

(3) 79 eV

(4) 20 eV

10. An ideal capacitor of capacitance 0.2 μF is charged to a potential difference of 10 V. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance 0.5 mH. The current at a time when the potential difference across the capacitor is 5 V, is :

(1) 0.34 A

(2) 0.17 A

(3) 0.25 A

(4) 0.15 A

11. A Carnot’s engine works as a refrigerator between 250 K and 300 K. It receives 500 cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :

(1) 420 J

(2) 2520 J

(3) 772 J

(4) 2100 J

12. A planoconvex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.

If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length 10 cm. The refractive index of the material of lens is :

(1) 1.75

(2) 1.50

(3) 1.55

(4) 1.51

13. Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are λ_{1} and λ_{2}, their de Broglie wavelength in the frame of reference attached to their centre of mass is :

(1)

(2)

(3) λ_{CM} = λ_{1} = λ_{2}

(4)

14. Take the mean distance of the moon and the sun from the earth to be 0.4 × 10^{6} km and 150 × 10^{6} km respectively. Their masses are 8 × 10^{22} kg and 2 × 10^{30} kg respectively. The radius of the earth is 6400 km. Let ∆F_{1} be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ∆F_{2} be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to is :

(1) 10^{−}^{2}

(2) 2

(3) 0.6

(4) 6

15. The equivalent capacitance between A and B in the circuit given below, is :

(1) 3.6 μF

(2) 4.9 μF

(3) 5.4 μF

(4) 2.4 μF

16. Light of wavelength 550 nm falls normally on a slit of width 22.0 × 10^{−}^{5} The angular position of the second minima from the central maximum will be (in radians) :

(1) π/6

(2) π/4

(3) π/8

(4) π/12

17. A tuning fork vibrates with frequency 256 Hz and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is 340 ms^{−}^{1})

(1) 190 cm

(2) 200 cm

(3) 220 cm

(4) 180 cm

18. A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R/2, and the other mass, in a circular orbit of radius 3R/2. The difference between the final and initial total energies is :

(1)

(2)

(3)

(4)

19. In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is :

(1) 0.3150 cm

(2) 0.4300 cm

(3) 0.2150 cm

(4) 0.0430 cm

20. A solution containing active cobalt having activity of 0.8 μCi and decay constant λ is injected in an animal’s body. If 1 cm^{3} of blood is drawn from the animal’s body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? (1 Ci = 3.7 × 10^{10} decays per second and at t = 10 hrs e^{−λ}^{t} = 0.84)

(1) 6 liters

(2) 5 liters

(3) 7 liters

(4) 4 liters

21. In the given circuit all resistances are of value R ohm each. The equivalent resistance between A and B is :

(1) 3R

(2) 2R

(3) 5R/3

(4) 5R/2

22. The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively.

(1) 225.5 m and 10 s

(2) 112.5 m and 15 s

(3) 112.5 and 22.5 s

(4) 337.5 m and 25s

23.

A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m, x) values is recorded. The appropriate variables that give a straight line, when plotted, are :

(1) m, 1/x

(2) m, x^{2}

(3) m, x

(4) m, 1/x^{2}

24. The number of amplitude modulated broadcast stations that can be accommodated in a 300 kHz band width for the highest modulating frequency 15 kHz will be :

(1) 8

(2) 15

(3) 10

(4) 20

25. A charge Q is placed at a distance a/2 above the centre of the square surface of edge as as shown in the figure

The electric flux through the square surface is :

(1) Q/ϵ_{0}

(2) Q/6ϵ_{0}

(3) Q/2ϵ_{0}

(4) Q/3ϵ_{0}

26. A Helmholtz coil has a pair of loops, each with N turns and radius R. They are placed coaxially at distance R and the same current I flows through the loops in the same direction. The magnitude of magnetic field at P, midway between the centres A and C, is given by [Refer to figure given below] :

(1)

(2)

(3)

(4)

27. A particle is oscillating on the X-axis with an amplitude 2 cm about the point x_{0} = 10 cm, with a frequency ω. A concave mirror of focal length 5 cm is placed at the origin (see figure).

Identify the **correct **statements.

(A) The image executes periodic motion.

(B) The image executes non-periodic motion.

(C) The turning points of the image are asymmetric w.r.t. the image of the point at x = 10 cm.

(D) The distance between the turning points of the oscillation of the image is

(1) (B), (D)

(2) (B), (C)

(3) (A), (D)

(4) (A), (C), (D)

28. One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double pressure at room temperature, 27° The work done on the gas will be :

(1) 300 R ln 7

(2) 300 R ln 2

(3) 300 R

(4) 300 R ln 6

29. The B-H curve for a ferromagnet is sown in the figure. The ferromagnet is placed inside a long solenoid with 1000 turns/ cm. The current that should be passed in the solenoid to demagnetize the ferromagnet completely is :

(1) 20 μA

(2) 40 μA

(3) 2 mA

(4) 1 mA

30. A force of 40 N acts on a point B at the end of an L-shaped object, as shown in the figure. The angle θ that will produce maximum moment of the force about point A is given by :

(1) tan θ = 2

(2) tan θ = 4

(3) tan θ = 1/2

(4) tan θ = 1/4

1. Which of the following statements about colloids is **False**?

(1) When excess of electrolyte is added to colloidal solution, colloidal particle will be precipitated.

