# JEE Main 2017 Online CBT Examination Held on Dt-08-04-2017

JEE Main 2017 Online CBT Examination Held on Dt-08-04-2017

Physics

1. There is a uniform electrostatic field in a region. The potential at various points on a small sphere, centred at P, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60° with the direction of the field?

(1)  589.5 V

(2)  589.4 V

(3)  589.2 V

(4)  589.6 V

2. In a certain region static electric and magnetic fields exists. The magnetic field is given  If a test charge moving with a velocity  experiences no force in that region, then the electric field in the region, In SI units, is :

(1)

(2)

(3)

(4)

3. A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by ∆ The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young’s modulus, and α it coefficient of linear expansion. Then, F is equal to :

(1)

(2)  A Yα ∆T

(3)  l2 Yα ∆T

(4)  lA Yα ∆T

4. A magnetic dipole in a constant magnetic field has :

(1)  minimum potential energy when the torque is maximum.

(2)  zero potential energy when the torque is minimum.

(3)  maximum potential energy when the torque is maximum.

(4)  zero potential energy when the torque is maximum.

5. Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

(1)  [M] = [T1 C2h]

(2)  [M] = [T1C2h1]

(3)  [M] = [T1C2h]

(4)  [M] = [TC2h]

6. A small circular loop of wirer of radius is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = Io cos (ωt). The emf induced in the smaller inner loop is nearly :

(1)

(2)

(3)

(4)

7. Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)

(1)  30.2 MeV

(2)  23.6 MeV

(3)  32.4 MeV

(4)  25.8 MeV

8. In an experiment a sphere of aluminium of mass 0.20 kg is heated upto 150℃. Immediately, it is put into water of volume 150 cc at 27℃ kept in a claroimeter of water equivalent to 0.025 kg. Final temperature of the system is 40℃. The specific heat of aluminium is :

(take 4.2 Joule = 1 calorie)

(1)  315 J/kg-℃

(2)  378 J/kg-℃

(3)  476 J/kg-℃

(4)  434 J/kg-℃

9. In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

(1)  Left arm is shorter than the right arm

(2)  Both the arms are of same length

(3)  Every object that is weighed using this balance appears lighter than its actual weight.

(4)  Left arm is longer than the right arm

10. The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s1. At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is

(1)

(2)  500 m/s2

(3)  750 m/s2

(4)

11. An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp) and at constant volume (Cv) is :

(1)

(2)

(3)  6

(4)

12. The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 μC charge, its radius will be :

(1)  28 mm

(2)  32 mm

(3)  20 mm

(4)  16 mm

13. An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t → ∞ is

(1)

(2)  ∞

(3)

(4)  2h

14. According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n = principal quantum number)

(1)  n5

(2)  n4

(3)  n3

(4)  n2

15. Let the refractive index of a denser medium with respect to a rarer medium be n12 and its critical angle be θC. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90°. Angle A is given by :

(1)  cos1 (sin θC)

(2)

(3)  tan1 (sin θC)

(4)

16. A single slit of width b is illuminated by a coherent monochromatic light of wavelength λ. If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)

(1)  4.5 cm

(2)  6.0 cm

(3)  3.0 cm

(4)  1.5 cm

17. Two wires W1 and W2 have the same radius r and respective densities ρ1 and ρ2 such that ρ2 = 4ρ1. They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be an ode. The ratio of the number of antinodes formed in W1 to W2 is :

(1)  4 : 1

(2)  1 : 1

(3)  1 : 2

(4)  1 : 3

18. A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

(1)

(2)

(3)

(4)

19. Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

(1)

(2)

(3)

(4)

20. The V-I characteristics of a diode is shown in the figure. The ratio of forward to reverse bias resistance is :

(1)  10

(2)  106

(3)  100

(4)  106

21. The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

(1)

(2)

(3)

(4)  V

22. A potentiometer PQ is set up to compare two resistance as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K3 is open. The balance point is at a length l1 cm from P when two way key K3 is plugged in between 2 and 1, while the balance point is at a length l2 cm from P when key K3 is plugged in between 3 and 1. The ratio of two resistances  is found to be :

(1)

(2)

(3)

(4)

23. A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 Volts. Choose the correct

(1)  Modulation index = 0.2, side frequency bands are at 1220 kHz and 1180 kHz

(2)  Modulation index = 5, side frequency bands are at 21.2 kHz and 18.8 kHz

(3)  Modulation index = 5, side frequency bands are at 1400 kHz and 1000 kHz

(4)  Modulation index = 0.8, side frequency bands are at 1180 kHz and 1220 kHz

24. Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is Io as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

(1)

(2)

(3)

(4)

25. If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh  Radius of the Earth is 6400 km and g = 10 m/s2.

26. Magnetic field in a plane electromagnetic wave is given by

Expression for corresponding electric field will be :

Where c is speed of light.

