NSEJS 2023 Question Paper

Question 1

Select the correct order of dielectric constant, refractive index and intermolecular forces for water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ and heavy water $\left(\mathrm{D}_{2} \mathrm{O}\right)$ at 293 K respectively among those given below

(i) Dielectric constant $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (ii) Dielectric constant $-\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$ (iii) Refractive index $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (iv) Refractive index $-\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$

(v) Intermolecular forces $-\mathrm{H}_{2} \mathrm{O}>\mathrm{D}_{2} \mathrm{O}$ (vi) Intermolecular forces - $\mathrm{D}_{2} \mathrm{O}>\mathrm{H}_{2} \mathrm{O}$ The option containing all correct statements is

(a) (i), (iii), (vi)

(b) (i), (iv), (v)

(d) (i), (iv), (vi)

Question 2

Among the elements of atomic number (Z) from 1 to 92 (i.e., from H to U), the elements having atomic number ____ and ____ are not found in nature.

(a) 89, 92

(b) 83,89

(d) None of these

Question 3

Which state of matter exists at very high temperature and at very low temperature (near absolute zero) respectively? BEC stands for Bose Einstein Condensate.

(a) BEC, fermionic condensate

(b) Plasma, BEC

(d) Gas, BEC

Question 4

Two blocks A and B of masses 1 kg and 4 kg respectively are moving with equal kinetic energies Read the following statements $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ Statement $\mathrm{S}_{1}$ : Ratio of speed of the block A to that of B is $1: 2$ Statement $S_{2}$ : Ratio of magnitude of linear momentum of $A$ to that of $B$ is $1: 2$ Now choose the correct option:

(a) Both $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are true

(b) Both $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are false

(d) $\mathrm{S}_{1}$ is false, $\mathrm{S}_{2}$ is true

Question 5

The mass of a straight copper wire is 20.95 g and its electrical resistance is $0.065 \Omega$. If the density and resistivity of copper are $\mathrm{d}=8900 \mathrm{ kg} / \mathrm{m}^{3}$ and $\rho=1.7 \times 10^{-8}$ ohm-meter respectively, the length of the copper wire is

(a) 3 m

(b) 6 m

(d) date is insufficient

Question 6

It is known that the speed of sound in a gas is directly proportional to square root of its absolute temperature T measured in Kelvin i.e. $v \propto \sqrt{T}$ Speed of sound in air at $0^{\circ} \mathrm{C}$ is $332 \mathrm{ m} / \mathrm{s}$. On a hot day, the speed of sound was measured $360 \mathrm{ m} / \mathrm{s}$ in NCR Delhi, the temperature of air in Delhi on that very day must have been close to

(a) $40^{\circ} \mathrm{C}$

(b) $42^{\circ} \mathrm{C}$

(d) $48^{\circ} \mathrm{C}$

Question 7

A small bar magnet is allowed to fall vertically through a metal ring lying in a horizontal plane. During its fall, the acceleration of the magnet in the region close to the ring must be (g is the acceleration due to gravity)

(a) equal to g

(b) less than $g$ and uniform

(d) greater than g and uniform

Question 8

An object pin is placed at a distance 10 cm from first focus of a thin convex lens on its principal axis, the lens forms a real and inverted image of this object pin at a distance 40 cm beyond the second focus. The focal length of the lens is

(a) 16 cm

(b) 20 cm

(d) 40 cm

Question 9

A bullet of mass 0.25 kg moving horizontally with velocity $v(\mathrm{ m} / \mathrm{s})$ strikes a stationary block of mass 1.00 kg suspended by a long inextensible string of negligible mass and length $\ell$. The bullet gets embedded in the block and the system rises up to maximum height $\mathrm{h}=19.6 \mathrm{ cm}$ (as shown in the figure. The string still remains taut). The value of initial speed $v$ of the bullet is

(a) $5.9 \mathrm{ m} / \mathrm{s}$

(b) $7.8 \mathrm{ m} / \mathrm{s}$

(d) $11.8 \mathrm{ m} / \mathrm{s}$

Question 10

The equivalent resistance between points A and B in the following electrical network is

(a) $\frac{3}{4} \Omega$

(b) $\frac{4}{3} \Omega$

(d) $\frac{9}{14} \Omega$

Question 11

The order of magnitude of the pressure (in pascal) exerted by an adult human on the Earth when he stands bare footed on the Earth on both of his legs, is

(a) $10^{2}$

(b) $10^{4}$

(d) $10^{9}$

Question 12

On the board of an experiment, three bulbs $\mathrm{B}_{1}(100 \mathrm{ W}, 200 \mathrm{ V})$, $\mathrm{B}_{2}(60 \mathrm{ W}, 200 \mathrm{ V})$ and $\mathrm{B}_{3}(40 \mathrm{ W}, 200 \mathrm{ V})$ are connected to a 200 V fluctuating supply with a fuse in series as shown in the figure. The electric current rating of the fuse required in the circuit to protect all the three bulbs must be

(a) 0.2 Amp

(b) 0.3 Amp

(d) 1.0 Amp

Question 13

An ant is sitting on the principal axis of a convex mirror of focal length f , at a distance 2 f from the pole in front of the mirror. It starts moving on principal axis towards the mirror. During the course of motion, the distance between the ant and its image

(a) throughout increases

(b) throughout decreases

(d) first decreases, then increases

Question 14

You are given three resistance of values $2 \Omega, 4 \Omega$ and $6 \Omega$. Which of the following values of equivalent resistance is not possible to get by using/arranging these three resistors in any circuit?