(2) Colloidal particles can pass through ordinary filter paper.

(3) When silver nitrate solution is added to potassium iodide solution, a negatively charged colloidal solution is formed.

(4) Freezing pint of colloidal solution is lower than true solution at same concentration of a solute.

2. Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying 0.5 V when the radiation of 250 nm is used. The work function of the metal is :

(1) 4.5 eV

(2) 5 eV

(3) 5.5 eV

(4) 4 eV

3. In which of the following reactions, an increase in the volume of the container will favour the formation of products?

(1) 2NO_{2}(g) ⇌ 2NO(g) + O_{2}(g)

(2) 4NH_{3}(g) + 5O_{2}(g) ⇌ 4NO(g) + 6H_{2}O(l)

(3) 3O_{2}(g) ⇌ 2O_{3}(g)

(4) H_{2}(g) + I_{2}(g) ⇌ 2HI(g)

4. When an electric current is passed through acidified water, 112 mL of hydrogen gas at N.T.P. was collected at the cathode in 965 seconds. The current passed, in ampere, is :

(1) 0.5

(2) 0.1

(3) 1.0

(4) 2.0

5.

6. The decreasing order of bond angles in BF_{3}, NH_{3}, PF_{3} and I_{3}^{−} is :

(1) I_{3}^{−} > NH_{3} > PF_{3} > BF_{3}

(2) BF_{3} > I_{3}^{−} > PF_{3} > NH_{3}

(3) BF_{3} > NH_{3} > PF_{3} > I_{3}^{−}

(4) I_{3}^{−} > BF_{3} > NH_{3} > PF_{3}

7. In graphite and diamond, the percentage of p-characters of the hybrid orbitals in hybridization are respectively :

(1) 33 and 25

(2) 33 and 75

(3) 67 and 75

(4) 50 and 75

8. A sample of NaClO_{3} is converted by heat to NaCl with a loss of 0.16 g of oxygen. The residue is dissolved in water and precipitated as AgCl. The mass of AgCl (in g) obtained will be : (Given : Molar mass of AgCl = 143.5 g mol^{−}^{1})

(1) 0.54

(2) 0.41

(3) 0.48

(4) 0.35

9. N_{2}O_{5} decomposes to NO_{2} and O_{2} and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from 50 mmHg to 8.75 mmHg. The pressure of the gaseous mixture after 100 minute at constant temperature will be :

(1) 116.25 mmHg

(2) 106.25 mmHg

(3) 136.25 mmHg

(4) 175.0 mmHg

10. Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance?

(1)

(2)

(3)

(4)

11. The IUPAC name of the following compound is :

(1) 3-ethyl-4-methylhex-4-ene

(2) 4, 4-dithyl-3-methylbut-2-ene

(3) 4-methyl-3-ethylhex-4-ene

(4) 4-ethyl-3-methylhex-2-ene

12. For which of the following reactions, ∆H is equal to ∆U?

(1) 2HI(g) → H_{2}(g) + I_{2}(g)

(2) 2NO_{2}(g) → N_{2}O_{4} (g)

(3) N_{2}(g) + 3H_{2}(g) → 2NH_{3}(g)

(4) 2SO_{2}(g) + O_{2}(g) → 2SO_{3}(g)

13. For Na^{+}, Mg^{2+}, F^{−} and O^{2}^{−} ; the correct order of increasing ionic radii is :

(1) Na^{+} < Mg^{2+} < F^{−} < O^{2}^{−}

(2) Mg^{2+} < O^{2}^{−} < Na^{+} < F^{−}

(3) Mg^{2+} < Na^{+} < F^{−} < O^{2}^{−}

(4) O^{2}^{−} < F^{−} < Na^{+} < Mg^{2+}

14. The minimum volume of water required to dissolve 0.1 g lead (II) chloride to get a saturated solution (K_{sp} of PbCl_{2} = 3.2 × 10^{−}^{8}; atomic mass of Pb = 207 u) is :

(1) 17.98 L

(2) 0.18 L

(3) 1.798 L

(4) 0.36 L

15. An ideal gas undergoes a cyclic process a show in Figure.

∆U_{BC} = −5 kJ mol^{−}^{1}, q_{AB} = 2 kJ mol^{−}^{1}

W_{AB} = −5 kJ mol^{−}^{1}, W_{CA} = 3 kJ mol^{−}^{1}

Heat absorbed by the system during process CA is :

