Q. A proton and an alpha particle are accelerated under the same potential difference. The ratio of de-Broglie wavelengths of the proton and the alpha particle is

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

Q. Mass numbers of the elements $A$, $B$, $C$ and $D$ are $30$, $60$, $90$ and $120$ respectively. The specific binding energy of them are $5MeV$, $8.5MeV$, $8MeV$ and $7MeV$ respectively. Then, in which of the following reaction/s energy is released?
(a) $D\to 2B$
(b) $C\to B+A$
(c) $B\to 2A$

1. Only in (a)
2. In (b), (c)
3. In (a), (c)
4. In (a), (b) and (c)

Q. In this diagram, the potential difference between $A$ and $B$ is $60V$. The potential difference across $6\mu F$ capacitor is _______ $V$.

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

Q. A person throws balls into air vertically upward in regular intervals of time of one second. The next ball is thrown when the velocity of the ball thrown earlier becomes zero. The height to which the balls rise is _____
(Assume, $g=10m{s}^{-2}$)

1. $5m$
2. $10m$
3. $20m$
4. $7.5m$

Q. In the uniform electric field of $E=1\times {10}^{4}N{C}^{-1}$, an electron is accelerated from rest. The velocity of the electron when it has travelled a distance of $2\times {10}^{-2}m$ is nearly ________ $m{s}^{-1}$ $(\frac{e}{m}$ of electron $\simeq 1.8\times {10}^{11}C{kg}^{-1}$)

1. $1.6\times {10}^6$
2. $0.85\times {10}^6$
3. $0.425\times {10}^6$
4. $8.5\times {10}^6$

Q. In the circuit, the value of $I_2$ is

1. $0.2A$
2. $0.3A$
3. $0.4A$
4. $0.6A$

Q. Copper and Germanium are cooled from room temperature to $100K$. Then the resistance of

1. Germanium decreases, Copper increases
2. Germanium decreases, Copper decreases
3. Germanium increases, Copper decreases
4. Germanium increases, Copper increases

Q. Spectrum of sunlight is an example for

1. Band emission spectrum
2. Continuous emission spectrum
3. Line absorption spectrum
4. Continuous absorption spectrum

Q. One mole of an ideal gas is taken from $A$ to $B$, from $B$ to $C$ and then back to $A$. The variation of its volume with temperature for that change is as shown. Its pressure at $A$ is $P_0$, volume is $V_0$. Then, the internal energy

1. At $A$ is more than at $B$
2. At $C$ is less than at $B$
3. At $A$ and $B$ are equal
4. At $B$ is more than at $A$

Q. For sustained interference fringes in double slit experiment, essential condition/s is/are
(a) sources must be coherent
(b) the intensities of the two sources must be equal
Here, the correct option/s is/are

1. Both (a) (b)
2. Only (a)
3. Only (b)
4. Neither (a) nor (b)

Q. A point source of light is kept below the surface of water $(n_w=4/3)$ at a depth of $\sqrt{7}m$. The radius of the circular bright patch of light noticed on the surface of water is ______ $m$.

1. $\frac{3}{\sqrt{7}}$
2. $3$
3. $\frac{\sqrt{7}}{3}$
4. $\sqrt{7}$

Q. In single slit experiment, the width of the slit is reduced. Then, the linear width of the principal maxima ________

1. increases but becomes less bright.
2. decreases but becomes more bright.
3. increases but becomes more bright.
4. decreases but becomes less bright.

Q. Decay constants of two radio-active samples $A$ and $B$ are $15x$ and $3x$ respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in $A$ and $B$ after a time $\frac{1}{6x}$ is

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

Q. Which of the following is incorrect?

1. If the wave is longitudinal, it must be a mechanical wave
2. If the wave is mechanical, it may OR may not be a transverse wave
3. Mechanical waves cannot propagate in vacuum
4. 'Diffraction' helps us to distinguish between sound wave and light wave

