# JEE Main 2014 Online Exam Question Paper

JEE Main 2014 Online Exam Question Paper

Physics

1. From a sphere of mass M and radius R, a smaller sphere of radius R/2 is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is :

(1)

(2)

(3)

(4)

2. A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3 m and that of kerosene 2 m. When the hole is opened the velocity of fluid coming out from it is nearly :

(take g = 10 ms−2 and density of water = 103 kg m−3)

(1)  7.6 ms1

(2)  10.7 ms1

(3)  8.5 ms1

(4)  9.6 ms1

3. The average mass of rain drops is 3.0 × 10−5 kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.

(1)  3.5 × 105 J

(2)  9.0 × 104 J

(3)  4.0 × 104 J

(4)  4.05 × 104 J

4. A body of mass 5 kg under the action of constant force  has velocity at t= 0s as  and at t = 10s as  The force  is :

(1)

(2)

(3)

(4)

5. An electromagnetic wave of frequency 1 × 104 hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ϵ0 = 8.8 × 10−12 C2/N-m2, then average energy density of electric field will be :

(1)  35.2 × 1010 J/m3

(2)  35.2 × 1011 J/m3

(3)  35.2 × 1013 J/m3

(4)  35.2 × 1012 J/m3

6. Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be :

(1)  8

(2)  4

(3)  10

(4)  2

7. Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is :

(1)  16/9

(2)  7/1

(3)  49/1

(4)  4/3

8. In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be :

(1)  150

(2)  200

(3)  100

(4)  400

9. A radioactive nuclei with decay constant 0.5/s being produced at constant rate of 100 nuclei/s. If at t = 0 there were no nuclei, the time when there are 50 nuclei is :

(1)  1 s

(2)

(3)

(4)  ln 2 s

10 A small ball of mass ms starts at a point A with speed v0 and moves along a frictionless track AB as shown. The track BC has coefficient of friction μ. The ball comes to stop at C after travelling a distance L which is :

(1)

(2)

(3)

(4)

11. In the circuit diagrams (A, B, C and D) shown below, R is a high resistance and S is a resistance of the order of galvanometer resistance G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as :

(1)

(2)

(3)  Circuit B with G = S

(4)  Circuit C with G = S

12. A parallel plate capacitor is made of two plates of length l, width w and separated by distance d. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force  where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x(see figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is :

(1)

(2)

(3)

(4)

13. In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively :

(1)  4.5 and 1

(2)  3.5 and 2

(3)  3 and 2.5

(4)  2.5 and 3

14. In terms of resistance R and time T, the dimensions of ratio μ/∈ of the permeability μ and permittivity ∈ is :

(1)  [R2]

(2)  [RT2]

(3)  [R2T2]

(4)  [R2T1]

15. An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section 8.0 × 10−3 m2. Initially the gas is at 300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed state as shown in figure. the gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring 800 N/m and the atmospheric pressure I s 1.0 × 105 N/m2. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :

(Neglect the heat los through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

(1)  300 K

(2)  500 K

(3)  800 K

(4)  1000 K

16. The Bulk moduli of Ethanol, Mercury and water are given as 0.9, 25 and 2.2 respectively in units of 109 Nm−2. For a given value of pressure, the fractional compression in volume is ∆V/V. Which of the following statements about ∆V/V of these three liquids is correct?

(1)  Water > Ethanol > Mercury

(2)  Ethanol > Water > Mercury

(3)  Mercury > Ethanol > Water

(4)  Ethanol > Mercury > Water

17. During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly :

(R = 8.3 JK−1 mol−1)

(1)  20 K

(2)  33 K

(3)  40 K

(4)  14 K

18. A coil of circular cross-section having 1000 turns and 4 cm2 face area is placed with its axis parallel to a magnetic field which decreases by 10−2 Wb m−2 in 0.01 s. The e.m.f. induced in the coil is :