(1) −5 kJ mol^{−}^{1}

(2) +5 kJ mol^{−}^{1}

(3) −18 kJ mol^{−}^{1}

(4) 18 kJ mol^{−}^{1}

16. The main reduction product of the following compound with NaBH_{4} in methanol is :

(1)

(2)

(3)

(4)

17. Which of the following will most readily give the dehydrohalogenation product?

(1)

(2)

(3)

(4)

18. The correct combination is :

(1) [NiCl_{4}]^{2}^{−} −square-planar ; [Ni(CN)_{4}]^{ 2}^{−} −paramagnetic

(2) [NiCl_{4}]^{ 2}^{−} − diamagnetic; [Ni(CO)_{4}] −square-planar

(3) [NiCl_{4}]^{ 2}^{−} − tetrahedral; [Ni(CO)_{4}] –paramagnetic

(4) [NiCl_{4}]^{ 2}^{−} − paramagnetic; [Ni(CO)_{4}] –tetrahedral

19. Which of the following is a Lewis acid?

(1) B(CH_{3})_{3}

(2) PH_{3}

(3) NF_{3}

(4) NaH

20. The copolymer formed by addition polymerization of styrene and acrylonitrile in the presence of peroxide is

(1)

(2)

(3)

(4)

21. The major product of the following reaction is :

(1)

(2)

(3)

(4)

22. Xenon hexafluoride on partial hydrolysis produces compounds ‘X’ and ‘Y’ Compounds ‘X’ and ‘Y’ and the oxidation state of Xe are respectively :

(1) XeOF_{4} (+6) and XeO_{3} (+6)

(2) XeOF_{4} (+6) and XeO_{2}F_{2 }(+6)

(3) XeO_{2}F_{2 }(+6) and XeO_{2 }(+4)

(4) XeO_{2 }(+4) and XeO_{3 }(+6)

23. The correct match between times of **List-I** and **List-II** is :

(1) (A)-(R), (B)-(P), (C)-(S), (D)-(Q)

(2) (A)-(R), (B)-(P), (C)-(Q), (D)-(S)

(3) (A)-(P), (B)-(S), (C)-(R), (D)-(Q)

(4) (A)-(R), (B)-(S), (C)-(P), (D)-(Q)

24. A white sodium salt dissolves readily in water to give a solution which is neutral to litmus. When silver nitrate solution is added to the aforementioned solution, a white precipitate is obtained which does not dissolve in dil. nitric acid. The anion is :

(1) SO_{4}^{2}^{−}

(2) CO_{3}^{2}^{−}

(3) Cl^{−}

(4) S^{2}^{−}

25. In the molecular orbital diagram for the molecular ion, N_{2}^{+}, the number of electrons in the σ_{2p} molecular orbital is :

(1) 2

(2) 1

(3) 0

(4) 3

26. The reagent (s) required for the following conversion are :

(1) (i) B_{2}H_{6} (ii) SnCl_{2}/HCl (iii) H_{3}O^{+}

(2) (i) B_{2}H_{6} (ii) DIBAL-H (iii) H_{3}O^{+}

(3) (i) LiAlH_{4} (ii) H_{3}O^{+}

(4) (i) NaBH_{4} (ii) Raney Ni/H_{2} (iii) H_{3}O^{+}

27. Which of the following is the correct structure of Adenosine?

(1)

(2)

(3)

(4)

28. Identify the pair in which the geometry of the species is T-shape and square-pyramidal, respectively :

(1) IO_{3}^{−} and IO_{2}F_{2}^{−}

(2) XeOF_{2} and XeOF_{4}

(3) ICl_{2}^{−} and ICl_{5}

(4) ClF_{3} and IO_{4}^{−}

29. Which of the following will not exist in zwitter ionic from at pH = 7?

(1)

(2)

(3)

(4)

30. The increasing order of nitration of the following compounds is :

(1) (a) < (b) < (d) < (c)

(2) (b) < (a) < (d) < (c)

(3) (b) < (a) < (c) < (d)

(4) (a) < (b) < (c) < (d)

1. Consider the following two binary relations on the set A = {a, b, c} :

R_{1} = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and

R_{2} = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.

Then :

(1) R_{1} is not symmetric but it is transitive.

(2) both R_{1} and R_{2} are transitive.

(3) both R_{1} and R_{2} are not symmetric.

(4) R_{2} is symmetric but it is not transitive.