(1)

(2)

(3)

(4)

27. An engine operates by taking n moles of an ideal gas through the cycle ABCDA show in figure. The thermal efficiency of the engine is :

(Take CV = 1.5 R, where R is gas constant)

(1)  0.32

(2)  0.15

(3)  0.24

(4)  0.08

28. A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :

(1)

(2)

(3)  2 Hz

(4)

29.

A 9 V battery with internal resistance of 0.5 Ω is connected across an infinite network as shown in the figure. All ammeters A1, A2, A3 and voltmeter V are ideal.

Choose correct statement.

(1)  Reading of V is 9 V

(2)  Reading of A1 is 18 A

(3)  Reading of A1 of is 2 A

(4)  Reading of V is 7 V

30. What is the conductivity of semiconductor sample having electron concentration of 5 × 1018 m3, hole concentration of 5 × 1019 m3, electron mobility of 2.0 m2 V1 s1 and hole mobility of 0.01 m2 V1 s1 ?

(Take charge of electron as 1.6 × 1019 C)

(1)  0.59 (Ω-m)1

(2)  1.20 (Ω-m)1

(3)  1.69 (Ω-m)1

(4)  1.83 (Ω-m)1

Chemistry

31. Which of the following statements is not true about partition chromatography ?

(1)  Separation depends upon equilibrium of solute  between a mobile and a stationary phase

(2)  Stationary phase is a finely divided solid adsorbent

(3)  Mobile phase can be a gas

(4)  Paper chromatography is an example of partition chromatography

32. Which of the following is paramagnetic ?

(1)  B2

(2)  CO

(3)

(4)  NO+

33. The major product of the following reaction is :

(1)  CH3CH = C = CHCH2CH3

(2)  CH2 = CHCH = CHCH2CH3

(3)  CH3CH = CH – CH = CHCH3

(4)  CH2 = CHCH2CH = CHCH3

34. Excess of NaOH (aq) was added to 100 mL of FeCl3 (aq) resulting into 2.14 g of Fe(OH)3. The molarity of FeCl3 (aq) is :

[Given molar mass of Fe = 56 g mol1 and molar mass of Cl = 35.5 g mol1)

(1)  1.8 M

(2)  0.2 M

(3)  0.6 M

(4)  0.3 M

35. The IUPAC name of the following compound is :

(1)  1, 1-Dimethyl-2-ethylcyclohexane

(2)  2-Ethyl1-1, 1-dimethylcyclohexane

(3)  2, 2-Dimethyl-1-ethylcyclohexane

(4)  1-Ethyl-2, 2-dimethylcyclohexane

36. If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of He+ is :

(1)

(2)

(3)

(4)

37. Identify the pollutant gases largely responsible for the discoloured and lusterless nature of marble of the Taj Mahal.

(1)  SO2 and NO2

(2)  SO2 and O3

(3)  O3 and CO2

(4)  CO2 and NO2

38. The Major product of the following reaction is :

(1)

(2)

(3)

(4)

39. The major product expected from the following reaction is :

(1)

(2)

(3)

(4)

40. The pair of compounds having metals in their highest oxidation state is :

(1)  MnO2 and CrO2Cl2

(2)  [FeCl4] and Co2O3

(3)  [Fe(CN)6]3 and [Cu(CN)4]2

(4)  [NiCl4]2 and [CoCl4]2

41. Among the following, the essential amino acid is :

(1)  Valine

(2)  Aspartic acid

(3)  Serine

(4)  Alanine

42. Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of pH 6. If ionization constant of HA is 105, the ratio of salt to acid concentration in the buffer solution will be :

(1)  10 : 1

(2)  4 : 5

(3)  1 : 10

(4)  5 : 4

43. Among the following, the incorrect statement is :

(1)  At very large volume, real gases show ideal behaviour.

(2)  At Boyle’s temperature, real gases show ideal behaviour.

(3)  At very low temperature, real gases show ideal behaviour.

(4)  At low pressure, real gases show ideal behaviour.

44. The rate of a reaction A doubles on increasing the temperature from 300 to 310 K. By how much, the temperature of reaction B should be increased from 300 K so that rate doubles if activation energy of the reaction B is twice to that of reaction A.

