1 A light wave of wavelength $\lambda$ is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at a distance of D. If the linear width of the principal maxima is equal to the width of the slit, then the distance D is A) $\frac{2\lambda}{d}$ B) $\frac{d^{2}}{2\lambda}$ C) $\frac{2\lambda^{2}}{d}$ D) $\frac{d^{}}{\lambda}$
2 A radioactive nucleus emits 4 $\alpha$ -particles and 7 $\beta$-particles in succession. The ratio of number of neutrons of that of protons is [A= mass number, Z= atomic number] A) $\frac{A-Z-13}{Z-2}$ B) $\frac{A-Z-15}{Z-1}$ C) $\frac{A-Z-13}{Z-1}$ D) $\frac{A-Z-11}{Z-2}$
3 An obstacle is moving towards the source with velocity v. The sound is reflected from the obstacle. If c is the speed of sound and $\lambda$ is the wavelength, then the wavelength of the reflected wave, $\lambda_{r}$is A) $\lambda_{r}=\left(\frac{C-V}{C+V}\right)\lambda$ B) $\lambda_{r}=\left(\frac{C+V}{C-V}\right)\lambda$ C) $\lambda_{r}=\left(\frac{C-V}{C}\right)\lambda$ D) $\lambda_{r}=\left(\frac{C+V}{C}\right)\lambda$
4 In a communication system, a repeater is used to extend the range to transmission. It is the combination of A) IF stage and amplifier B) rectifier and detector C) recevier and transmitter D) modulator and power amplifier
5 The light of wavelength $\lambda$ incident on the surface of metal having work function $\phi$ emits the electrons. The maximum velocity of electrons emitted is [c= velocity of light, h= planck's constant, m= mass of electron] A) $\left[\frac{2(hv-\phi)\lambda}{mc}\right]$ B) $\left[\frac{2(hc-\lambda\phi)}{m\lambda}\right]^{1/2}$ C) $\left[\frac{2(hc-\lambda)}{m\lambda}\right]^{1/2}$ D) $\left[\frac{2(hc-\phi)}{m\lambda}\right]^{}$
6 A large open tank containing water has two holes to its wall. A square hole of side a is made at a depth of y and a circular hole of radius r is made at a depth of 16 y from the surface of the water. If an equal amount of water comes out through both the holes per second, then the relation between r and a will be A) $r=\frac{a}{2\sqrt{\pi}}$ B) $r=\frac{a}{2\pi}$ C) $r=\frac{2a}{\pi}$ D) $r=\frac{2a}{\sqrt{\pi}}$
7 A spherical rubber balloon carries a charge, uniformly distributed over the surface. As the balloon is blown up and increase in size. The total electric flux coming out of the surface A) increases B) remains unchanged C) becomes zero D) decreases
8 A absolute zero temperature, pure silicon behaves as A) non-metal B) insulator C) metal D) extrinsic semiconductor
9 Five capacitors each of capacity C are connected as shown in the figure. If their resultant capacity is 2 $\mu$ F, then the capacity of each condenser is A) 5 $\mu$ F B) 2 $\mu$ F C) 2.5 $\mu$ F D) 10 $\mu$ F
10 In conversion of moving coil galvanometer into an ammeter of required range, the resistance of ammeter , so formed is [ S= shunt and G= resistance of galvanometer] A) $\frac{S+G}{SG}$ B) $\frac{SG}{S+G}$ C) $\frac{S-G}{SG}$ D) $\frac{SG}{S-G}$
11 In the system of two particles of masses m1 and m2, the first particle is moved by a distance d towards the centre of mass.To keep the centre of mass unchanged, the second particle will have to be moved by a distance A) $\frac{m_{2}}{m_{1}}d,$ towards the centre of mass B) $\frac{m_{1}}{m_{2}}d,$ away fron the centre of mass C) $\frac{m_{1}}{m_{2}}d,$ towards the centre of mass D) $\frac{m_{2}}{m_{1}}d,$ away from the centre of mass
12 The graph of stopping potential Vs against frequency v of incident radiation is plotted for two different metals P and Q as shown in the graph, $\phi_{P}$ and $\phi_{Q}$ are work-functions of P and Q respectively, then A) $\phi_{P} > \phi_{Q}$ B) $\phi_{P} < \phi_{Q}$ C) $\phi_{P} = \phi_{Q}$ D) $v_{0} ' < v_{0}$
13 The angle subtended by the vector $A=4\hat{i}+3\hat{j}+12\hat{k}$ with the X-axis is A) $\cos^{-1}\left(\frac{3}{13}\right)$ B) $\sin^{-1}\left(\frac{3}{13}\right)$ C) $\sin^{-1}\left(\frac{4}{13}\right)$ D) $\cos^{-1}\left(\frac{4}{13}\right)$
14 Two bodies A and B of equal mass are suspended from two separate massless springs of force constant k1 and k2, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body A to that of body B is A) $\sqrt{\frac{k_{2}}{k_{1}}}$ B) $\frac{k_{2}}{k_{1}}$ C) $\frac{k_{1}}{k_{2}}$ D) $\sqrt{\frac{k_{1}}{k_{2}}}$
15 A uniform wire has length L mass M and density $\rho$ . it is under tension T and v is the speed of transverse wave along the wire. The area of cross-section of the wire is A) $\frac{T}{v^{2}\rho}$ B) $\frac{v^{2}\rho}{T^{2}}$ C) $T^{2}v^{}\rho$ D) $T^{}v^{2}\rho$
