If in the circuit, power dissipation is 150 W, then $R$ is
(1) $2\,\Omega$
(2) $6\,\Omega$
(3) $5\,\Omega$
(4) $4\,\Omega$

If in a circular coil $A$ of radius $R$, current $I$ is flowing and in another coil $B$ of radius $2R$ a current $2I$ is flowing, then the ratio of the magnetic fields $\mathrm{B}_A$ and $\mathrm{B}_B$, produced by them will be
(1) 1
(2) 2
(3) $1/2$
(4) 4

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its
(1) speed
(2) mass
(3) charge
(4) magnetic induction

A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. A magnetic induction $B$ constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field. The induced emf is
(1) zero
(2) $RvB$
(3) $VBL/R$
(4) $VBL$

The inductance between A and D is
(1) 3.66 H
(2) 9 H
(3) 0.66 H
(4) 1 H

The power factor of an AC circuit having resistance ($R$) and inductance ($L$) connected in series and an angular velocity $\omega$ is
(1) $R/\omega L$
(2) $R/(R^2 + \omega^2 L^2)^{1/2}$
(3) $\omega L/R$
(4) $R/(R^2 - \omega^2 L^2)^{1/2}$

In a transformer, number of turns in the primary coil are 140 and that in the secondary coil are 280. If current in primary coil is 4 A, then that in the secondary coil is
(1) 4 A
(2) 2 A
(3) 6 A
(4) 10 A

Wavelength of light used in an optical instrument are $\lambda_1 = 4000\,\AA$ and $\lambda_2 = 5000\,\AA$, then ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$) is
(1) $16 : 25$
(2) $9 : 1$
(3) $4 : 5$
(4) $5 : 4$

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of the wavelengths is nearest to
(1) $1 : 2$
(2) $4 : 1$
(3) $2 : 1$
(4) $1 : 4$

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $n = 2$ is
(1) 10.2 eV
(2) 0 eV
(3) 3.4 eV
(4) 6.8 eV

If $\mathrm{N}_0$ is the original mass of the substance of half-life period $\mathrm{t}_{1/2} = 5$ years, then the amount of substance left after 15 years is
(1) $\mathrm{N}_0/8$
(2) $\mathrm{N}_0/16$
(3) $\mathrm{N}_0/2$
(4) $\mathrm{N}_0/4$

Uncertainty in position of a minute particle of mass 25 g in space is $10^{-5}\mathrm{~m}$. What is the uncertainty in its velocity (in $\mathrm{ms}^{-1}$)? ($\mathrm{h} = 6.6 \times 10^{-34}\,\mathrm{Js}$)
(1) $2.1 \times 10^{-34}$
(2) $0.5 \times 10^{-34}$
(3) $2.1 \times 10^{-28}$
(4) $0.5 \times 10^{-23}$

Consider the following two statements: (A) Linear momentum of a system of particles is zero (B) Kinetic energy of a system of particles is zero Then
(1) $A$ does not imply $B$ and $B$ does not imply $A$
(2) $A$ implies $B$ but $B$ does not imply $A$
(3) $A$ does not imply $B$ but $B$ implies $A$
(4) $A$ implies $B$ and $B$ implies $A$

A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$, and another disc $Y$ of radius 4R is made from an iron plate of thickness $\frac{t}{4}$. Then the relation between the moment of inertia $\mathrm{I}_{\mathrm{X}}$ and $\mathrm{I}_{\mathrm{Y}}$ is
(1) $\mathrm{I}_{\mathrm{Y}} = 32\mathrm{I}_{\mathrm{x}}$
(2) $\mathrm{I}_{\mathrm{Y}} = 16\mathrm{I}_{\mathrm{X}}$
(3) $\mathrm{I}_{\mathrm{Y}} = \mathrm{I}_{\mathrm{X}}$
(4) $\mathrm{I}_{\mathrm{Y}} = 64\mathrm{I}_{\mathrm{X}}$

A particle performing uniform circular motion has angular frequency is doubled \& its kinetic energy halved, then the new angular momentum is
(1) $\frac{\mathrm{L}}{4}$
(2) 2L
(3) 4L
(4) $\frac{\mathrm{L}}{2}$

Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$ and $\vec{T}$ be the torque of this force about the origin. Then
(1) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} = 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} \neq 0$
(2) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} \neq 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} = 0$
(3) $\vec{r} \cdot \vec{T} \neq 0$ and $\vec{F} \cdot \vec{T} \neq 0$
(4) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} = 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} = 0$

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become
(1) 10 hours
(2) 80 hours
(3) 40 hours
(4) 20 hours

Two spherical bodies of mass $M$ and $5M$ \& radii $R$ \& $2R$ respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
(1) 2.5 R
(2) 4.5 R
(3) 7.5 R
(4) 1.5 R

The escape velocity for a body projected vertically upwards from the surface of earth is $11 \mathrm{~km/s}$. If the body is projected at an angle of $45^{\circ}$ with the vertical, the escape velocity will be
(1) $11\sqrt{2} \mathrm{~km/s}$
(2) $22 \mathrm{~km/s}$
(3) $11 \mathrm{~km/s}$
(4) $\frac{11}{\sqrt{2}} \mathrm{~km/s}$

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_{p}/C_{v}$ for the gas is
(1) $\frac{4}{3}$
(2) 2
(3) $\frac{5}{3}$
(4) $\frac{3}{2}$

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes $\frac{5\mathrm{~T}}{3}$. Then the ratio of $\frac{m}{M}$ is
(1) $\frac{3}{5}$
(2) $\frac{25}{9}$
(3) $\frac{16}{9}$
(4) $\frac{5}{3}$

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constant $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is
(1) $\sqrt{\frac{\mathrm{k}_{1}}{\mathrm{k}_{2}}}$
(2) $\frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}$
(3) $\sqrt{\frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}}$
(4) $\frac{\mathrm{k}_{1}}{\mathrm{k}_{2}}$

The displacement of a particle varies according to the relation $x = 4(\cos\pi t + \sin\pi t)$. The amplitude of the particle is
(1) $-4$
(2) $4$
(3) $4\sqrt{2}$
(4) $8$

A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy (T.E) are measured as a function of displacement $x$. Which of the following statements is true?
(1) K.E. is maximum when $x = 0$
(2) T.E is zero when $x = 0$
(3) K.E is maximum when x is maximum
(4) P.E. is maximum when $x = 0$

The displacement $y$ of a wave travelling in the $x$-direction is given by $y = 10^{-4}\sin\left(600t - 2x + \frac{\pi}{3}\right)$ metres where x is expressed in metres and t in seconds. The speed of the wave-motion, in $\mathrm{ms}^{-1}$, is
(1) 300
(2) 600
(3) 1200
(4) 200