(1)  9.84 K

(2)  19.67 K

(3)  2.45 K

(4)  4.92 K

45. The number of S = O and S – OH bonds present in peroxodisulphuric acid and pyrosulphuric acid respectively are :

(1)  (4 and 2) and (2 and 4)

(2)  (2 and 2) and (2 and 2)

(3)  (4 and 2) and (4 and 2)

(4)  (2 and 4) and (2 and 4)

46. Among the following, correct statement is :

(1)  One would expect charcoal to adsorb chlorine more than hydrogen sulphide.

(2)  Sols of metal sulphides are lyophilic.

(3)  Hardy Schulze law states that bigger the size of the ions, the greater is its coagulating power.

(4)  Brownian movement is more pronounced for smaller particles than for bigger-particles.

47. sp3d2 hybridization is not displayed by :

(1)  PF5

(2)  SF6

(3)  [CrF6]3

(4)  BrF5

48. For a reaction, A(g) → A(l); ∆H = −

The correct statement for the reaction is :

(1)  ∆H = ∆U ≠ O

(2)  |∆H| > |∆U|

(3)  |∆H| < |∆U|

(4)  ∆H = ∆U = O

49. A metal ‘M’ reacts with nitrogen gas to afford ‘M3N’ on heating at high temperature gives back ‘M’ and on reaction with water produces a gas ‘B’. Gas ‘B’ reacts with aqueous solution of CuSO4 to form a deep blue compound. ‘M’ and ‘B’ respectively are :

(1)  Li and NH3

(2)  Na and NH3

(3)  Al and N2

(4)  Ba and N2

50. What is the standard reduction potential (E°) for Fe3+ → Fe ?

Given that :

(1)  +0.30 V

(2)  −0.057 V

(3)  +0.057 V

(4)  −0.30 V

51. The major product of the following reaction is :

(1)

(2)

(3)

(4)

52. A solution containing a group-IV cation gives a precipitate on passing H2 A solution of this precipitate in dil. HCl produces a white precipitate with NaOH solution and bluish-white precipitate with basic potassium ferrocyanide. The cation is :

(1)  Mn2+

(2)  Zn2+

(3)  Co2+

(4)  Ni2+

53. 5 g of Na2SO4 was dissolved in x g of H2 The change in freezing point was found to be 3.82℃. If Na2SO4 is 81.5% ionised, the value of x

(Kf for water = 1.86℃ kg mol1) is approximately :

(molar mass of S = 32 g mol1 and that of Na = 23 g mol1)

(1)  45 g

(2)  65 g

(3)  25 g

(4)  15 g

54. Consider the following standard electrode potential (E° in volts) in aqueous solution :

Based on these data, which of the following statements is correct ?

(1)  Al+ is more stable than Al3+

(2)  Tl3+ is more s table than Al3+

(3)  Tl+ is more stable than Al3+

(4)  Tl+ is more stable than Al+

55. The reason for “drug induced poisoning” is :

(1)  Bringing conformational change in the binding site of enzyme

(2)  Binding reversibly at the active site of the enzyme

(3)  Binding irreversibly to the active site of the enzyme

(4)  Binding at the allosteric sites of the enzyme

56. A mixture containing the following four compounds is extracted with 1 M HCl. The compound that goes to aqueous layer is :

(1)  (II)

(2)  (IV)

(3)  (I)

(4)  (III)

57. In which of the following reactions, hydrogen peroxide acts as an oxidizing agent ?

(1)  PbS + 4H2O2 → PbSO4 + 4H2O

(2)

(3)  I2 + H2O2 + 2OH → 2I + 2H2O + O2

(4)  HOCl + H2O2 → H3O+ + Cl + O2

58. Consider the following ionization enthalpies of two elements ‘A’ and ‘B’.

Which of the following statements is correct ?

(1)  Both ‘A’ and ‘B’ belong to group-1 where ‘B’ comes below ‘A’.

(2)  Both ‘A’ and ‘B’ belong to group-2 where ‘A’ comes below ‘B’.

(3)  Both ‘A’ and ‘B’ belong to group-2 where ‘B’ comes below ‘A’.

(4)  Both ‘A’ and ‘B’ belong to group-1 where ‘A’ comes below ‘B’.