(1)  4 mV

(2)  400 mV

(3)  200 mV

(4)  0.4 mV

19. An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 2. What is distance between the screen and the object ?

(1)  124.5 cm

(2)  65.0 cm

(3)  99.0 cm

(4)  144.5 cm

20. A cone of base radius R and height h is located in a uniform electric field parallel to its base. The electric flux entering the cone is :

(1)  4 E h R

(2)  2 E h R

(3)  E h R

(4)

21. An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density 103 kg/m3. The pressure inside the bubble is 1100 Nm−2 greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid ? (g =9.8 ms−2)

(1)  0.1 m

(2)  0.20 m

(3)  0.15 m

(4)  0.25 m

22. A thin bar of length L has a mass per unit length λ, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is λ0, then the distance of the centre of m ass from the lighter end is :

(1)

(2)

(3)

(4)

23. A photon of wavelength λ is scattered from an electron, which was at rest. the wavelength shift Δλ is three times of λ and the angle of scattering θ is 60°. The angle at which the electron recoiled is ϕ. The value of tan ϕ is : (electron speed is much smaller than the speed of light)

(1)  0.16

(2)  0.25

(3)  0.22

(4)  0.24

24. Match the List-I (Phenomenon associated with electromagnetic radiation) with List-II(Part of electromagnetic spectrum) and select the correct code from the choices given below the lists :

(1)  (I)-(B), (II)-(A), (III)-(D), (IV)-(A)

(2)  (I)-(A), (II)-(B), (III)-(C), (IV)-(C)

(3)  (I)-(A), (II)-(B), (III)-(B), (IV)-(C)

(4)  (I)-(D), (II)-(C), (III)-(A), (IV)-(B)

25. A hot body, obeying Newton’s law of cooling is cooling down from its peak value 80°C to an ambient temperature of 30°C. It takes 5 minutes in cooling down from 80°C to 40°C. How much time will it take to cool down from 62°C to 32°C ?

(Given ln 2 = 0.693, ln 5 = 1.609)

(1)  6.5 minutes

(2)  9.6 minutes

(3)  3.75 minutes

(4)  8.6 minutes

26. Three Identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around https://www.entranceindia.com/wp-content/uploads/2018/08/26.pngthem look as follows :

Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P) :

(1)  A↔P, B↔F, C↔D

(2)  A↔F, B↔D, C↔P

(3)  A↔F, B↔P, C↔D

(4)  A↔D, B↔P, C↔F

27. The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target ?

(1)  1.0 m

(2)  9.8 m

(3)  6.1 m

(4)  4.2 m

28. Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is :

(1)  9 × 104 N toward left

(2)  6 × 104 N toward left

(3)  Zero

(4)  3 × 104 N toward right

29. A Zener diode is connected to a battery and a load as shown below :

The currents I, IZ and IL are respectively

(1)  12.5 mA, 7.5 mA, 5 mA

(2)  15 mA, 5 mA, 10 mA

(3)  12.5 mA, 5 mA, 7.5 mA

(4)  15 mA, 7.5 mA, 7.5 mA

30. The angular frequency of the damped oscillator is given by,  where k I s the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio r2/mk is 8%, the change in time period compared to the undamped oscillator is approximately as follows :

(1)  increases by 1 %

(2)  increases by 8%

(3)  decreases by 8%

(4)  decreases by 1%

Chemistry

31. An organic compound A, C5H8O; reacts with H1O, NH3 and CH3COOH as described below :

(1)

(2)

(3)

(4)

32. In allene (C3H4), the type(s) of hybridization of the carbon atoms is (are) :

(1)  sp2 and sp

(2)  sp2 and sp3

(3)  only sp2

(4)  sp and sp3

33. For the reaction, 2N2O5 → 4NO2+ O2, the rate equation can be expressed in two ways  and k´ are related as :

(1)  k = k´

(2)  k = 4k´

(3)  k = 2k´

(4)  2k = k´

34. Tischenko reaction is a modification of :

(1)  Claisen condensation

(2)  Pinacol-pinacolon reaction

(3)  Cannizzaro reaction

(4)  Aldol condensation

35. The following reaction

is known as :

