Length of a string tied to two rigid supports is 40 cm. Maximum length (wave length in cm) of a stationary wave produced on it is
(1) 20
(2) 80
(3) 40
(4) 120

Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube $A$ and $B$ is
(1) $1 : 2$
(2) $1 : 4$
(3) $2 : 1$
(4) $4 : 1$

A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2 beats/sec. The frequency of the unknown fork is
(1) 286 cps
(2) 292 cps
(3) 294 cps
(4) 288 cps

A wave $y = a\sin(\omega t - kx)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is
(1) $y = a\sin(\omega t + kx)$
(2) $y = -a\sin(\omega t + kx)$
(3) $y = a\sin(\omega t - kx)$
(4) $y = -a\sin(\omega t - kx)$

On moving a charge of 20 coulombs by $2\mathrm{~cm}$, $2\mathrm{~J}$ of work is done, then the potential difference between the points is
(1) 0.1 V
(2) 8 V
(3) 2 V
(4) 0.5 V

If a charge $q$ is placed at the centre of the line joining two equal charges $Q$ such that the system is in equilibrium then the value of $q$ is
(1) $Q/2$
(2) $-Q/2$
(3) $Q/4$
(4) $-Q/4$

If there are $n$ capacitors in parallel connected to $V$ volt source, then the energy stored is equal to
(1) $CV$
(2) $\frac{1}{2}\mathrm{n}CV^2$
(3) $CV^2$
(4) $\frac{1}{2n}CV^2$

Capacitance (in $F$) of a spherical conductor with radius 1 m is
(1) $1.1 \times 10^{-10}$
(2) $10^{-6}$
(3) $9 \times 10^{-9}$
(4) $10^{-3}$

A wire when connected to 220 V mains supply has power dissipation $\mathrm{P}_1$. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_2$. Then $P_2 : P_1$ is
(1) 1
(2) 4
(3) 2
(4) 3

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) $0.5 \times 10^{-23}$

A car, moving with a speed of $50 \mathrm{~km} / \mathrm{hr}$, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of $100 \mathrm{~km} / \mathrm{hr}$, the minimum stopping distance is
(1) 12 m
(2) 18 m
(3) 24 m
(4) 6 m

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) $\frac{\mathrm{L}}{2}$