59. The enthalpy change on freezing of 1 mol of water at 5 ℃ to ice at −5℃ is :

(Given ∆fusH = 6  kJ mol1 at 0℃, Cp(H2O, l) = 75.3 J mol1 K1, Cp(H2O, s) = 36.8 J mol1 K1)

(1)  5.81 kJ mol1

(2)  5.44 kJ mol1

(3)  6.00 kJ mol1

(4)  6.56 kJ mol1

60. Which of the following compounds will not undergo Friedel Craft’s reaction with benzene ?

(1)

(2)

(3)

(4)

Mathematics

61. Let f(x) = 210 ∙ x and g(x) = 310 x ∙ x – 1. If (fog) (x) = x, then x is equal to :

(1)

(2)

(3)

(4)

62. If the sum of the first n terms of the series  then n equals :

(1)  29

(2)  18

(3)  15

(4)  13

63. If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles  and sec1(7) at the centre respectively, then the distance between these chords, is :

(1)

(2)

(3)

(4)

64. If  then  is equal to :

(1)  225 y2

(2)  224 y2

(3)  225 y

(4)  125 y

65. The locus of the point of intersection of the straight lines,

tx – 2y – 3t = 0

x – 2ty + 3 = 0 (t ϵ R), is :

(1)  an ellipse with eccentricity

(2)  a hyperbola with eccentricity

(3)  a hyperbola with the length of conjugate axis 3

(4)  an ellipse with the length of major axis 6

66. If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then  is equal to :

(1)

(2)

(3)

(4)

67. The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :

(1)  35

(2)  30

(3)  40

(4)  25

68. Let A be any 3 × 3 invertible matrix. Then which one of the following is not always true ?

(4)  adj (A) = |A| ∙ A1

69. If the common tangents to the parabola, x2 = 4y and the circle, x2 + y2 = 4 intersect at the point P, then the distance of P from the origin, is :

(1)

(2)

(3)

(4)

70. The proposition (~p) ⋁ (p ⋀ ~ q) is equivalent to :

(1)  p ⋁ ~ q

(2)  p → ~ q

(3)  q → p

(4)  p ⋀ ~ q

71. The area (in sq. units) of the parallelogram whose diagonals are along the vectors  is :

(1)  65

(2)  52

(3)  26

(4)  20

72. The curve satisfying the differential equation, ydx – (x + 3y)2dy = 0 and passing through the point (1, 1), also passes through the point :

(1)

(2)

(3)

(4)

73. The integral  equals :

(1)

(2)

(3)

(4)

74. The tangent at the point (2, −2) to the curve, x2y2 – 2x = 4(1 – y) does not pass through the point :

(1)  (−2, −7)

(2)  (8, 5)

(3)

(4)  (−4, −9)

75. The integral  is equal to  :

(where C is a constant of integration)

(1)

(2)

(3)

(4)

76. An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

(1)

(2)

(3)

(4)

77. The number of real values of λ for which the system of linear equations

2x + 4y – λ z = 0

4x + λ y + 2z = 0

λ x + 2y + 2z = 0

has infinitely many solutions, is :

(1)  3

(2)  1

(3)  2

(4)  0

78. The coordinates of the foot of the perpendicular from the point (1, −2, 1) on the plane containing the lines,  and  is :

(1)  (1, 1, 1)

(2)  (0, 0, 0)

(3)  (−1, 2, −1)

(4)  (2, −4, 2)

79. The line of intersection of the planes  and  is :

(1)

(2)

(3)

(4)

20. If (27)999 is divided by 7, then the remainder is :

(1)  2

(2)  6

(3)  3

(4)  1

21. If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :

(1)  45th

(2)  46th

(3)  47th

(4)  44th

22. Let z ϵ C, the set of complex numbers. Then the equation, 2|x + 3i| − |z – i| = 0 represents :

(1)  a circle with diameter

(3)  an ellipse with length of major axis

(4)  an ellipse with length of minor axis

83. If  then  is equal to :

(1)

(2)

(3)

(4)

84. If a point P h as co-ordinates (0, −2) and Q is any point on the circle, x2 + y2 – 5x – y + 5 = 0, then the maximum value of (PQ)2 is :

(1)

(2)

(3)

(4)

85. The area (in sq. units) of the smaller portion enclosed between the curves, x2 + y2 = 4 and y2 = 3x, is :

(1)

(2)

(3)

(4)

86.  is equal to :

(1)

(2)

(3)

(4)

87. The value of  is equal to :

(1)

(2)

(3)

(4)

88. Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis. If its eccentricity is  and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :

(1)  40

(2)  32

(3)  80

(4)  8

89. Let p(x) be a quadratic polynomial such that p(0) = 1. If p(x) leaves remainder 4 when divided by x – 1 and it leaves remainder 6 when divided by x + 1; then :

(1)  p(−2) = 19

(2)  p(2) = 19

(3)  p(−2) = 11

(4)  p(2) = 11

90. Three persons P, Q and R independently try hit a target. If the probabilities of their hitting the target are  respectively, then the probability that the target is hit by P or Q but not by R is :

(1)

(2)

(3)

(4)