JEE Mains 2018

Which type of 'defect' has the presence of cations in the interstitial sites? (a) Schottky defect (b) Vacancy defect (c) Frenkel defect (d) Metal deficiency defect

Topic:

The Solid State

Exam:

JEE Mains 2018

View 2 solutions

Question 2

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

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

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

Topic:

Chemical Bonding and Molecular Structure

Exam:

JEE Mains 2018

View 3 solutions

Question 3

A particle is moving with a uniform speed in a circular orbit of radius

R

in a central force inversely proportional to the

n

th power of

R

. If the period of rotation of the particle is

T

, then:
(a)

T \propto R^{3/2}

for any

n

T \propto R^{\frac{n}{2} + 1}

T \propto R^{(n + 1) /2}

T \propto R^{n /2}

Topic:

System of Particles and Rotational Motion

Exam:

JEE Mains 2018

View 7 solutions

Question 4

made of a soft material of bulk modulus

A solid sphere of radius

r

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 the sphere,

(\frac{d r}{r})

is
(a)

\frac{K a}{m g}

\frac{K a}{3 m g}

\frac{m g}{3 K a}

\frac{m g}{K a}

Topic:

Mechanical Properties of Solids

Exam:

JEE Mains 2018

View 5 solutions

Question 5

Two moles of an ideal monoatomic gas occupies a volume

V

2 7^{\circ} C

. The gas expands adiabatically to a volume

2 V

.
Calculate (i) the final temperature of the gas and (ii) change in its internal energy.
(a) (i)

189 K

2.7 kJ

(b) (i)

195 K

- 2.7 kJ

189 K

- 2.7 k

]
(d) (i)

195 K

2.7 kJ

Topic:

Thermodynamics

Exam:

JEE Mains 2018

View 7 solutions

Question 6

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of

1 0^{12}

per second. What is the force constant of the bonds connecting one atom with the other? (Take, molecular weight of silver

= 108

and Avogadro number

= 6.02 \times 1 0^{23} g mol^{- 1}

)

$6.4 N / m$
$7.1 N / m$
$2.2 N / m$
$5.5 N / m$

Topic:

Oscillations

Exam:

JEE Mains 2018

View 5 solutions

Question 7

Easy

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 = \frac{5}{3}

is inserted between the plates, the magnitude of the induced charge will be
(a)

1.2 nC

0.3 nC

2.4 nC

0.9 nC

Topic:

Electrostatic Potential and Capacitance

Exam:

JEE Mains 2018

View 9 solutions

Question 8

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

\frac{B _{1}}{B _{2}}

is
(a) 2
(b)

3

2

\frac{1}{2}

Topic:

Moving Charges and Magnetism

Exam:

JEE Mains 2018

View 3 solutions

Question 9

circuit, the instantaneous emf and current are given by

In an

AC

e = 100 sin 30 t, i = 20 sin (30 t - \frac{π}{4})

In one cycle of

AC

, the average power consumed by the circuit and the wattless current are, respectively
(a) 50,10
(b)

\frac{1000}{2}, 10

circuit driven with voltage of amplitude

\frac{50}{2}, 0

(d) 50,0

Topic:

Alternating Current

Exam:

JEE Mains 2018

View 7 solutions

Question 10

Easy

For an

R - L - C

v_{m}

and frequency

ω_{0} = \frac{1}{L C}

, the current exhibits resonance. The quality factor,

Q

is given by
(a)

\frac{ω _{0} L}{R}

\frac{ω _{0} R}{L}

\frac{R}{ω _{0} C}

\frac{CR}{ω _{0}}

Topic:

Alternating Current

Exam:

JEE Mains 2018

View 2 solutions

Question 11

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

E_{1} = E_{01} \hat{x} cos [2 π v (\frac{z}{c} - t)]

in air and

E_{2} = E_{02} \hat{x} cos [k (2 z - c t)]

in medium, where the wave number

k

and frequency

v

refer to their values in air. The medium is non-magnetic.
If

ε_{r_{1}}

refer to relative permittivities of air and medium respectively, which of the following options is correct? [JEE Main 2018]
(a)