2. A box ‘A’ contains 2 white, 3 red and 2 black balls. Another box ‘B’ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ‘B’ is :

(1) 7/16

(2) 7/8

(3) 9/32

(4) 9/16

3. An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z – 1 = 0 and 5x + 8y + 2z + 14 = 0, is :

(1)

(2)

(3)

(4)

4. Two parabolas with a common vertex and with axes long x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

(1) x + 2y + 3 = 0

(2) 4(x + y) + 3 = 0

(3) 3(x + y) + 4 = 0

(4) 8(2x + y) + 3 = 0

5. If x_{1}, x_{2}, . . ., x_{n} and are two A.P.s such that x_{3} = h_{2} = 8 and x_{8} = h_{7} = 20, then x_{5}∙h_{10} equals :

(1) 3200

(2) 2560

(3) 2650

(4) 1600

6. If (P ⋀ ~q) ⋀ (p ⋀ r) → ~ p ⋁ q is false, then the truth values of p, q and r are, respectively :

(1) T, F, T

(2) F, F, F

(3) F, T, F

(4) T, T, T

7. Let S be the set of all real values of k for which the system of linear equations

x + y + z = 2

2x + y – z = 3

3x + 2y + kz = 4

has a unique solution. Then S is :

(1) an empty set

(2) equal to R – {0}

(3) equal to R

(4) equal to {0}

8. The area (i9n sq. units) of the region {x ϵ R : x ≥ 0, y ≥ 0, y ≥ x – 2 and y ≤ √x}, is :

(1) 13/3

(2) 10/3

(3) 5/3

(4) 8/3

9. If the tangents drawn to the hyperbola 4y^{2} = x^{2} + 1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is :

(1) x^{2} – 4y^{2} + 16x^{2}y^{2} = 0

(2) 4x^{2} – y^{2} – 16x^{2}y^{2} = 0

(3) 4x^{2} – y^{2} + 16x^{2}y^{2} = 0

(4) x^{2} – 4y^{2} – 16x^{2}y^{2} = 0

10. If β is one of the angles between the normals to the ellipse, x^{2} + 3y^{2} = 9 at the points (3 cos θ, √3 sinθ) and (−3 sin θ, √3 cos θ); then is equal to :

(1) √3/4

(2) 2/√3

(3) √2

(4) 1/√3

11. If are unit vectors such that is equal to :

(1) √15/4

(2) √15/16

(3) 15/16

(4) 1/4

12. n-digit numbers are formed suing only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :

(1) 9

(2) 6

(3) 7

(4) 8

13. If x^{2} + y^{2} + sin y = 4, then the value of at the point (−2, 0) is :

(1) −34

(2) −32

(3) 4

(4) −2

14. If tan A and tan B are the roots of the quadratic equation, 3x^{2} – 10x – 25 = 0, then the value of 3 sin^{2}(A + B) – 10 sin(A + B) ∙ cos(A + B) – 25 cos^{2}(A + B) is :

(1) 25

(2) 10

(3) −25

(4) −10

15. The value of the integral is :

(1)

(2) 3/4

(3)

(4) 0

16. The set of all α ϵ R, for which is a purely imaginary number, for all z ϵ C satisfying |z| = 1 and Re z ≠ 1 is :

(1) equal to R

(2) an empty set

(3) {0}

(4)

17. Let y = (x) be the solution of the differential equation where

If y (0) = 0, the is :

(1)

(2)

(3)

(4)

18. A variable plane passes through a fixed point (3, 2, 1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz-plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn parallel to xy-plane through C. Then the locus of the point of intersection of these three planes, is :

(1)

(2)

(3)

(4) x + y + z = 6

19. The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to :

(1) 4/3

(2) 1/3

(3) 2/3

(4) 10/3

20. Let S = {λ, μ) ϵ R × R : f(t) = (|λ| e^{|t|} − μ), sin (2|t|), t ϵ R, is a differentiable function}. Then S is a subset of :

(1) R × (−∞, 0)

(2) R × [0, ∞)

(3) [0, ∞) × R

(4) (−∞, 0) × R

21. If n is the degree of the polynomial, and m is the coefficient of x^{n} in it, then the ordered pair (n, m) is equal to :

(1) (12, (20)^{4})

(2) (8, 5(10)^{4})

(3) (24, (10)^{8})

(4) (12, 8(10)^{4})

22. An aeroplane flying at a constant speed, parallel to the horizontal ground, √3 km above it, is observed at an elevation of 60° from a point on the ground. If, after five seconds, its elevation from the same point, is 30°, then the speed (in km/hr) of the aeroplane, is :

(1) 750

(2) 1440

(3) 1500

(4) 720

23. If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

(1) [10, ∞)

(2) (−∞, −10]

(3) (−10, 0)

(4) (0, 10)

24. Let A be a matrix such that is a scalar matrix and |3A| = 108. Then A^{2} equals :

(1)

(2)

(3)

(4)

25. If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the the curved surface area (in cm^{2}) of this cone is :

(1) 8√3 π

(2) 8√2 π

(3) 6√2 π

(4) 6√3 π

26. If then

(1) does not exist.

(2) exists and is equal to 0.

(3) exists and is equal to 2.

(4) exists and is equal to −2.

