**JEE Main Offline Examination Held on 02-04-2017**

**Physics**

1. A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of

(1) 9

(2)

(3) 81

(4)

2. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

(1)

(2)

(3)

(4)

3. A body of mass m = 10^{−}^{2} kg is moving in a medium and experiences a frictional force F = −kv^{2}. Its initial speed is v_{0} = 10 ms^{−}^{1}. If, after 10 s, its energy is the value of k will be

(1) 10^{−}^{3} kg m^{−}^{1}

(2) 10^{−}^{3} kg s^{−}^{1}

(3) 10^{−}^{4} kg m^{−}^{1}

(4) 10^{−}^{1} kg m^{−}^{1} s^{−}^{1}

4. A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 second will be

(1) 4.5 J

(2) 22 J

(3) 9 J

(4) 18 J

5. The moment of inertia of a uniform cylinder of length ℓ and radius R about its perpendicular bisector is I. What is the ratio such that the moment of inertia is minimum ?

(1)

(2)

(3) 1

(4)

6. A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is

(1)

(2)

(3)

(4)

7. The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth’s radius) :

(1)

(2)

(3)

(4)

8. A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75°C. T is given by :

(Given : room temperature = 30°C, specific heat of copper = 0.1 cal/gm°C)

(1) 800℃

(2) 885℃

(3) 1250℃

(4) 825℃

9. An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by :

(1)

(2)

(3)

(4)

10. C_{p} and C_{v} are specific heats at constant pressure and constant volume respectively. It is observed that

C_{p} – C_{v} = a for hydrogen gas

C_{p} – C_{v} = b for nitrogen gas

The correct relation between a and b is :

(1)

(2) a = b

(3) a = 14b

(4) a = 28b

11. The temperature of an open room of volume 30 m^{3} increases from 17℃ to 27℃ due to the sunshine. The atmospheric pressure in the room remains 1 × 10^{5} If n_{i} and n_{f} are the number of molecules in the room before and after heating, then n_{f} – n_{i} will be

(1) −1.61 × 10^{23}

(2) 1.38 × 10^{23}

(3) 2.5 × 10^{25}

(4) −2.5 × 10^{25}

12. A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like :

(1)

(2)

(3)

(4)

13. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 × 108 ms^{–1})

(1) 10.1 GHz

(2) 12.1 GHz

(3) 17.3 GHz

(4) 15.3 GHz

14. An electric dipole has a fixed dipole moment which makes angle θ with respect x-axis. When subjected to an electric field it experiences a torque When subjected to another electric field it experiences a torque . The angle θ is

(1) 30°

(2) 45°

(3) 60°

(4) 90°

15. A capacitance of 2 μF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 μF capacitors are available which can withstand a potential difference of not more than 300 V.

The minimum number of capacitors required to achieve this is

(1) 2

(2) 16

(3) 24

(4) 32

16. In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :

(1) CE

(2)

(3)

(4)

17.

In the above circuit the current in each resistance is

(1) 1 A

(2) 0.25 A

(3) 0.5 A

(4) 0 A

18. A magnetic needle of magnetic moment 6.7 × 10^{−}^{2} Am^{2} and moment of inertia 7.5 × 10^{−}^{6} kg m^{2} is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillation is

(1) 6.65 s

(2) 8.89 s

(3) 6.98 s

(4) 8.76 s

19. When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0-10 V is

(1) 1.985 × 10^{3} Ω

(2) 2.045 × 10^{3} Ω

(3) 2.535 × 10^{3} Ω

(4) 4.005 × 10^{3} Ω

20. In a coil of resistance 100 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is

(1) 200 Wb

(2) 225 Wb

(3) 250 Wb

(4) 275 Wb

21. An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If λ_{min} is the smallest possible wavelength of X-ray in the spectrum, the variation of log λ_{min} with log V is correctly represented in

(1)

(2)

(3)

(4)

22. A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is

(1) Real and at a distance of 40 cm from convergent lens

(2) Virtual and at a distance of 40 cm from convergent lens

(3) Real and at a distance of 40 cm from the divergent lens

(4) Real and at a distance of 6 cm from the convergent lens

23. In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is

(1) 1.56 mm

(2) 7.8 mm

(3) 9.75 mm

(4) 15.6 mm

24. A particle A of mass m and initial velocity v collides with a particle B of mass which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λ_{A} to λ_{B} after the collision is

(1)

(2)

(3)

(4)

25. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = λ_{1}/λ_{2}, is given by

(1)

(2)

(3)

(4)

26. A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by

(1)

(2)

(3)

(4)

27. In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be

(1) 45°

(2) 90°

(3) 135°

(4) 180°

28. In amplitude modulation, sinusoidal carrier frequency used is denoted by ω_{c} and the signal frequency is denoted by ω The bandwidth (∆ω_{m}) of the signal is such that ∆ω_{m} << ω_{c}. Which of the following frequencies is not contained in the modulated wave ?

