*IIT MAINS 2018 SOLUTION*

*IIT MAINS 2018 SOLUTION*

April 8, 2018

Kumar Physics Classes IIT JEE PHYSICS MAINS SOLUTION 2018 Physics Classes/TUTOR In GK 2/GK1/KALKAJI/C R PARK/ALAKNANDA/SOUTH EX/EOK/VASANT KUNJ/DEFENCE COLONY/SOUTH EX /KAILASH HILL

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61)

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 mm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Y oung’ 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.)

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 :-

Ans. (4)- 25 micro mt

62. An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ln, lg be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let Ln be the wavelength of the emitted photon in the transition from the nth state to the ground state. For large n, (A, B are constants)

Ans. (4)

63. The reading of the ammeter for a silicon diode

Ans. 11.5 ma

65. An electron, a proton and an alpha particle

having the same kinetic energy are moving in circular orbits of radii re, rp, ra respectively in a uniform magnetic field B. The relation between r , r , r is:-

64.

(1) 3.5 %

(3) 6 %

(2) 4.5 % (4) 2.5 %

epa (1)re <rp =ra

(2)re <rp <ra (4) re > rp = ra

(3) re < ra < rp Ans. (1)

66.

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

ALLEN

séa2 -b2 +cù (1)eêb ú

in the given circuit is :-

200W

(2) 11.5 mA (4) 0

0ëû séb2-c2+aù

(2)eêb ú 0ëû

(1) 15 mA

(3) 13.5 mA

Ans. (2)

(4)eêa ú 0ëû

séb2 -c2 +aù (3)eêc ú

3V

0ëû séa2 -b2 +cù

Ans. (1)

1

JEE(MAIN)-2018

67. Two masses m1 = 5kg and m2 = 10kg, 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 m2 to stop the motion is :-

71. It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd and pc are respectively :

(1) (.28, .89) (2) (0, 0)

(3) (0, 1) (4) (.89, .28)

Ans. (4)

m

m2 T

(1) 27.3 kg

(3) 10.3 kg

T

m1g

(2) 43.3 kg (4) 18.3 kg

72.

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of

the loop is B . The ratio B1 is : 2 B2

(2) 2

(4) 2

Ans. (1)

68. A particle is moving in a circular path of radius

a under the action of an attractive potential U=– k .Itstotalenergyis:-

(2)Zero

(4) — k 4a2

(1) 3 1

m1

2r2 2a2

(3) 2

(1) k

Ans. (2)

73. 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 W, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

(3) -3 k 2 a2

Ans. (2)

69. A parallel plate capacitor of capacitance

90 pF is connected to a battery of emf 20V. If a dielectric material of dielectric constant

K = 5 is inserted between the plates, the 3

magnitude of the induced charge will be :-

(1) 1.5 W

(3) 2.5 W Ans. (1)

(2) 2 W (4) 1 W

ALLEN

(1) 0.3 n C

(3) 0.9 n C

(2) 2.4 n C (4) 1.2 n C

Ans. (4)

70. A silver atom in a solid oscillates in simple

harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other ? (Mole wt. of silver =108 and Avagadro number = 6.02 × 1023 gm mole–1)

74. 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) 7.1 N/m

(3) 5.5 N/m

Ans. (1)

(2) 2.2 N/m (4) 6.4 N/m

(1) 2 × 104 (3) 2 × 106

Ans. (2)

(2) 2 × 105 (4) 2 × 103

2

75. 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 1 . Now another 2

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) 30o (2) 45o

(3) 60o (4) 0o

Ans. (2)

78.

CODE-C

In a collinear collision, a particle with an initial speed v0 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) 2v (3) v0

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) 1 =2 Îr2

(2) 1 = Îr2 4

v (2) 0

02 (4) v0

76. 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 kW. How much was the resistance on the left slot before interchanging the resistances ?

79.

An EM wave from air enters a medium. The electric fields are

r éæzöù

E 1 = E 0 1 xˆ c o s ê 2 p n ç c — t ÷ ú i n

values in air. The medium is non-magnetic. If

Îr1 and Îr2 refer to relative permittivities of air and

medium respectively, which of the following options is correct ?

(1) 505 kW (3) 910 kW

(2) 550 kW (4) 990 kW

2 02 ë û

wave number k and frequency v refer to their

Ans. (2)

77. From a uniform circular disc of radius R and

mass 9M, a small disc of radius R is removed

3 Îr Îr1

Ans. (1)

24

a i r

r ( ) in medium, where the

ë è øû E=Exˆcosk2ézct- ù

a n d

(3)Îr1 =1 Îr2 2

Ans. (2)

(4)Îr1 =4 Îr2

ALLEN

R

2R 3

80.

For an RLC circuit driven with voltage of

amplitude vm and frequency w0 = 1 the LC

current exibits resonance. The quality factor, Q is given by :

40 2 (1) 9 MR

(2) 10 MR2

(1) w0R (2) R

(w0C) 9 CRw0L

(3) 37MR2

(4) 4 MR

L

2

Ans. (4) (3) w0 (4) R

Ans. (4)

3

JEE(MAIN)-2018

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

distance

(1)

position

(2)

velocity

(3)

velocity

(4)

83. 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) n+1 T μ R 2

(3)TμRn/2 Ans. (2)

time

time

time

position

T μ R ( n +1) / 2 (4)TμR3/2 foranyn

84. If the series limit frequency of the Lyman series is vL, then the series limit frequency of the Pfund series is :

(1) 16 vL (3) vL/25

(2) vL/16 (4) 25 vL

Ans. (3)

85. In an a. c. circuit, the instantaneous e.m.f. and

current are given by e = 100 sin 30 t

æ 30t — p ö i = 20 sin ç 4 ÷

(2)

ALLEN

Ans. (1)

82. Two batteries with e.m.f 12 V and 13 V are

connected in parallel across a load resistor of 10 W. The internal resistances of the two batteries are 1 W and 2 W respectively. The voltage across the load lies between.

(1) 11.5 V and 11.6 V (2) 11.4 V and 11.5 V

(3) 11.7 V and 11.8 V (4) 11.6 V and 11.7 V

Ans. (1)

4

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

(1) 1000 , 10 (2) 50 , 0 22

(3) 50, 0 (4) 50, 10

Ans. (1)

86. Two moles of an ideal monoatomic gas

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

(1) (a) 195 K (b) –2.7 kJ

(2) (a) 189 K (b) –2.7 kJ

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

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

Ans. (2)

èø

87. 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 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

CODE-C

89. The mass of a hydrogen molecule is 3.32 × 10–27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45° to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly :

(1) 4.70 × 103 N/m2 (2) 2.35 × 102 N/m2 (3) 4.70 × 102 N/m2 (4) 2.35 × 103 N/m2

Ans. (4)

90. 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 :

æ dr ö

the sphere, ç r ÷, is :

(1) Ka 3mg

mg (3) Ka

èø

Ans. (2)

88. 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 × 103 kg/m3 and its Young’s modulus is 9.27 × 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?

P O

(2) mg 3Ka

Ka (4) mg

(1) 2.5 kHz

(3) 7.5 kHz

Ans. (4)

(2) 10 kHz (4) 5 kHz

55

(1) 2 MR2

73

(2) 2 MR2

(3) 181 MR2 22

(4) 19 MR2

Ans. (3)

ALLEN

5