(a) Less than $2 \Omega$

(b) Equal to $4.4 \Omega$

(d) Equal to $7.6 \Omega$

Question 15

ABC is a 0.8 meter long curved wire track in a vertical plane. A bead of mass 3 g is released from rest at A . It slides along the wire and comes to rest at C . The average frictional force opposing the motion in a single trip from A to C is

(a) $18.40 \times 10^{-3} \mathrm{ N}$

(b) $29.4 \times 10^{-3} \mathrm{ N}$

(d) $7.36 \times 10^{-3} \mathrm{ N}$

Question 16

Two long straight conductors 1 and 2, carrying parallel currents $\mathrm{I}_{1}$ and $\mathrm{I}_{2}$ in the same direction, are lying parallel and close to each other, as shown in the figure. $\mathrm{F}_{\mathrm{e}}$ and $\mathrm{F}_{\mathrm{m}}$ respectively represent the electric and the magnetic forces, applied by conductor 1 on conductor 2 . Choose the correct alternative regarding nature of $\mathrm{F}_{\mathrm{e}}$ and $\mathrm{F}_{\mathrm{m}}$

(a) $F_{e}$ is repulsive while $F_{m}$ is attractive

(b) $\mathrm{F}_{\mathrm{e}}$ is repulsive and $\mathrm{F}_{\mathrm{m}}$ is repulsive too

(d) $\mathrm{F}_{\mathrm{e}}$ is zero and $\mathrm{F}_{\mathrm{m}}$ is attractive

Question 17

A doctor measures the temperature of a patient by a digital thermometer as $37.3^{\circ} \mathrm{C}$. As a Physics student you will record his temperature in Kelvin as

(a) 310.30 K

(b) 310.45 K

(d) 310.31 K

Question 18

Two planets $P_{1}$ and $P_{2}$ are moving around the Sun, in circular orbits of radii $10^{13} \mathrm{ m}$ and $10^{12} \mathrm{ m}$ respectively. The ratio of the orbital speeds of planets $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ in their respective orbits is

(a) $\sqrt{10}$

(b) 10

(d) $\frac{1}{\sqrt{10}}$

Question 19

Select the correct statement(s) pertaining to Bohr model of an atom.

(a) An electron near the nucleus is attracted more by the nucleus; thereby has lower potential energy.

(b) An electron continuously radiates energy as long as it revolves in a discrete orbit.

(d) This is the first atomic model based on quantization of energy.

Question 20

The correct order(s) of first ionization energy for the following pairs is/are:

(a) $\mathrm{Ag}<\mathrm{Au}$

(b) $\mathrm{Pd}<\mathrm{Pt}$

(d) $\mathrm{Sb}>\mathrm{Bi}$

Question 21

Crane A and crane B take 1 minute and 2 minute respectively to lift a car of mass 2 ton ( 2000 kg ) upward through a vertical height $h=3$ meter. If the efficiencies of the engines (defined as the ratio of work output to fuel energy input) of both the cranes are equal, your inference is that

(a) the power supplied by crane B is 1000 kW

(b) the crane A and the crane B consume equal amount of fuel

(d) the crane A consumes more fuel in lifting the car than the crane B

Question 22

Two tungsten filament bulbs with rating 100 watt, 200 volt and 60 watt, 200 volt are connected in series with a variable supply of $0-400 \mathrm{ V}$ range, as shown. The supply voltage is gradually increased from 0 to 400 V . Choose the correct statement(s).

(a) When supply voltage is 200 volt, 60 W bulb glows brighter

(b) When supply voltage is 200 volt, total power dissipated in both the bulbs is greater than 37.5 W

(d) When supply voltage becomes 400 V , none of the bulbs glow

Question 23

A solid sphere of radius $R=10 \mathrm{ cm}$ floats in water with $60 %$ of its volume submerged. In an oil, this sphere floats with $80 %$ of its volume submerged. If the density of water is $1000 \mathrm{ kg} / \mathrm{m}^{3}$. The correct statement(s) is/are that

(a) the density of the material of sphere is $600 \mathrm{ kg} / \mathrm{m}^{3}$

(b) the density of the oil is $750 \mathrm{ kg} / \mathrm{m}^{3}$

(d) the loss in weight of the sphere when floating in oil is close to 30.82 N

Question 24

A particle starts moving from origin O along $x$ axis. The velocity-time graph of motion of particle is given below. The positive values of $v$ refer to direction of motion along $+x$ axis, the negative values of $v$ refer to direction of motion along $-x$ direction. Choose the correct statement(s).

(a) Initial acceleration of the particle is $4 \mathrm{ m} / \mathrm{s}^{2}$

(b) The displacement of particle from origin is 130 m after 16 second

(d) Somewhere during the motion for $0-16$ second, the retardation of the particle is $10 \mathrm{ m} / \mathrm{s}^{2}$ Rough Work