(1) ω_{m}

(2) ω_{c}

(3) ω_{m} + ω_{c}

(4) ω_{c} – ω_{m}

29. Which of the following statements is false?

(1) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude

(2) In a balanced Wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed

(3) A rheostat can be used as a potential divider

(4) Kirchhoff’s second law represents energy conservation

30. The following observations were taken for determining surface tension T of water by capillary method : diameter of capillary, D = 1.25 × 10^{−}^{2} m rise of water, h = 1.45 × 10^{−}^{2} m rise of water, h = 1.45 × 10^{−}^{2}

Using g = 9.80 m/s^{2} and the simplified relation the possible error in surface tension is closest to

(1) 0.15%

(2) 1.5%

(3) 2.4%

(4) 10%

**Chemistry**

31. Given

C_{(graphite)} + O_{2}(g) → CO_{2}(g);

∆_{r}H° = −393.5 kJ mol^{−}^{1}

∆_{r}H° = −285.8 kJ mol^{−}^{1}

CO_{2}(g) + 2H_{2}O(I) → CH_{4}(g) + 2O_{2}(g);

∆_{r}H° = +890.3 kJ mol^{−}^{1}

Base on the above thermochemical equations, the value of ∆_{r}H° at 298 K for the reaction

C_{(graphite)} + 2H_{2}(g) → CH_{4}(g) will be

(1) −74.8 kJ mol^{−}^{1}

(2) −144.0 kJ mol^{−}^{1}

(3) +74.8 kJ mol^{−}^{1}

(4) +144.0 kJ mol^{−}^{1}

32. 1 gram of a carbonate (M_{2}CO_{3}) on treatment with excess HCl produces 0.01186 mole of CO_{2}. The molar mass of M_{2}CO_{3} in g mol^{−}^{1} is

(1) 118.6

(2) 11.86

(3) 1186

(4) 84.3

34. The Tyndall effect is observed only when following conditions are satisfied

(a) The diameter of the dispersed particles is much smaller than the wavelength of the light used.

(b) The diameter of the dispersed particle is not much smaller than the wavelength of the light used

(c) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude

(d) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude

(1) (a) and (c)

(2) (b) and (c)

(3) (a) and (d)

(4) (b) and (d)

35. A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be

(1)

(2)

(3) 2a

(4)

36. Given

Among the following, the strongest reducing agent is

(1) Cr^{3+}

(2) Cl^{−}

(3) Cr

(4) Mn^{2+}

37. The freezing point of benzene decreases by 0.45ºC when 0.2 g of acetic acid is added to 20 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be

(K_{f} for benzene = 5.12 K kg mol^{−}^{1})

(1) 74.6%

(2) 94.6%

(3) 64.6%

(4) 80.4%

38. The radius of the second Bohr orbit of hydrogen atom is

(Planck’s Const. h = 6.6262 × 10^{−}^{34} Js;

mass of electron = 9.1091 × 10^{−}^{31} kg;

charge of electron e = 1.60210 × 10^{−}^{19} C;

permittivity of vacuum

ε_{0} = 8.854185 × 10^{−}^{12} kg^{−}^{1} m^{−}^{3} A^{2})

(1) 0.529 Å

(2) 2.12 Å

(3) 1.65 Å

(4) 4.76 Å

39. Two reactions, R_{1} and R_{2} have identical prexponential factors. Activation energy of R_{1} exceeds that of R_{2} by 10 kJ mol^{−}^{1}. If k_{1} and k_{2} are rate constants for reactions R_{1} and R_{2} respectively at 300 K, then ln(k_{2}/k_{1}) is equal to

(R = 8.314 J mole^{−}^{1} K^{−}^{1})

(1) 6

(2) 4

(3) 8

(4) 12

40. pK_{a} of a week acid (HA) and pK_{b} of a weak base (BOH) are 3.2 and 3.4, respectively, The pH of their salt (AB) solution is

(1) 7.0

(2) 1.0

(3) 7.2

(4) 6.9

41. Both lithium and magnesium display several similar properties due to the diagonal relationship, however, the one which is incorrect, is

