Q. The de-Broglie wavelength of an electron in $4^{th}$ orbit is ________. ($r=$ radius of $1^{st}$ orbit)

1. $4\pi r$
2. $2\pi r$
3. $8\pi r$
4. $16\pi r$

Q. In electromagnetic spectrum, the frequencies of $\gamma$-rays, X-rays and ultraviolet rays are denoted by $n_1,n_2$ and $n_3$ respectively. Then

1. $n_1>n_2<n_3$
2. $n_1<n_2<n_3$
3. $n_1<n_2>n_3$
4. $n_1>n_2>n_3$

Q. Two coherent sources of intensity ratio '$\alpha$' interfere. In interference pattern $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=$

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

Q. Gases exert pressure on the walls of the container because the gas molecules

1. obey Boyle's law
2. have finite volume
3. possess momentum
4. collide with one another

Q. Magnetic induction produced at the centre of a circular loop carrying current is 'B'. The magnetic moment of the loop of radius 'R' is______. (${\mu }_0=$ permeability of free space)

1. $\frac{B{R}^3}{2\pi {\mu }_0}$
2. $\frac{2\pi B{R}^3}{{\mu }_0}$
3. $\frac{2\pi B{R}^2}{{\mu }_0}$
4. $\frac{B{R}^2}{2\pi {\mu }_0}$

Q. A particle at rest is moved along a straight line by a machine giving constant power. The distance moved by the particle in time 't' is proportional to :

1. $t^{1/2}$
2. $t^{2/3}$
3. $t$
4. $t^{3/2}$

Q. A plane light wave travelling with velocity '$v$' in a medium A reaches a point on the interface of medium A and medium B. If velocity of sound in medium B is $2v$, the angle of incidence for total internal reflection of the wave will be greater than _____. $(\sin {30}^o=0.5$ and $\sin {90}^o=1)$

1. ${15}^o$
2. ${30}^o$
3. ${45}^o$
4. ${90}^o$

Q. In air, a charged soap bubble of radius 'r' is in equilibrium having outside and inside pressures being equal. The charge on the bubble is ______.

1. $4\pi r^2\sqrt{\frac{2T{ϵ}_0}{r}}$
2. $4\pi r^2\sqrt{\frac{4T{ϵ}_0}{r}}$
3. $4\pi r^2\sqrt{\frac{6T{ϵ}_0}{r}}$
4. $4\pi r^2\sqrt{\frac{8T{ϵ}_0}{r}}$

Q. In electromagnetic wave, according to Maxwell, changing electric field gives _______.

1. conduction current
2. stationary magnetic field
3. displacement current
4. eddy current

Q. The ratio of magnetic dipole moment of an electron of charge 'e' and mass 'm' in Bohr's orbit in hydrogen atom to its angular momentum is

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

Q. In vacuum, to travel distance 'd', light takes time 't' and in a medium to travel distances '$5d$', it takes time 'T'. The critical angle of the medium is

1. ${\sin }^{-1}\left(\frac{5T}{t}\right)$
2. ${\sin }^{-1}\left(\frac{3t}{5T}\right)$
3. ${\sin }^{-1}\left(\frac{5t}{3T}\right)$
4. ${\sin }^{-1}\left(\frac{5t}{T}\right)$

Q. An object of radius 'R' and mas 'M' is rolling horizontally without slipping with speed 'V'. It the rolls up the hill to a maximum height $h=3v^2/4g$. The moment of inertia of the object is:

1. $\frac{2}{5}M{R}^2$
2. $\frac{M{R}^2}{2}$
3. $M{R}^2$
4. $\frac{3}{2}M{R}^2$

Q. If 'N' is the number of turns in a circular coil then the value of self inductance varies as

1. $N^0$
2. N
3. $N^2$
4. $N^{-2}$

Q. In common base circuit of a transistor, current amplification factor is $0.95$. Calculate the emitter current if base current is $0.2$mA.

1. $2$mA
2. $4$mA
3. $6$mA
4. $8$mA

Q. A block is pushed momentarily on a horizontal surface with initial velocity $v$. If $\mu$ is the coefficient of sliding friction between the block and surface, the block will come to rest after time ______.

1. $\frac{v}{\mu g}$
2. $\frac{vg}{\mu }$
3. $\frac{v\mu }{g}$
4. $\frac{\mu g}{v}$

Q. Surface density of charge on a sphere of radius $R$ in terms of electricity intensity $E$ at a distance $r$ in free space is ________.