27. If λ ϵ **R** is such that the sum of the cubes of the roots of the equation, x^{2} + (2 – λ)x + (10 – λ) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :

(1) 4√2

(2) 20

(3) 20√5

(4) 2√7

28. A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y – 4x + 3 = 0, then its radius is equal to :

(1) 2

(2) √2

(3) √5

(4) 1

29. In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4. Then area of ∆ABC (in sq. units) is :

(1) 12

(2) 4

(3) 5

(4) 9

30. If then ∫f(x) dx is equal to :

(where C is a constant of integration)

(1) 12 log_{e} |1 – x| − 3x + C

(2) −12 log_{e} |1 – x| + 3x + C

(3) −12 log_{e} |1 – x| − 3x + C

(4) 12 log_{e} |1 – x| + 3x + C

**JEE Main Offline Examination Held on 08-04-2018 Code A**

1. The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is

(1) 2.5%

(2) 3.5%

(3) 4.5%

(4) 6%

2. All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

(1)

(2)

(3)

(4)

3. Two masses m_{1}= 5 kg and m_{2}= 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m_{2} to stop the motion is

(1) 18.3 kg

(2) 27.3 kg

(3) 43.3 kg

(4) 10.3 kg

4. A particle is moving in a circular path of radius a under the action of an attractive potential Its total energy is

(1)

(2)

(3) Zero

(4)

5. In a collinear collision, a particle with an initial speed v_{0} strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is

(1)

(2)

(3)

(4)

6. Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is

(1)

(2)

(3)

(4)

7. From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is

(1) 4MR^{2}

(2)

(3) 10MR^{2}

(4)

8. A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then

(1) T ∝ R^{3/2 } for any n

(2)

(3) T ∝ R^{(n + 1)/2}

(4) T ∝ R^{n/2}

9. A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area of a floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, (dr/r), is

(1)

(2)

(3)

(4)

10. Two moles of an ideal monoatomic gas occupies a volume V at 27°C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

(1) (a) 189 K (b) 2.7 kJ

(2) (a) 1195 K (b) −2.7 kJ

(3) (a) 189 K (b) −2.7 kJ

(4) (a) 195 K (b) 2.7 kJ

11. The mass of a hydrogen molecule is 3.32 × 10^{−27} If 10^{23} hydrogen molecules strike, per second, a fixed wall of area 2 cm^{2} at an angle of 45° to the normal, and rebound elastically with a speed of 10^{3} m/s, then the pressure on the wall is nearly

(1) 2.34 × 10^{3} N/m^{2}

(2) 4.70 × 10^{3} N/m^{2}

(3) 2.35 × 10^{2} N/m^{2}

(4) 4.70 × 10^{2} N/m^{2}

12. A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 10^{12}/second. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagadro number = 6.02 × 10^{23} gm mole^{−1})

(1) 6.4 N/m

(2) 7.1 N/m

(3) 2.2 N/m

(4) 5.5 N/m

13. A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 10^{3} kg/m^{3} and its Young’s modulus is 9.27 × 10^{10} What will be the fundamental frequency of the longitudinal vibrations?

(1) 5 kHz

(2) 2.5 kHz

(3) 10 kHz

(4) 7.5 kHz

14. Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, −σ and + σ respectively. The potential of shell B is

(1)

(2)

(3)

(4)

15. A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be

(1) 1.2 nC

(2) 0.3 nC

(3) 2.4 nC

(4) 0.9 nC

16. In an a.c. circuit, the instantaneous e.m.f. and current are given by

e = 100 sin 30t

In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

(1) 50, 10

(2)

(3)

(4) 50, 0

17. Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 Ω. The internal resistances of the two batteries are 1 Ω and 2 Ω respectively. The voltage across the load lies between

(1) 11.6 V and 11.7 V

(2) 11.5 V and 11.6 V

(3) 11.4 V and 11.5 V

(4) 11.7 V and 11.8 V

18. An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_{e}, r_{p}, r_{α} respectively in a uniform magnetic field B. The relation between r_{e}, r_{p}, r_{α} is

(1) r_{e} > r_{p} = r_{α}

(2) r_{e} < r_{p} = r_{α}

(3) r_{e} < r_{p} < r_{α}

(4) r_{e} < r_{α} < r_{p}

19. The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B_{1}. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B_{2}. The ratio B_{1}/B_{2} is

(1) 2

(2)

(3)

(4)

20. For an RLC circuit driven with voltage of amplitude v_{m} and frequency the current exhibits resonance. The quality factor, Q is given by

(1)

(2)

(3)

(4)

21. An EM wave from air enters a medium. The electric fields are in air and in medium, where the wave number k and frequency ν refer to their values in air. The medium is non-magnetic. If refer to relative permittivities of air and medium respectively, which of the following options is correct?

(1)

(2)

(3)

(4)

22. Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is

(1) 0°

(2) 30°

(3) 45°

(4) 60°

23. The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 μm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance?

(i.e. distance between the centres of each slit.)