(1) Both form nitrides

(2) Nitrates of both Li and Mg yield NO_{2} and O_{2} on heating

(3) Both form basic carbonates

(4) Both form soluble bicarbonates

42. Which of the following species is not paramagnetic ?

(1) O_{2}

(2) B_{2}

(3) NO

(4) CO

43. Which of the following reactions is an example of a redox reaction ?

(1) XeF_{6} + H_{2}O → XeOF_{4} + 2HF

(2) XeF_{6} + 2H_{2}O → XeO_{2}F_{2} + 4HF

(3) XeF_{4} + O_{2}F_{2} → XeF_{6} + O_{2}

(4) XeF_{2} + PF_{5} → [XeF]^{+} PF_{6}^{−}

44. A water sample has ppm level concentration of following anions

The anion/anions that make/makes the water sample unsuitable for drinking is/are

(1) Only F^{−}

(2)

(3)

(4)

45. The group having isoelectronic species is

(1) O^{2}^{−}, F^{−}, Na, Mg^{2+}

(2) O^{−}, F^{−}, Na^{+}, Mg^{2+}

(3) O^{2}^{−}, F^{−}, Na^{+}, Mg^{2+}

(4) O^{−}, F^{−}, Na, Mg^{+}

46. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are

(1) Cl^{−} and ClO^{−}

(2) Cl^{−} and ClO_{2}^{−}

(3) ClO^{−} and ClO_{3}^{−}

(4) ClO_{2}^{−} and ClO_{3}^{−}

47. In the following reactions, ZnO is respectively acting as a/an

(a) ZnO + Na_{2}O → Na_{2}ZnO_{2}

(b) ZnO + CO_{2} → ZnCO_{3}

(1) Acid and acid

(2) Acid and base

(3) Base and acid

(4) Base and base

48. Sodium salt of an organic acid ‘X’ produces effervescence with conc. H_{2}SO_{4}. ‘X’ reacts with the acidified aqueous CaCl_{2} solution to give a white precipitate which decolourises acidic solution of KMnO_{4}. ‘X’ is

(1) CH_{3}COONa

(2) Na_{2}C_{2}O_{4}

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

(4) HCOONa

49. The most abundant elements by mass in the body of a healthy human adult are :

Oxygen (61.4%); Carbon )22.9%); Hydrogen (10.0%) and Nitrogen (2.6%).

The weight which a 75 kg person would gain if all ^{1}H atoms are replaced by ^{2}H atoms is

(1) 7.5 kg

(2) 10 kg

(3) 15 kg

(4) 37.5 kg

50. On treatment of 100 mL of 0.01 M solution of CoCl_{3} ∙ 6H_{2}O with excess AgNO_{3}; 1.2 × 10^{22} ions are precipitated. The complex is

(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

51. Which of the following compounds will form significant amount of meta product during mono-nitration reaction ?

(1)

(2)

(3)

(4)

52. Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine?

(1)

(2)

(3)

(4)

53. The formation of which of the following polymers involves hydrolysis reaction?

(1) Nylon 6, 6

(2) Terylene

(3) Nylon 6

(4) Bakelite

54. Which of the following molecules is least resonance stabilized?

(1)

(2)

(3)

(4)

55. The increasing order of the reactivity of the following halides for the S_{N}1 reaction is

(1) (I) < (III) < (II)

(2) (II) < (III) < (I)

(3) (III) < (II) < (I)

(4) (II) < (I) < (III)

56. The major product obtained in the following reaction is

(1) (+)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}

(2) (−)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}

(3) (±)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}

(4) C_{6}H_{5}CH = CHC_{6}H_{5}

57. Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?

(1)

(2)

(3)

(4)

58. 3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is

(1) Two

(2) Four

(3) Six

(4) Zero

59. The correct sequence of reagents for the following conversion will be

(1) CH_{3}MgBr, [Ag(NH_{3})_{2}]^{+}OH^{−}, H^{+}/CH_{3}OH

(2) [Ag(NH_{3})_{2}]^{+}OH^{−}, CH_{3}MgBr, H^{+}/CH_{3}OH

(3) [Ag(NH_{3})_{2}]^{+}OH^{−}, H^{+}/CH_{3}OH, CH_{3}MgBr

(4) CH_{3}MgBr, H^{+}/CH_{3}OH, [Ag(NH_{3})_{2}]^{+}OH^{−}

60. The major product obtained in the following reaction is

(1)

(2)

(3)

(4)

