Q. A charge $+q$ is placed at the origin O of $X-Y$ axes as shown in the figure. The work done in taking a charge $Q$ from A to B along the straight line AB is :

1. $\frac{qQ}{4\pi {ϵ}_0}\left(\frac{a-b}{ab}\right)$
2. $\frac{qQ}{4\pi {ϵ}_0}\left(\frac{b-a}{ab}\right)$
3. $\frac{qQ}{4\pi {ϵ}_0}(\frac{b}{a^2}-\frac{1}{b})$
4. $\frac{qQ}{4\pi {ϵ}_0}(\frac{a}{b^2}-\frac{1}{b})$

Q. What is the phase difference between two simple harmonic motions represented by $x_1=A\sin (\omega t+\frac{\pi }{6})$ and $x_2=A\cos \left(\omega t\right)$?

1. $\frac{\pi }{6}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{2}$
4. $\frac{2\pi }{3}$

Q. A particle is projected from the ground with a kinetic energy E at an angle of ${60}^{\circ }$ with the horizontal. Its kinetic energy at the highest point of its motion will be :

1. $\frac{E}{\sqrt{2}}$
2. $\frac{E}{4}$
3. $\frac{E}{2}$
4. $\frac{E}{8}$

Q. What current will flow through the $2k\Omega$ resistor in the circuit shown in the figure?

1. $3mA$
2. $6mA$
3. $12mA$
4. $36mA$

Q. An electric bulb marked as $50W-200V$ is connected across a $100V$ supply. The present power of the bulb is

1. $37.5W$
2. $10W$
3. $12.5W$
4. $25W$

Q. In a mercury thermometer, the ice point (lower fixed point) is marked as ${10}^0$ and the steam point (upper fixed point) is marked as ${130}^0$. At ${40}^{0}C$ temperature, what will this thermometer read?

1. ${78}^0$
2. ${66}^0$
3. ${58}^0$
4. ${62}^0$

Q. The de-Broglie wavelength of an electron moving with a velocity $\frac{c}{2}$ (where c is velocity of light in vacuum) is equal to the wavelength of a photon. The ratio of the kinetic energies of electron and photon is:

1. $2:1$
2. $1:2$
3. $1:1$
4. $1:4$

Q. The decimal number equivalent to a binary number $1011001$ is:

1. $13$
2. $178$
3. $17$
4. $89$

Q. A particle is travelling along a straight line $OX$. The distance $x$ (in metre) of the particle from $O$ at a time ${}^{\prime }{t}^{\prime }$ is given by $x=37+27t-t^3$, where 't' is time in second. The distance of the particle from $O$ , when it comes to rest is:

1. $81m$
2. $111m$
3. $91m$
4. $101m$

Q. A Wheatstone bridge has the resistance $10\Omega ,10\Omega ,10\Omega$ and $30\Omega$ in its four arms. What resistance joined in parallel to $30\Omega$ resistance will bring it to the balanced condition?

1. $2\Omega$
2. $10\Omega$
3. $15\Omega$
4. $5\Omega$

Q. If $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ have scalar magnitudes of $5,4,3$ units respectively, then the angle between $\overrightarrow{A}$ and $\overrightarrow{C}$ is:

1. ${\cos }^{-1}\left(3/5\right)$
2. ${\cos }^{-1}\left(4/5\right)$
3. $\pi /2$
4. ${\sin }^{-1}\left(3/4\right)$

Q. The frequency of the first overtone of a closed pipe of length $l_1$ is equal to that of the first overtone of an open pipe of length $l_2$. The ratio of their lengths $(l_1:l_2)$ is

1. $3:4$
2. $2:3$
3. $4:5$
4. $3:5$

Q. Two element A and B with atomic numbers $Z_A$ and $Z_B$ are used to produce characteristic X-rays with frequencies $v_A$ and $v_B$ respectively. If $Z_A:Z_B=1:2$, then $v_A:v_B$ will be

1. $1:8$
2. $1:4$
3. $4:1$
4. $1:\sqrt{2}$

Q. A box of mass $2kg$ is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. Coefficient of static friction between the box and the roof of the car is $0.2$ and $g=10m{s}^{-2}$. This maximum acceleration of the car, for the box to remain stationary is :

1. $6m{s}^{-2}$
2. $4m{s}^{-2}$
3. $2m{s}^{-2}$
4. $8m{s}^{-2}$

Q. Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as:

1. relative velocity
2. terminal velocity
3. critical velocity
4. particle velocity

Q. If the velocity of light in vacuum is $3\times {10}^{8}m{s}^{-1}$, the time taken (in nanosecond) to travel through a glass plate of thickness $10cm$ and refractive index $1.5$ is :

1. $0.5$
2. $1.0$
3. $2.0$
4. $3.0$

Q. In a slide caliper, $(m+1)$ number of vernier divisions is equal to $m$ number of smallest main scale divisions. If $d$ units is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is:

