Q. Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions.

1. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
2. Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is false.

Q. Two fixed frictionless inclined plane making an angle ${30}^o$ and ${60}^o$ with the vertical are shown in the figure. Two blocks A and $B$ are placed on the two planes. What is the relative vertical acceleration of A with respect to $B$ ?

1. $4.9m{s}^{-2}$ in horizontal direction
2. $4.9m{s}^{-2}$ in vertical direction
3. $9.8m{s}^{-2}$ in vertical direction
4. zero

Q. A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length$s=t^3+5$, where $s$ is in metres and $t$ is in seconds. The radius of the path is $20$ $m$. The acceleration of $P$ when $t=2s$ is nearly :

1. $13$ $m/s^2$
2. $12$ $m/s^2$
3. $7.2$ $m/s^2$
4. $14$ $m/s^2$

Q. A nucleus of mass $M+\Delta m$ is at rest and decays into two daughter nuclei of equal mass of $\frac{M}{2}$ each. The speed of light is c, Then speed of daughter nuclei is?

1. $c\frac{\Delta m}{M+\Delta m}$
2. $c\sqrt{\frac{2\Delta m}{M}}$
3. $c\sqrt{\frac{\Delta m}{M+\Delta m}}$
4. $c\sqrt{\frac{\Delta m}{M}}$

Q. In a series LCR circuit $R=200Omega$ and the voltage and the frequency of the main supply is $220$ $V$ and $50$ $Hz$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by ${30}^0$. On taking out the inductor from the circuit the current leads the voltage by ${30}^0$. The power dissipated in the LCR circuit is

1. $305$ $W$
2. $210$ $W$
3. $ZeroW$
4. $242$ $W$

Q. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ${30}^0$ with each other. When suspended in a liquid of density 0.8 $gc{m}^{-3}$, the angle remains the same. lf density of the material of the sphere is 1.6 $gc{m}^{-3}$, the dielectric constant of the liquid is:

1. 3
2. 4
3. 2
4. 1

Q. The binding energy per nucleon for the parent nucleus is $E_1$ and that for the daughter nuclei is $E_2$.Then

1. $E_2=2E_1$
2. $E_1>E_2$
3. $E_2>E_1$
4. $E_1=2E_2$

Q. A rectangular loop has a sliding connector PQ of length $l$ and resistance $R\Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1,I_2$ and $I$ are

1. $I_1=-I_2=\frac{Blv}{R},I=\frac{2Blv}{R}$
2. $I_1=I_2=\frac{Blv}{3R},I=\frac{2Blv}{3R}$
3. $I_1=I_2=I=\frac{Blv}{R}$
4. $I_1=I_2=\frac{Blv}{6R},I=\frac{Blv}{3R}$

Q. For a particle in uniform circular motion the acceleration $\overrightarrow{a}$ at a point $P(R,\theta )$ on the circle of radius $R$ is (here 'v' is the speed of the particle and $\theta$ is measured from the x-axis)

1. $-\frac{v^2}{R}\cos \theta \hat{i}+\frac{v^2}{R}\sin \theta \hat{j}$
2. $-\frac{v^2}{R}\sin \theta \hat{i}+\frac{v^2}{R}\cos \theta \hat{j}$
3. $-\frac{v^2}{R}\cos \theta \hat{i}-\frac{v^2}{R}\sin \theta \hat{j}$
4. $\frac{v^2}{R}\hat{i}+\frac{v^2}{R}\hat{j}$

Q. As the beam enters the medium, it will

1. diverge
2. converge
3. diverge near the axis and converge near the periphery
4. travel as a cylindrical beam

Q. A radioactive nucleus (initial mass number A and atomic number Z) emits $3$ $\alpha$-particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

1. $\frac{A-Z-8}{Z-4}$
2. $\frac{A-Z-4}{Z-8}$
3. $\frac{A-Z-12}{Z-4}$
4. $\frac{A-Z-4}{Z-2}$

Q. The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left(x\right)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where $a$ and $b$ are constants and $x$ is the distance between the atoms. lf the dissociation energy of the molecule is $D=\left[U\right(x=\infty )-U_{atequilibrium}],$ then $D$ is equal to

1. $\frac{b^2}{2a}$
2. $\frac{b^2}{12a}$
3. $\frac{b^2}{4a}$
4. $\frac{b^2}{6a}$

Q. lf a source of power $4kW$ produces ${10}^{20}$ photons/second, the radiation belong to a part of the spectrum called :

1. $X$-rays
2. Ultraviolet rays
3. Microwaves
4. $\gamma -$rays

Q. A diatomic ideal gas is used in a Car engine as the working substance. lf during the adiabatic expansion part of the cycle, volume of the gas increases from $V$ to $32$ $V$ the efficiency of the engine is

1. $0.5$
2. $0.75$
3. $0.25$
4. $0.99$

Q. The equation of a wave on a string of linear mass density $0.04kg{m}^{-1}$ is given by $y=0.02\left(m\right)\sin \left[2\pi (\frac{t}{0.04\left(s\right)}-\frac{x}{0.50\left(m\right)})\right]$. The tension in the string is

1. $0.5N$
2. $6.25N$
3. $4.0N$
4. $12.5N$

Q. The figure shows the position time (x-t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

1. 0.8 Ns
2. 1.6 Ns
3. 0.4 Ns
4. 0.2 Ns

Q. In the circuit shown below, the key K is closed at t = 0. The current through the battery is:

1. $\frac{V{R}_1{R}_2}{\sqrt{R_1^2+R_2^2}}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$
2. $\frac{V}{R_2}$ at $t=0$ and $\frac{V(R_1+R_2)}{R_1{R}_2}$ at $t=\infty$
3. $\frac{V}{R_2}$ at $t=0$ and $\frac{V{R}_1{R}_2}{\sqrt{R_1^2+R_2^2}}$ at $t=\infty$
4. $\frac{V(R_1+R_2)}{R_1{R}_2}$ at $t=0$ and $\frac{V}{R_2}$ at $t=\infty$

Q. Two long parallel wires are at a distance $2d$ apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX' is given by

1. 
   