(1)  Gattermann reaction

(2)  Perkin reaction

(3)  Gattermann-Koch Formylation

(4)  Kolbe’s reaction

36. Shapes of certain interhalogen compounds are stated below. Which one of them is not correctly stated?

(1)  BrF5 : trigonal bipyramid

(2)  IF7 : pentagonal bipyramid

(3)  BrF3 : planar T – shaped

(4)  ICl3 : planar dimeric

37. The appearance of colour in solid alkali metal halides is generally due to :

(1)  Frenkel defect

(2)  Schottky defect

(3)  Interstitial position

(4)  F-centres

38. The correct order of bond dissociation energy among N2, O2, O2 is shown in which of the following arrangements?

(1)  O2 > O2 > N2

(2)  N2 > O2 > O2

(3)  N2 > O2 > O2

(4)  O2 > O2 > N2

39. Consider the coordination compound, [Co(NH3)6]Cl3. In the formation of this complex, the species which acts as the Lewis acid is :

(1)  Co3+

(2)  [Co(NH3)6]3+

(3)  NH3

(4)  Cl

40. Which of the following statements about the depletion of ozone layer is correct?

(1)  Oxides of nitrogen also do not react with ozone in stratosphere.

(2)  The problem of ozone depletion is more serious at poles because ice crystals in the clouds over poles act as catalyst for photochemical reactions involving the decomposition of ozone by Cl and ClO radicals.

(3)  The problem of ozone depletion is less serious at poles because NO2 solidifies and is not available for consuming ClO

(4)  Freons, chlorofluorocarbons, are inert chemically, they do not react with ozone in stratosphere.

41. Assuming that the degree of hydrolysis is mall, the pH of 0.1 M solution of sodium acetate (Ka = 1.0 × 10−5) will be :

(1)  9.0

(2)  8.0

(3)  5.0

(4)  6.0

42. The initial volume of a gas cylinder is 750.0 mL. If the pressure of gas inside the cylinder changes from 840.0 mm Hg to 360.0 mm Hg, the final volume the gas will be :

(1)  1.750 L

(2)  4.032 L

(3)  7.50 L

(4)  3.60 L

43. Which of the following statements about Na2O2 is not correct ?

(1)  It is diamagnetic in nature.

(2)  It is the super oxide of sodium.

(3)  Na2O2 Oxidizes Cr3+ and CrO42 in acid medium.

(4)  It is a derivative of H2O2

44. Based on the equation :

the wavelength of the light that must be absorbed to excite hydrogen electron from level

n = 1 to level n = 2 will be

(h = 6.625 × 10−34 Js, C = 3 × 108 ms−1)

(1)  1.325 × 1010 m

(2)  1.325 × 107 m

(3)  2.650 × 107 m

(4)  5.300 × 1010 m

45. Complete reduction of benzene-diazonium chloride with Zn/HCl gives :

(1)  Aniline

(2)  Hydrazobenzene

(3)  Azobenzene

(4)  Phenylhydrazine

46. A gaseous compound of nitrogen and hydrogen contains 12.5% (by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is

(1)  N3H

(2)  NH2

(3)  NH3

(4)  N2H4

47. The reagent needed for converting

is :

(1)  H2/Lindlar Cat.

(2)  Li/NH3

(3)  LiAlH4

(4)  Cat. Hydrogenation

48. In the reaction of formation of sulphur trioxide by contact process 2SO2+ O2 ⇌ 2SO3 the rate of reaction was measured as  The rate of reaction in terms of [SO2] in mol L−1 s−1 will be :

(1)  −2.50 × 104

(2)  −5.00 × 104

(3)  −1.25 × 104

(4)  −3.75 × 104

49. If λ0 and λ be the threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is :

(1)

(2)

(3)

(4)

50. Which of the following series correctly represents relations between the elements from X to Y?

51. The molar heat capacity (CP) of CD2O is 10 cals at 1000 K. The change in entropy associated with cooling of 32 g of CD2O vapour from 1000 K to 100 K at constant pressure will be :