(1) 25 μm

(2) 50 μm

(3) 75 μm

(4) 100 μm

24. An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λ_{n}, λ_{g} be the de Broglie wavelength of the electron in then nth state and the ground state respectively. Let Λ_{n} be the wavelength of the emitted photo in the transition from the nth state to the ground state. For large n, (A, B are constants)

(1)

(2) Λ_{n} ≈ A + Bλ_{n}

(3)

(4)

25. If the series limit frequency of the Lyman series is ν_{L}, then the series limit frequency of the P fund series is

(1) 25 ν_{L}

(2) 16 ν_{L}

(3) ν_{L}/16

(4) ν_{L}/25

26. It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p_{d}; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p_{d} and p_{c} are respectively

(1) (.89, .28)

(2) (.28, .89)

(3) (0, 0)

(4) (0, 1)

27. The reading of the ammeter for a silicon diode in the given circuit is

(1) 0

(2) 15 mA

(3) 11.5 mA

(4) 13.5 mA

28. A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz?

(1) 2 × 10^{3}

(2) 2 × 10^{4}

(3) 2 × 10^{5}

(4) 2 × 10^{6}

29. In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5 Ω, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

(1) 1 Ω

(2) 1.5 Ω

(3) 2 Ω

(4) 2.5 Ω

30. On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 kΩ. How much was the resistance on the left slot before interchanging the resistances?

(1) 990 Ω

(2) 505 Ω

(3) 550 Ω

(4) 910 Ω

31. The ratio of mass percent of C and H of an organic compound (C_{X}H_{Y}O_{Z}) is 6 : 1. If one molecule of the above compound (C_{X}H_{Y}O_{Z}) contains half as much oxygen as required to burn one molecule of compound C_{X}H_{Y} completely CO_{2} and H_{2} The empirical formula of compound C_{X}H_{Y}O_{Z} is

(1) C_{3}H_{6}O_{3}

(2) C_{2}H_{4}O

(3) C_{3}H_{4}O_{2}

(4) C_{2}H_{4}O_{3}

32. Which type of ‘defect’ has the presence of cations in the interstitial sites?

(1) Schottky defect

(2) Vacancy defect

(3) Frenkel defect

(4) Metal deficiency defect

33. According to molecular orbital theory, which of the following will not be a viable molecule?

(1)

(2)

(3)

(4)

34. Which of the following lines correctly show the temperature dependence of equilibrium constant K, for an exothermic reaction?

(1) A and B

(2) B and C

(3) C and D

(4) A and D

35. The combustion of benzene (l) gives CO_{2} (g) and H_{2}O(I). Given that heat of combustion of benzene at constant volume is –3263.9 kJ mol^{−1} at 25°C; heat of combustion (in kJ mol^{−1}) of benzene at constant pressure will be

(R = 8.314 JK^{−1} mol^{−1})

(1) 4152.6

(2) −452.46

(3) 3260

(4) −3267.6

36. For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?

(1) [Co(H_{2}O)_{6}]Cl_{3}

(2) [Co(H_{2}O)_{5}Cl]Cl_{2} ∙ H_{2}O

(3) [Co(H_{2}O)_{4}Cl_{2}]Cl ∙ 2H_{2}O

(4) [Co(H_{2}O)_{3}Cl_{3}] ∙ 3H_{2}O

37. An aqueous solution contains 0.10 M H_{2}S and 0.20 M HCl. If the equilibrium constant for the formation of HS^{−} from H_{2}S is 1.0 × 10^{−7} and that of S^{2−} from HS^{−} ions is 1.2 × 10^{−13} then the concentration of S^{2−} ions in aqueous solution is

(1) 5 × 10^{−8}

(2) 3 × 10^{−20}

(3) 6 × 10^{−21}

(4) 5 × 10^{−19}

38. An aqueous solution contains an unknown concentration of Ba^{2+}. When 50 mL of a 1 M solution of Na_{2}SO_{4} is added, BaSO_{4} just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO_{4} is 1 × 10^{−10}. What is original concentration of Ba^{2+}?

(1) 5 × 10^{−9} M

(2) 2 × 10^{−9} M

(3) 1.1 × 10^{−9} M

(4) 1.0 × 10^{−10} M

39. At 518°C, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 torr, was 1.00 torr s^{−1} when 5% had reacted and 0.5 torr s^{−1} when 33% had reacted. The order of the reaction is

(1) 2

(2) 3

(3) 1

(4) 0

40. How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane? (Atomic weight of B = 10.8 u)

(1) 6.4 hours

(2) 0.8 hours

(3) 3.2 hours

(4) 1.6 hours

41. The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required to make teeth enamel harder by converting [3Ca_{3}(PO_{4})_{2} . Ca(OH)_{2}] to

(1) [CaF_{2}]

(2) [3(CaF_{2}). Ca(OH)_{2}]

(3) [3Ca_{3}(PO_{4})_{2}. CaF_{2}]

(4) [3{Ca(OH)_{2}}. CaF_{2}]