2. 
   
3. 
   
4. 
   

Q. The respective number of significant figures for the numbers $23.023,0.0003$ and $2.1\times {10}^{-3}$ are :

1. 5, 1, 5
2. 4, 4, 2
3. 5, 1, 2
4. 5, 5, 2

Q. A particle is moving with velocity $\overrightarrow{v}=K(y\hat{i}+x\hat{j})$, where $K$ is a constant. The general equation for its path is :

1. $y=x^2+$ constant
2. $xy=$ constant
3. $y^2=x+$ constant
4. $y^2=x^2+$ constant

Q. Two conductors have the same resistance at $0^{o}C$ but their temperature coefficients of resistance are ${\alpha }_1$ and ${\alpha }_2$. The respective temperature coefficients of their series and parallel combinations are nearly

1. ${\alpha }_1+{\alpha }_2,\frac{{\alpha }_1+{\alpha }_2}{2}$
2. $\frac{{\alpha }_1+{\alpha }_2}{2},{\alpha }_1+{\alpha }_2$
3. ${\alpha }_1+{\alpha }_2,\frac{{\alpha }_1{\alpha }_2}{{\alpha }_1+{\alpha }_2}$
4. $\frac{{\alpha }_1+{\alpha }_2}{2},\frac{{\alpha }_1+{\alpha }_2}{2}$

Q. A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\overrightarrow{E}$ at the centre $O$ is :

1. $\frac{q}{4{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$
2. $-\frac{q}{4{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$
3. $-\frac{q}{2{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$
4. $\frac{q}{2{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$

Q. The combination of gates shown below yields

1. OR gate
2. XOR gate
3. NOT gate
4. NAND gate

Q. A small particle of mass $m$ is projected at an angle $\theta$ with the $x$ axis with an initial velocity $v_0$ in the $xy$ plane as shown in the figure. At a time $t<\frac{v_0\sin \theta }{g}$, the angular momentum of the particle is:
(here $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along $x,y$ and $z$-axis respectively)

1. $-mg{v}_0{t}^2\cos \theta \hat{j}$
2. $-\frac{1}{2}mg{v}_0{t}^2\cos \theta \hat{k}$
3. $\frac{1}{2}mg{v}_0{t}^2\cos \theta \hat{i}$
4. $mg{v}_{0}t\cos \theta \hat{k}$

Q. Let $C$ be the capacitance of a capacitor discharging through a resistor R. Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be

1. $\frac{1}{2}$
2. 1
3. $\frac{1}{4}$
4. 2

Q. A ball is made of a material of density $\rho$ where ${\rho }_{oil}<\rho <{\rho }_{water}$ with ${\rho }_{oil}$ and ${\rho }_{water}$ representing the densities of oil and water, respectively. The oil and water are immiscible. lf the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position ?

1. 
   
2. 
   
3. 
   
4. 
   

Q. Statement-l : When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{max}$. When the ultraviolet light is replaced by X- rays, both $V_0$ and $K_{max}$ increase.
Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

1. Statement-1 is false, Statement-2 is true.
2. Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
3. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
4. Statement-1 is true, Statement-2 is false.

Q. Let there be a spherically symmetric charge distribution with charge density varying as $p\left(r\right)=p_0(\frac{5}{4}-\frac{r}{R})$ upto $r=R$, and $p\left(r\right)=0$ for $r>R$, where $r$ is the distance from the origin. The electric field at a distance $r(r<R)$ from the origin is given by :

1. $\frac{4\pi p_{0}r}{3{ϵ}_0}(\frac{5}{3}-\frac{r}{R})$
2. $\frac{4p_{0}r}{3{ϵ}_0}(\frac{5}{4}-\frac{r}{R})$
3. $\frac{p_{0}r}{4{ϵ}_0}(\frac{5}{4}-\frac{r}{R})$
4. $\frac{p_{0}r}{4{ϵ}_0}(\frac{5}{3}-\frac{r}{R})$

Q. An initially parallel cylindrical beam travels in a medium of refractive index$\mu \left(I\right)={\mu }_0+{\mu }_{2}I$ , where ${\mu }_0$ and ${\mu }_2$ are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The speed of light in the medium is

1. minimum on the axis of the beam
2. the same everywhere in the beam
3. maximum on the axis of the beam
4. directly proportional to the intensity I

Q. An initially parallel cylindrical beam travels in a medium of refractive index $\mu \left(I\right)={\mu }_0+{\mu }_{2}I$, where ${\mu }_0$ and ${\mu }_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The initial shape of the wave front of the beam is

1. Convex
2. Concave
3. Convex near the axis and concave near the periphery
4. Planar