Q. Pick out the WRONG statement.

1. The gain in the K.E. of the electron moving at right angles to the magnetic field is zero
2. When an electron is shot at right angles to the electric field, it traces a parabolic path
3. An electron moving in the direction of the electric field gains K.E.
4. An electron at rest experiences no force in the magnetic field

Q. Intensity level of sound whose intensity is ${10}^{-8}w{m}^{-2}$ is ______ dB.

1. $8$
2. $4$
3. $40$
4. $80$

Q. The circular motion of a particle with constant speed is

1. Periodic but not SHM
2. SHM but not periodic
3. Periodic and also SHM
4. Neither periodic nor SHM

Q. In hydrogen atom, electron excites from ground state to higher energy state and its orbital velocity is reduced to $\frac{1}{3^{rd}}$ of its initial value. The radius of the orbit in the ground state is $R$. The radius of the orbit in that higher energy state is:

1. $2R$
2. $27R$
3. $3R$
4. $9R$

Q. A monochromatic beam of light is travelling from medium $A$ of refractive index $n_1$ to a medium $B$ of refractive index $n_2$. In the medium $A$, there are $x$ number of waves in certain distance. In the medium $B$, there are $y$ number of waves in the same distance. Then, refractive index of medium $A$ with respect to medium $B$ is _______.

1. $\frac{y}{x}$
2. $\sqrt{\frac{x}{y}}$
3. $\frac{x}{y-x}$
4. $\frac{x}{y}$

Q. A planet moving around sun sweeps area $A_1$ in $2$ days, $A_2$ in $3$ days and $A_3$ in $6$ days. Then the relation between $A_1,A_2$ and $A_3$ is:

1. $2A_1=3A_2=6A_3$
2. $3A_1=2A_2=6A_3$
3. $6A_1=3A_2=2A_3$
4. $3A_1=2A_2=A_3$

Q. Frequencies of light incident on a system of scattering particles are in the ratio of $1:2$. Then, the intensity of scattered light in a particular direction is:

1. $1:4$
2. $1:2$
3. $1:8$
4. $1:16$

Q. Fill in the blank.

1. ${71}^{o}C$
2. ${29}^{o}C$
3. ${63}^{o}C$
4. ${37}^{o}C$

Q. In this circuit, when certain current flows, the heat produced in $5\Omega$ is $4.05J$ in a time $t$. The heat produced in $2\Omega$ coil in the same time interval is

1. $1.44$
2. $2.88$
3. $2.02$
4. $5.76$

Q. The most stable particle in the Baryon group is

1. Neutron
2. Sigma particle
3. Lambda particle
4. Proton

Q. A straight current carrying conductor is kept along the axis of circular loop carrying current. The force exerted by the straight conductor on the loop is _______

1. perpendicular to the plane of the loop.
2. on the plane of the loop, towards the center.
3. in the plane of the loop, away from the center.
4. zero.

Q. Milk is an example for:

1. inelastic gel
2. foam
3. elastic gel
4. emulsion

Q. The dimensional formula of physical quantity is $M^a{L}^b{T}^c$. Then that physical quantity is

1. Surface tension if $a=1,b=1,c=-2$
2. Angular frequency if $a=0,b=0,c=-1$
3. Force if $a=1,b=1,c=2$
4. Spring constant if $a=1,b=-1,c=-2$

Q. A resistor of $500\Omega$, an inductance of $0.5H$ are in series with an a.c. which is given by $V=100\sqrt{2}\sin \left(1000t\right)$. The power factor of the combination is

1. $0.5$
2. $0.6$
3. $\frac{1}{\sqrt{2}}$
4. $\frac{1}{\sqrt{3}}$

Q. The ratio of the magnetic dipole moment to the angular momentum of the electron in the $1^{st}$ orbit of hydrogen atom is

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

Q. In Young's double slit experiment, fringes of width $\beta$ are produced on a screen kept at a distance of $1m$ from the slit. When the screen is moved away by $5\times {10}^{-2}m$, fringe width changes by $3\times {10}^{-5}m$. The separation between the slits is $1\times {10}^{-3}m$. The wavelength of the light used is ________ $nm$.

1. $500$
2. $600$
3. $400$
4. $700$