42. Which of the following compounds contain(s) no covalent bond(s)?

KCl, PH_{3}, O_{2}, B_{2}H_{6}, H_{2}SO_{4}

(1) KCl, B_{2}H_{6}, PH_{3}

(2) KCl_{2}, H_{2}SO_{4}

(3) KCl

(4) KCl, B_{2}H_{2}

43. Which of the following are Lewis acids?

(1) PH_{3} and BCl_{3}

(2) AlCl_{3} and SiCl_{4}

(3) PH_{3} and SiCl_{4}

(4) BCl_{3} and AlCl_{3}

44. Total number of lone pair of electron in ion is

(1) 3

(2) 6

(3) 9

(4) 12

45. Which of the following salts is the most basic in aqueous solution?

(1) Al(CN)_{3}

(2) CH_{3}COOK

(3) FeCl_{3}

(4) Pb(CH_{3}COO)_{2}

46. Hydrogen peroxide oxidises [Fe(CN)_{6}]^{4−} to [Fe(CN)_{6}]^{ 3−} in acidic medium but reduces [Fe(CN)_{6}]^{ 3−} to [Fe(CN)_{6}]^{ 4−} in alkaline medium. The other product formed are, respectively.

(1) (H_{2}O + O_{2}) and H_{2}O

(2) (H_{2}O + O_{2}) and (H_{2}O + OH^{–})

(3) H_{2}O and (H_{2}O + O_{2})

(4) H_{2}O and (H_{2}O + OH^{–})

47. The oxidation states of

Cr in [Cr(H_{2}O)_{6}]Cl_{3}, [Cr(C_{6}H_{6})_{2}], and K_{2}[Cr(CN)_{2}(O)_{2} (NH_{3})] respectively are

(1) +3 , +4 and +6

(2) +3, +2, and +4

(3) +3, 0and +6

(4) +3, 0 and +4

48. The compound that does not produce nitrogen gas by the thermal decomposition is

(1) Ba(N_{3})_{2}

(2) (NH_{4})_{2}Cr_{2}O_{7}

(3) NH_{4}NO_{2}

(4) (NH_{4})_{2}SO_{4}

49. When metal ‘M’ is treated with NaOH, a white gelatinous precipitate ‘X’ is obtained, which is soluble in excess of NaOH. Compound ‘X’ when heated strongly gives an oxide which is used in chromatography as an adsorbent. The metal ‘M’ is

(1) Zn

(2) Ca

(3) Al

(4) Fe

50. Consider the following reaction and statements

[Co(NH_{3})_{4}Br_{2}]^{+} + Br^{−} → [Co(NH_{3})_{3}Br_{3}] + NH_{3}

(I) Two isomers are produced if the reactant complex ion is a cis-isomer

(II) Two isomers are produced if the reactant complex ion is a trans-isomer.

(III) Only one isomer is produced if the reactant complex ion is a trans-isomer.

(IV) Only one isomer is produced if the reactant complex ion is a cis-isomer.

The correct statements are:

(1) (I) and (II)

(2) (I) and (III)

(3) (III) and (IV)

(4) (II) and (IV)

51. Glucose on prolonged heating with HI gives

(1) n-Hexane

(2) 1-Hexene

(3) Hexanoic acid

(4) 6-iodohexanal

52. The trans-alkenes are formed by the reduction of alkynes with

(1) H_{2} – Pd/C, BaSO_{4}

(2) NaBH_{4}

(3) Na/liq. NH_{3}

(4) Sn – HCl

53. Which of the following compounds will be suitable for Kjeldahl’s method for nitrogen estimation?

(1)

(2)

(3)

(4)

54. Phenol on treatment with CO_{2} in the presence of NaOH followed by acidification produces compound X as the major product. X on treatment with (CH_{3}CO)_{2}O in the presence of catalytic amount of H_{2}SO_{4} produces

(1)

(2)

(3)

(4)

55. An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination?

56. The predominant form of histamine present in human blood is (pK_{a}, Histidine = 6.0)

(1)

(2)

(3)

(4)

57. Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with Br_{2} to form product B. A and B are respectively

(1)

(2)

(3)

(4)

58. The increasing order of basicity of the following compound is

(1) (a) < (b) < (c) < (d)

(2) (b) < (a) < (c) < (d)

(3) (b) < (a) < (d) < (c)

(4) (d) < (b) < (a) < (c)

59. The major product formed in the following reaction is

(1)

(2)

(3)

(4)

60. The major product of the following reaction is

(1)

(2)

(3)

(4)

61. Two sets A and B are as under :

A = {(a, b) ∈ R × R : |a – 5| < 1 and |b – 5| < 1}

B = {(a, b) ∈ R × R : 4(a – 6)^{2} + 9(b – 5)^{2} ≤ 36},

then

(1) B ⊂ A

(2) A ⊂ B

(3) A ∩ B = ϕ (an empty set)

