NSEJS 2020 Question Paper

Question 1

Gravitational collapse is the contraction of an astronomical object under its own gravity. This draws the matter inwards towards the centre of gravity. A neutron star is an example of the collapsed core of a giant star. A certain neutron star of radius 10 km is of mass $1.5 M_{\odot}$. The acceleration due to gravity on the surface of the neutron star is nearly

(a) $2.0 \times 10^{8} \mathrm{ m} / \mathrm{s}^{2}$

(b) $2.0 \times 10^{12} \mathrm{ m} / \mathrm{s}^{2}$

(d) $2.6 \times 10^{20} \mathrm{ m} / \mathrm{s}^{2}$

Question 2

Two illuminated point objects $\mathrm{O}_{1}$ and $\mathrm{O}_{2}$ are placed at a distance 24 cm from each other along the principal axis of a thin convex lens of focal length 9 cm such that images of both the objects are formed at the same position. Then the respective distances of the lens from $\mathrm{O}_{1}$ and $\mathrm{O}_{2}$ (in cm ) are

(a) 12 and 12

(b) 18 and 6

(d) 16 and 8

Question 3

A nuclear reactor is working at $30 %$ efficiency (i.e. conversion of nuclear energy to electrical energy). In this reactor ${ }_{92}^{235} \mathrm{U}$ nucleus undergoes fission and releases 200 MeV energy per atom. If 1000 kW of electrical power is obtained in this reactor, then the number of atoms disintegrated (undergone fission) per second in the reactor is

(a) $1.04 \times 10^{17}$

(b) $6.5 \times 10^{12}$

(d) $3.25 \times 10^{32}$

Question 4

Two blocks $A$ and $B$ are in contact with each other and are placed on a frictionless horizontal surface. A force of 90 N is applied horizontally on block A (situation I ) and the same force is applied horizontally on block B (situation II). Mass of A is 20 kg and B is 10 kg . Then the correct statement is

(a) Since both the blocks are in contact, magnitude of force by block A on B will be 90 N (situation I) and magnitude of force by block B on A will also be 90 N (situation II).

(b) Magnitude of force by block A on B is 30 N (situation I) and magnitude of force by block B on $A$ is 60 N (situation II).

(c) Magnitude of force by block A on B is 60 N (situation I) and magnitude of force by block B on A is 30 N (situation II).

(d) The 90 N force will produce acceleration of different magnitudes in A and B .

Question 5

In the adjoining circuit, $R=5 \Omega$. It is desired that the voltage across $R_{x}$ should be 6 V , then the value of $R_{x}$ should be

(a) $4 \Omega$

(b) $12 \Omega$

(d) $20 \Omega$

Question 6

If $x^{2}+a x+b=0$ and $x^{2}+b x+a=0$ have one common root, then

(a) $a+b=0$

(b) $a+b=1$

(d) $a^{2}+b^{2}=1$

Question 7

Six circles each of radius 3 cm are inscribed in an equilateral triangle ABC such that they touch each other and also touch the sides of the triangle as shown in the adjacent figure. Then height of triangle $A B C$ is

(a) $6(2 \sqrt{3}+3)$

(b) $3(2 \sqrt{3}+6)$

(d) $6(2+\sqrt{3})$

Question 8

Find the remainder when $x^{51}$ is divided by $x^{2}-3 x+2$

(a) $X$

(b) $\left(2^{51}-2\right) x+2-2^{51}$

(d) 0

Question 9

If $\frac{3}{x-2}<1$, where $x$ is a real number, then

(a) $2<x<5$

(b) $x<2$ or $5<x$

(d) None of these

Question 10

If $100^{25}-25$ is written in decimal notations, then the sum of its digits is

(a) 444

(b) 442

(d) 422

Question 11

$A B C$ is a triangle, the bisector of angle $A$ meets $B C$ in $D$. The relation between $A D, A B$ and $A C$ is

(a) $A D>\sqrt{A B \cdot A C}$

(b) $A D>A B \cdot A C$

(d) $A D<\sqrt{A B \cdot A C}$ PART: A - 2 MORE THAN ONE CORRECT OPTIONS. BUBBLE ALL CORRECT OPTIONS ONLY.

Question 12

An infinitely long conductor when carrying current $I$, produces a magnetic field $B$ around it. If such a conductor is placed along the X-axis, then the magnitude of $B$ at a distance $r$ is given by the relation $B=\frac{\mu_{0}}{4 \pi} \frac{2 I}{r}$, (where $\frac{\mu_{0}}{4 \pi}=10^{-7} \mathrm{NA}^{-2}$ is a constant). The following figure shows such an infinitely long conductor placed along X -axis carrying current $I$ and $B$ at $S$ is $2 \times 10^{-4} \mathrm{ T}$, directed into the plane of the paper at S . Given $r=1 \mathrm{ cm}$. Then, the correct statements are

(a) $I=10 \mathrm{ A}$

(b) The number of electrons transported across the cross section of the conductor during time 1s is $6.25 \times 10^{19}$

(d) The electrons will flow in the direction $X_{2}$ to $X_{1}$.

Question 13

The ratio of the charge of an ion or subatomic particle to its mass $(q / m)$ is called specific charge. Then the correct options are

(a) SI unit of specific charge can be written as $\mathrm{A} \cdot \mathrm{s} / \mathrm{kg}$.

(b) If all the isotopes of hydrogen are ionized then tritium will have least specific charge among them.

(d) specific charge ratio of an electron is $1.75 \times 10^{11} \mathrm{C} / \mathrm{kg}$.

Question 14

If $0 \leq x \leq \pi$ and $81^{\sin ^{2} x}+81^{\cos ^{2} x}=30$, then $x=$

(a) $\frac{\pi}{6}$

(b) $\frac{\pi}{3}$

(d) $\frac{2 \pi}{3}$ [0pt] [Useful information: $\pi^{c}=180^{\circ}, \sin (180-\theta)=\sin \theta, \sin \theta \geq 0$ when $0 \leq \theta \leq 180^{\circ}$ ]

Question 15

Given $(a-b)^{2}+(a-c)^{2}=(b-c)^{2}$, then which of the following statements are true?

(a) equation is valid when $b=c$ and $a \neq c$

(b) equation is valid when $a=b$

(d) Given equation is not valid when $a, b$ and $c$ are distinct.