(D = deuterium, at. mass = 2 u)

(1)  2.303 cal deg1

(2)  23.03 cal deg1

(3)  −2.303 cal deg1

(4)  −23.03 cal deg1

52. The gas liberated by the electrolysis of Dipotassium succinate solution is :

(1)  Ethyne

(2)  Ethane

(3)  Propene

(4)  Ethene

53. Which one of the following statements is not correct?

(1)  Acid strength of alcohols decreases in the following order RCH2OH > R2CHOH > R3COH

(2)  Alcohols are weaker acids than water

(3)  The bond angle  in methanol is 108.9°

(4)  Carbon-oxygen bond length in methanol, CH3OH is shorter than that of C – O bond length in phenol.

54. Given

Fe3+(aq) + e → Fe2+  (aq); E° = +0.77 V

Al3+(aq) + 3e → Al(s);  E° = −1.66 V

Br2(aq) + 2e → 2Br ; E° = +1.09 V

Considering the electrode potentials, which of the following represents the correct order of reducing power?

(1)  Al < Br < Fe2+

(2)  Fe2+ < Al < Br

(3)  Al < Fe2+ < Br

(4)  Br < Fe2+ < Al

55. Which of the following name formula combinations is not correct ?

56. Which one of the following does not have a pyramidal shape ?

(1)  P(SiH3)3

(2)  (SiH3)3N

(3)  P(CH3)3

(4)  (CH3)3N

57. Consider the following equilibrium

AgCl ↓ + 2NH3 ⇌ [Ag(NH3)2]++ Cl

White precipitate of AgCl appears on adding which of the following?

(1)  NH3

(2)  aqueous HNO3

(3)  aqueous NH4Cl

(4)  aqueous NaCl

58. In some solutions, the concentration of H3O+ remains constant even when small amounts of strong acid or strong base are added to them. These solutions are known as :

(1)  Ideal solutions

(2)  Colloidal solutions

(3)  True solutions

(4)  Buffer solutions

59. Which one of the following is used as Antihistamine ?

(1)  Chloranphenicol

(2)  Omeprazole

(3)  Norethindrone

(4)  Diphenhydramine

60. Chlorobenzene reacts with trichloro acetaldehyde in the presence of H2SO4

The major product formed is :

(1)

(2)

(3)

(4)

Mathematics

61. Let f be an odd function defined on the set of real numbers such that for x ≥ 0, f(x) = 3 sin x + 4 cos x.

(1)

(2)

(3)

(4)

62. Let P(3 sec θ, 2 tan θ) and Q(sec ϕ, 2 tan ϕ) where  be two distinct points on the hyperbola  Then the ordinate of the point of intersection of the normals at P and Q is :

(1)  13/2

(2)  −11/3

(3)  11/3

(4)  −13/2

63. The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is :

(1)

(2)

(3)

(4)

64. If for n ≥ 1, then P10 – 90P8 is equal to :

(1)  −9

(2)  10

(3)  10e

(4)  −9e

65. The proposition ~(p⋁~q) ⋁ ~(p⋁q) is logically equivalent to :

(1)  ~p

(2)  q

(3)  ~q

(4)  p

66. The coefficient of x50 in the binomial expansion of

(1+x)1000 + x(1 + x)999 + x2 (1 + x)998 + ….+x1000 is :

(1)

(2)

(3)

(4)

67. A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x ∈ A is :

(1)  1/2

(2)  63/128

(3)  64/127

(4)  31/128

68. If α and β are roots of the equation, x2 – 4√2 kx + 2e 4 ln k – 1 = 0 for some k, and α2 + β2 = 66, then α3 + β3 is equal to :

(1)  −280√2

(2)  248√2

(3)  280√2

(4)  −32√2

69. The integral  is equal to :

(1)  x – (1 + x2) tan1 x + c

(2)  −x + (1 + x2) cot1x + c

(3)  −x + (1 + x2)tan1 x + c

(4)  x – (1 + x2)cot1 x + c

70. Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr. while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr) :