ε_{r_{2}}

\frac{ε _{r_{1}}}{ε _{r_{2}}} = 4

\frac{ε _{r_{1}}}{ε _{r_{2}}} = 2

\frac{ε _{r_{1}}}{ε _{r_{2}}} = \frac{1}{4}

A telephonic communication service is working at carrier frequency of

\frac{ε _{r_{1}}}{ε _{r_{2}}} = \frac{1}{2}

Topic:

Waves

Exam:

JEE Mains 2018

View 5 solutions

Question 12

Easy

10 GHz

. Only

10%

of it is utilised for transmission. How many telephonic channels can be transmitted simultaneously, if each channel requires a bandwidth of

5 kHz

?
(a)

2 \times 1 0^{3}

2 \times 1 0^{4}

2 \times 1 0^{5}

2 \times 1 0^{6}

Topic:

Semiconductor Electronics: Materials, Devices and Simple Circuits

Exam:

JEE Mains 2018

View 2 solutions

Question 13

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%

, the maximum error in determining the density is
(a)

1%

2.5%

3.5%

4.5%

6%

Topic:

Units and Measurements

Exam:

JEE Mains 2018

View 5 solutions

Question 14

A particle is moving in a circular path of radius

a

under the action of an attractive potential

U = - \frac{k}{2 r ^{2}}

. Its total energy is
(a)

- \frac{k}{4 a ^{2}}

\frac{k}{2 a ^{2}}

- \frac{3}{2} \frac{k}{a ^{2}}

Topic:

Work, Energy and Power

Exam:

JEE Mains 2018

View 19 solutions

Question 15

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
(a)

\frac{v _{0}}{4}

2 v_{0}

\frac{v _{0}}{2}

\frac{v _{0}}{2}

Topic:

Laws of motion

Exam:

JEE Mains 2018

View 12 solutions

Question 16

Seven identical circular planar discs, each of mass

M

and radius

R

are welded symmetrically as shown in the figure. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point

P

is

(a)

\frac{19}{2} M R^{2}

\frac{55}{2} M R^{2}

\frac{73}{2} M R^{2}

\frac{181}{2} M R^{2}

Topic:

System of Particles and Rotational Motion

Exam:

JEE Mains 2018

View 3 solutions

Question 17

From a uniform circular disc of radius

R

and mass 9

M

, a small disc of radius

\frac{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

(a)

4 M R^{2}

\frac{40}{9} M R^{2}

10 M R^{2}

\frac{37}{9} M R^{2}

Topic:

System of Particles and Rotational Motion

Exam:

JEE Mains 2018

View solution

Question 18

length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is

A granite rod of

60 cm

2.7 \times 1 0^{3} kg / m^{3}

and its Young's modulus is

9.27 \times 1 0^{10} Pa

. What will be the fundamental frequency of the longitudinal vibrations?
(a)

5 kHz

2.5 kHz

10 kHz

7.5 kHz

Topic:

Waves

Exam:

JEE Mains 2018

View 3 solutions

Question 19

Three concentric metal shells

A, B

C

of respective radii

a, b

have surface charge densities

c (a < b < c)

+ σ, - σ

, respectively. The potential of shell

+ σ

B

is
(a)

\frac{σ}{ε _{0}} [\frac{a ^{2} - b ^{2}}{a} + c]

\frac{σ}{ε _{0}} [\frac{a ^{2} - b ^{2}}{b} + c]

\frac{σ}{ε _{0}} [\frac{b ^{2} - c ^{2}}{b} + a]

\frac{σ}{ε _{0}} [\frac{b ^{2} - c ^{2}}{c} + a]

Topic:

Electric Charges and Fields

Exam:

JEE Mains 2018

View 10 solutions

Question 20

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 the

n

th state and the ground state, respectively. Let

Λ_{n}

be the wavelength of the emitted photon in the transition from the

n

th state to the ground state. For large

n, (A, B

are constants)
(a)

Λ_{n} \approx A + \frac{B}{λ _{n}^{2}}

Λ_{n} \approx A + B λ_{n}^{2}

Λ_{n}^{2} \approx A + B λ_{n}^{2}