**Mathematics**

61. The function defined as

(1) Injective but not surjective

(2) Surjective but not injective

(3) Neither injective nor surjective

(4) Invertible

62. If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1) (x + 2) + …+ has two consecutive integral solutions, then n is equal to

(1) 9

(2) 10

(3) 11

(4) 12

63. Let ω be a complex number such that 2ω + 1 = z where If then k is equal to

(1) z

(2) −1

(3) 1

(4) −z

64. If then adj (3A^{2} + 12A) is equal to

(1)

(2)

(3)

(4)

65. If S is the set of distinct values of b for which the following system of linear equations

x + y + z = 1

x + ay + z = 1

ax + by + z = 0

has no solution, then S is

(1) An infinite set

(2) A finite set containing two or more elements

(3) A singleton

(4) An empty set

66. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is

(1) 468

(2) 469

(3) 484

(4) 485

67. The value of (^{21}C_{1} – ^{10}C_{1}) + (^{21}C_{2} – ^{10}C_{2}) + (^{21}C_{3} – ^{10}C_{3}) + (^{21}C_{4} – ^{10}C_{4}) + … + (^{21}C_{10} – ^{10}C_{10}) is

(1) 2^{21} – 2^{10 }

(2) 2^{20} – 2^{9}

(3) 2^{20} – 2^{10 }

(4) 2^{21} – 2^{11}

68. For any three positive real numbers a, b and c, 9(25a^{2} + b^{2}) + 25(c^{2} – 3ac) = 15b(3a + c).

Then

(1) b, c and a are in A.P.

(2) a, and c are in A.P.

(3) a, b and c are in G.P.

(4) b, c and a are in G.P.

70. equals

(1)

(2)

(3)

(4)

71. If for the derivative of is then g(x) equals

(1)

(2)

(3)

(4)

72. The normal to the curve y(x − 2)(x − 3) = x + 6 at the point where the curve intersects the y-axis passes through the point

(1)

(2)

(3)

(4)

73. Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is

(1) 10

(2) 25

(3) 30

(4) 12.5

74. Let If I_{4} + I_{6} = a tan^{5} x + bx^{5} + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

(1)

(2)

(3)

(4)

75. The integral is equal to

(1) 2

(2) 4

(3) −1

(4) −2

76. The area (in sq. units) of the region {(x, y) : x ≥ 0, x + y ≤ 3, x^{2} ≤ 4y and y ≤1 + √x}

(1)

(2)

(3)

(4)

77. If and y(0) = 1, then is equal to

(1)

(2)

(3)

(4)

78. Let k be an integer such that the triangle with vertices (k, −3k), (5, k) and (−k, 2) has area 28 sq. units. Then the orthocenter of this triangle is at the point

(1)

(2)

(3)

(4)

79. The radius of a circle, having minimum area, which touches the curve y = 4 – x^{2} and the lines, y = |x| is

(1)

(2)

(3)

(4)

80. The eccentricity of an ellipse whose centre is at the origin is If one of its directrices is x = −4, then the equation of the normal to it at is

(1) 4x – 2y = 1

(2) 4x + 2y = 7

(3) x + 2y = 4

(4) 2y – x = 2

81. A hyperbola passes through the point and has foci at (±2, 0). Then the tangent to this hyperbola at P also passes through the point

(1)

(2)

(3)

(4)

82. The distance of the point (1, 3, −7) from the plane passing through the point (1, −1, −1), having normal perpendicular to both lines and is

(1)

(2)

(3)

(4)

83. If the image of the point P(1, −2, 3) in the plane 2x + 3y – 4z + 22 = 0 measured parallel to the line, is Q, then PQ is equal to

(1)

(2)

(3)

(4)

84. Let and Let be a vector such that and the angle between be 30°. Then is equal to

(1) 2

(2) 5

(3)

(4)

85. A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is

(1) 6

(2) 4

(3)

(4)

86. For three events A, B and C, P (Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = and P(All the three events occur simultaneously = Then the probability that at least one of the events occurs, is

(1)

(2)

(3)

(4)

87. If two different numbers are taken from the set {0, 1, 2, 3, ……, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is

(1)

(2)

(3)

(4)

88. If 5(tan^{2}x – cos^{2}x) = 2 cos 2x + 9, then the value of cos 4x is

(1)

(2)

(3)

(4)

89. Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β then tan β is

(1)

(2)

(3)

(4)

90. The following statement (p → q) → [(~ p → q) → q] is

(1) Equivalent to ~ p → q

(2) Equivalent to p → ~ q

(3) A fallacy

(4) A tautology

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