(4) Neither A ⊂ B nor B ⊂ A

62. Let S = {x ∈ R : x ≥ 0 and 2|√x – 3| + √x(√x – 6) + 6 = 0}. Then S :

(1) Is an empty set

(2) Contains exactly one element

(3) Contains exactly two elements

(4) Contains exactly four elements

63. If α, β ∈ C are the distinct roots, of the equation x^{2} – x + 1= 0, then α^{101} + β^{107} is equal to

(1) −1

(2) 0

(3) 1

(4) 2

64. If then the ordered pair (A, B) is equal to

(1) (−4, −5)

(2) (−4, 3)

(3) (−4, 5)

(4) (4, 5)

65. If the system of linear equations

x + ky + 3z = 0

3x + ky – 2z = 0

2x + 4y – 3z = 0

has a non-zero solution (x, y, z), then xz/y^{2} is equal to

(1) –10

(2) 10

(3) –30

(4) 30

66. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is

(1) At least 1000

(2) Less then 500

(3) At least 500 but less than 750

(4) At least 750 but less than 1000

67. The sum of the co-efficients of all odd degree terms in the expansion of is

(1) −1

(2) 0

(3) 1

(4) 2

68. Let a_{1}, a_{2}, a_{3}, …….., a_{49} be in A.P. such that

and a_{9} + a_{43} = 66.

If then m is equal to

(1) 66

(2) 68

(3) 34

(4) 33

69. Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1^{2} + 2.2^{2} + 3^{2} + 2.4^{2} + 5^{2} + 2.6^{2} + ….

If B – 2A = 100λ, then λ is equal to

(1) 232

(2) 248

(3) 464

(4) 496

70. For each t ∈ R, let [t] be the greatest integers less than or equal to t. Then

(1) Is equal to 0

(2) Is equal to 15

(3) Is equal to 120

(4) Does not exist (in R)

71. Let S = {t ∈ R : f(x) = |x – π| ∙(^{|x|} – 1)sin |x| is not differential at t}. Then the set S is equal to

(1) ϕ (an empty set)

(2) {0}

(3) {π}

(4) {0, π}

72. If the curves y^{2} = 6x, 9x^{2} + by^{2} = 16 intersect each other at right angles, then the value of b is

(1) 6

(2) 7/2

(3) 4

(4) 9/2

73. Let x ∈ R – {−1, 0, 1}. If then the local minimum value of h(X) is:

(1) 3

(2) −3

(3) −2√2

(4) 2√2

74. The integral is equal to

(1)

(2)

(3)

(4)

75. Then value of is :

(1) π/8

(2) π/2

(3) 4π

(4) π/4

76. Let g(x) = cos x^{2}, f(x) = √x, and α, β (α < β) be the roots of the quadratic equation 18x^{2} – 9πx + π^{2} = 0. Then the area (in sq. units) bounded by the curve y = (gof) (x) and the lines x = α, x = β and y = 0 is

(1)

(2)

(3)

(4)

77. Let y = y(x) be the solution of the differential equation x ∈ (0, π. If then y(π/6) is equal to :

(1)

(2)

(3)

(4)

78. A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

(1) 3x + 2y = 6

(2) 2x + 3y = xy

(3) 3x + 2y = xy

(4) 3x + 2y = 6xy

79. Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is

(1) √10

(2) 2√10

(3)

(4)

80. If the tangent at (1, 7) to the curve x^{2} = y – 6 touches the circle x^{2} + y^{2} + 16x + 12y + c = 0 then the value of c is

(1) 195

(2) 185

(3) 85

(4) 95

81. Tangent and normal are drawn at P(16, 16) on the parabola y^{2} = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then a value of tan θ is

(1) 1/2

(2) 2

(3) 3

(4) 4/3

82. Tangents are drawn to the hyperbola 4x^{2} – y^{2} = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of ∆PTQ is

(1) 45√5

(2) 54√3

(3) 60√3

(4) 36√5

83. If L_{1} is the the line of intersection of the planes 2x – 2y + 3z – 2 = 0, x – y + z + 1 = 0 and L_{2} is the line of intersection of the planes x + 2y – z – 3 = 0, 3x – y + 2z – 1 = 0, then the distance of the origin from the plane containing the lines L_{1} and L_{2}, is

(1)

(2)

(3)

(4)

84. The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7 is:

(1) 2/√3

(2) 2/3

(3) 1/3

(4)

85. Let be a vector coplanar with the vectors If is perpendicular to is equal to

(1) 336

(2) 315

(3) 256

(4) 84

86. A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

(1) 3/10

(2) 2/5

(3) 1/5

(4) 3/4

87. If then the standard deviation of the 9 items x_{1}, x_{2}, …. ., x_{9} is

(1) 9

(2) 4

(3) 2

(4) 3

88. If sum of all the solutions of the equation in [0, π] is kπ, then k is equal to :

(1) 2/3

(2) 13/9

(3) 8/9

(4) 20/9

89. PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45º, 30º and 30º, then the height of the tower (in m) is

(1) 100

(2) 50

(3) 100√3

(4) 50√2

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

(1) ~p

(2) p

(3) q

(4) ~q