1. $\frac{d}{m}$ units
2. $\frac{d}{(m+1)}$ units
3. $\frac{md}{(m+1)}$ units
4. $\frac{(m+1)d}{m}$ units

Q. Two infinite parallel metal planes, contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively and they are separated by a small distance in air. If the permittivity of air is ${ϵ}_0$, then the magnitude of the field between the two planes with its direction will be:

1. $\sigma /{ϵ}_0$ towards the positively charge plane
2. $\sigma /{ϵ}_0$ towards the negatively charged plane
3. $\sigma /\left(2{ϵ}_0\right)$ towards the positively charged plane
4. $0$ and towards any direction

Q. Heat is produced at a rate given by $H$ in a resistor when it is connected across a supply of voltage $V$. If now the resistance of the resistor is doubled and the supply voltage is made $V/3$, then the rate of production of heat in the resistor will be

1. $\frac{H}{18}$
2. $6H$
3. $\frac{H}{9}$
4. $18H$

Q. The magnetic flux linked with a coil satisfies the relation $\varphi =4t^2+6t+9$ Wb, where t is the time in second. The emf induced in the coil at $t=2s$ is

1. $18V$
2. $16V$
3. $22V$
4. $40V$

Q. Average distance of the Earth from the Sun is $L_1$. If one year of the Earth is equal to $D$ days, then one year of another planet whose average distance from the Sun is $L_2$ will be:

1. $D{\left(\frac{L_2}{L_1}\right)}^{\frac{1}{2}}days$
2. $D{\left(\frac{L_2}{L_1}\right)}^{\frac{3}{2}}days$
3. $D{\left(\frac{L_2}{L_1}\right)}^{\frac{2}{3}}days$
4. $D\left(\frac{L_2}{L_1}\right)days$

Q. When a spring is stretched by $10cm$, the potential energy stored is E. When the spring is stretched by $10cm$ more, the potential energy store in the spring becomes:

1. $2E$
2. $4E$
3. $6E$
4. $10E$

Q. From the top of a tower, $80m$ high from the ground, a stone is thrown in the horizontal direction with a velocity of $8m{s}^{-1}$. The stone reaches the ground after a time 't' and falls at a distance of 'd' from the foot of the tower.
Assuming $g=10m/s^2$, the time 't' and distance 'd' are given respectively by:

1. $6s,48m$
2. $4s,16m$
3. $4s,32m$
4. $6s,64m$

Q. A straight wire of length $2m$ carries a current of $10A$. If this wire is placed in a uniform magnetic field of $0.15T$ making an angle of ${45}^{\circ }$ with the magnetic field, the applied force on the wire will be:

1. $1.5N$
2. $3\sqrt{2}N$
3. $\frac{3}{\sqrt{2}}N$
4. $3N$

Q. A spherical ball A of mass $4kg$, moving along a straight line strikes another spherical ball B of mass $1kg$ at rest. After the collision, A and B move with velocities $v_{1}m{s}^{-1}$ and $v_{2}m{s}^{-1}$ respectively making angles of ${30}^{\circ }$ and ${60}^{\circ }$ with respect to the original direction of motion of ball A. The ratio $\frac{v_1}{v_2}$ will be:

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

Q. In a region, the intensity of an electric field is given by $E=2i+3j+k$ in $N{C}^{-1}$. The electric flux through a surface $S=10i{m}^2$ in the region is:

1. $10N{m}^2{C}^{-1}$
2. $5N{m}^2{C}^{-1}$
3. $20N{m}^2{C}^{-1}$
4. $15N{m}^2{C}^{-1}$

Q. The $I-V$ characteristics of a metal wire at two different temperatures $(T_1$ and $T_2)$ are given in the adjoining figure. Here, we can conclude that:

1. $T_1>T_2$
2. $T_1=T_2$
3. $T_1=2T_2$
4. $T_1<T_2$

Q. A bullet on penetrating $30cm$ into its target loses its velocity by $50$%. What additional distance will it penetrate into the target before it comes to rest?

1. $30cm$
2. $10cm$
3. $20cm$
4. $5cm$

Q. A train approaching a railway platform with a speed of $20m{s}^{-1}$, starts blowing the whistle. Speed of sound in air is $340m{s}^{-1}$. If the frequency of the emitted sound from the whistle is $640Hz$, the frequency of sound to a person standing on the platform will appear to be:

1. $600Hz$
2. $680Hz$
3. $720Hz$
4. $640Hz$

Q. The dimension of angular momentum is

1. $\left[M^1{L}^2{T}^{-2}\right]$
2. $\left[M^0{L}^1{T}^{-1}\right]$
3. $\left[M^1{L}^2{T}^{-1}\right]$
4. $\left[M^2{L}^1{T}^{-2}\right]$