(1)  80/37

(2)  80/√37

(3)  260/√37

(4)  260/37

71. A stair-case of length l rests against a vertical wall and a floor of a room,. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the stair-case begins to slide on the floor, then the locus of P is :

(1)

(2)

(3)

(4)

72. The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = √3 is :

(1)

(2)  4π

(3)

(4)  2π

73. Let A be a 3 × 3 matrix such that

Then A1 is:

(1)

(2)

(3)

(4)

74. Let L1 be the length of the common chord of the curves x2 + y2 = 9 and y2 = 8x, and L2 be the length of the latus rectum of y2 = 8x, then :

(1)  L1 > L2

(2)  L1 < L2

(3)

(4)  L1 = L2

75. If  then k is equal to :

(1)  2

(2)  0

(3)  3

(4)  1

76. The plane containing the line  and parallel to the line  passes through the point :

(1)  (−1, −3, 0)

(2)  (1, −2, 5)

(3)  (0, 3, −5)

(4)  (1, 0, 5)

77. The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be α. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to β. Then the height (in metres) of the tower is :

(1)

(2)

(3)

(4)

78. The set of all real values of λ for which exactly two common tangents can be drawn to the circles x2 + y2– 4x – 4y + 6 = 0 and x2 + y2 – 10x – 10y + λ = 0 is the interval :

(1)  (18, 42)

(2)  (12, 24)

(3)  (12, 32)

(4)  (18, 48)

79.

(1)  24

(2)  12

(3)  12√2

(4)  4√2

80. If  then 7 cos θ + 6 sin θ is equal to :

(1)  46/5

(2)  1/2

(3)  2

(4)  11/2

81. Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in x, pi ´(x) and pi ´´(x) be the first and second order derivatives of pi(x) respectively. Let,

and B(x) = [A(x)]T A(x). Then determinant of B(x) :

(1)  is a polynomial of degree 6 in x.

(2)  does not depend on x.

(3)  is a polynomial of degree 2 in x.

(4)  is a polynomial of degree 3 in x.

82. Let A(2, 3, 5), B(−1, 3, 2) and C (λ, 5, μ) be the vertices of a ΔABC. If the median through A is equally inclined to the coordinate axes, then :

(1)  10λ – 7μ = 0

(2)  5λ – 8μ = 0

(3)  8λ – 5μ = 0

(4)  7λ – 10μ = 0

83. For the curve y = 3 sin θ cos θ, x = eθ sin θ, 0 ≤ θ ≤ π, the tangent is parallel to x-axis when θ is :

(1)  π/6

(2)  3π/4

(3)  π/2

(4)  π/4

84. An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :

(1)  36 (7!)

(2)  18 (7!)

(3)  72 (7!)

(4)  40 (7!)

85. Let f(x) = x|x|, g(x) = sin x and h(x) = (gof)(x). Then

(1)  h´(x) is continuous at x = 0 but it is not differentiable at x = 0.

(2)  h´(x) is differentiable at x = 0.

(3)  h(x) is differentiable at x = 0, but h´(x) is not continuous at x = 0.

(4)  h(x) is not differentiable at x = 0.

86. In the general solution of the differentiable equation  for some function, Φ, is given by y ln|cx| = x, where c is an arbitrary constant, then Φ (2) is equal to :

(1)  −1/4

(2)  −4

(3)  4

(4)  1/4

87. The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + … and 1 + 6 + 11 + 16 + … , is :

(1)  4000

(2)  4020

(3)  4200

(4)  4220

88. In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is :

(1)  28

(2)  42

(3)  7

(4)  21

89. If z1, z2 and z3 , z4 are 2 pairs of complex conjugate numbers, then

(1)  0

(2)  π/2

(3)  π

(4)  3π/2

90. If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(x), the mean of variable X, is :

(1)  p/3

(2)  p/2

(3)  3 – p

(4)  2 – p