1. ${ϵ}_{0}E{\left(\frac{R}{r}\right)}^2$
2. $\frac{{ϵ}_{0}ER}{r^2}$
3. ${ϵ}_{0}E{\left(\frac{r}{R}\right)}^2$
4. $\frac{{ϵ}_{0}Er}{R^2}$

Q. A gas is compressed isothermally. The r.m.s velocity of its molecules ______.

1. increases
2. decreases
3. remains the same
4. first increases and then decreases

Q. In insulators________. (C.B is conduction band and V.B is valence band)

1. V.B. is partially filled with electrons
2. C.B. is partially filled with electrons
3. C.B. is filled with electrons and V.B. is empty
4. C.B. is empty and V.B. is filled with electrons

Q. In Wheatstone's bridge, three resistors P, Q, R are connected in three arms in order and $4^{th}$ arm S is formed by two resistors $s_1$ and $s_2$ connected in parallel. The condition for bridge to be balanced is: $\frac{P}{Q}=$

1. $\frac{R(s_1+s_2)}{s_1{s}_2}$
2. $\frac{R{s}_1{s}_2}{(s_1+s_2)}$
3. $\frac{s_1{s}_2}{R(s_1+s_2)}$
4. $\frac{(s_1+s_2)}{R{s}_1{s}_2}$

Q. A string of length 'L' and force constant 'K' is stretched to obtain extension '$l$'. It is further stretched to obtain extension '$l_1$'. The work done in second stretching is

1. $\frac{1}{2}K{l}_1(2l+l_1)$
2. $\frac{1}{2}K{l}_1^2$
3. $\frac{1}{2}K(l^2+l_1^2)$
4. $\frac{1}{2}K(l_1^2-l^2)$

Q. A block resting on the horizontal surface executes S.H.M in horizontal plane with amplitude 'A'. The frequency of oscillation for which the block just starts to slip is ________.

1. $\frac{1}{2\pi }\sqrt{\frac{\mu g}{A}}$
2. $2\pi \sqrt{\frac{A}{\mu g}}$
3. $4\pi \sqrt{\frac{A}{\mu g}}$
4. $\frac{1}{4\pi }\sqrt{\frac{\mu g}{A}}$

Q. Light of wavelength ${\lambda }_A$ and ${\lambda }_B$ falls on two identical metal plates A and B respectively. The maximum kinetic energy of photo-electrons in $K_A$ and $K_B$ respectively, then which one of the following relations is true? $({\lambda }_A=2{\lambda }_B)$

1. $K_A<\frac{K_B}{2}$
2. $2K_A=K_B$
3. $K_A=2K_B$
4. $K_A>2K_B$

Q. The equiconvex lens has focal length 'f'. If it is cut perpendicular to the principal axis passing through optical centre, then focal length of each half is :

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

Q. A body at rest starts sliding from top of a smooth inclined plane and requires $4$ seconds to reach bottom. How much time does it take, starting from rest at top, to cover one-fourth of a distance?

1. $1$ second
2. $2$ seconds
3. $3$ seconds
4. $4$ seconds

Q. In LCR series circuit, an alternating e.m.f. 'e' and current 'i' are given by the equations $e=100\sin \left(100t\right)$volt, $i=100\sin (100+\frac{\pi }{3})$mA. The average power dissipated in the circuit will be

1. $2.5$W
2. $100$W
3. $10$W
4. $5$W

Q. In cyclotron, for a given magnet, radius of the semicircle traced by positive ion is directly proportional to__________. (v=velocity of positron ion)

1. $v^{-2}$
2. $v^{-1}$
3. $v^2$
4. $v$
   

Q. Two concentric spheres kept in air have radii 'R' and 'r'. They have similar charge and equal surface charge density '$\sigma$'. The electric potential at their common centre is ______. (${ϵ}_0=$permittivity of free space)

1. $\frac{\sigma (R-r)}{{ϵ}_0}$
2. $\frac{\sigma (R+r)}{{ϵ}_0}$
3. $\frac{\sigma (R+r)}{2{ϵ}_0}$
4. $\frac{\sigma (R+r)}{4{ϵ}_0}$

Q. If an electron in hydrogen atom jumps from an orbit of level $n=3$ to an orbit of level $n=2$, emitted radiation has a frequency_______.

1. $\frac{3RC}{27}$
2. $\frac{RC}{25}$
3. $\frac{5RC}{36}$
4. $\frac{8RC}{9}$

Q. The velocity of water in river is $9km/hr$ of the upper surface. The river is $10m$ deep. If the coefficient of viscosity of water is ${10}^{-2}poise$, then the shearing stress between horizontal layers of water is

1. $0.25\times {10}^{-2}N/m^2$
2. $0.25\times {10}^{-3}N/m^2$
3. $0.5\times {10}^{-3}N/m^2$
4. $0.75\times {10}^{-3}N/m^2$

Q. A sphere 'P' of mass 'm' moving with velocity 'u' collides head-on with another sphere 'Q' of mass 'm' which is at rest. The ratio of final velocity of 'Q' to initial velocity of 'P' is ______. (e= coefficient of restitution)

1. $\frac{e-1}{2}$
2. ${\left[\frac{e+1}{2}\right]}^{1/2}$
3. ${\left[\frac{e+1}{2}\right]}^2$
4. $\frac{e+1}{2}$