Q. The ratio of the vapour densities of two gases at a given temperature is $9:8$. The ratio of the rms velocities of their molecules is

1. $3:2\sqrt{2}$
2. $2\sqrt{2}:3$
3. $9:8$
4. $8:9$

Q. If Young's double slit experiment of light, interference is performed in water, which one of the following is correct?

1. Fringe width will increase
2. Fringe width will decrease
3. There will be no fringe
4. Fringe width will remain unchanged

Q. Two trains, each moving with a velocity of $30{ms}^{-1}$, cross each other. One of the trains gives a whistle whose frequency is $600Hz$. If the speed of sound is $330{ms}^{-1}$, the apparent frequency for passengers sitting in the other train before crossing would be

1. $920Hz$
2. $600Hz$
3. $630Hz$
4. $720Hz$

Q. During the ${\beta }^{-}$ decay

1. An atomic electron is ejected
2. An electron, already present within the nucleus, is ejected
3. A proton in the nucleus decays emitting an electron
4. A neutron in the nucleus decays emitting an electron

Q. If a simple pendulum of length $L$ has maximum angular displacement $\alpha$ then the maximum kinetic energy of bob of mass $M$ is

1. $\frac{1}{2}\frac{ML}{g}$
2. $\frac{Mg}{2L}$
3. $MgL(1-\cos \alpha )$
4. $\frac{MgL\sin \alpha }{2}$

Q. A ray of light strikes a materials slab at an angle of incidence $${ 60 }^{ o }$$. If the reflected and refracted rays are perpendicular to each other, the refractive index of the material is

Q. A black body at a high temperature $T$ radiates energy at the rate of $U\left(inW/m^2\right)$. When the temperature falls to half (i.e $T/2$), the radiated energy $\left(inW/m^2\right)$ will be

1. $U/16$
2. $U/4$
3. $U/8$
4. $U/2$

Q. A spherical shell of radius $R$ has a change $+q$ units. The electric field due to the shell at a point

1. Inside is constant and varies as $r^{-2}$ outside it
2. Inside is zero and varies as $r^{-1}$ outside it
3. Inside is zero and varies as $r^{-2}$ outside it
4. Inside is constant and varies as $r^{-1}$ outside it

Q. For an object thrown at ${45}^o$ to horizontal, the maximum height ($H$) and horizontal range ($R$) are related are

1. $R=16H$
2. $R=8H$
3. $R=2H$
4. $R=4H$

Q. $R,L$ and $C$ represent the physical quantities resistance, inductance and capacitance respectively. Which one of the following combination has dimensions of frequency?

1. $\frac{1}{\sqrt{RC}}$
2. $\frac{R}{L}$
3. $\frac{1}{LC}$
4. $\frac{C}{L}$

Q. A particle starts from rest at $t=0$ and undergoes an acceleration $a$ in $m{s}^{-2}$ with time $t$ in seconds which is as shown.
Which one of the following plot represents velocity $v$ in $m{s}^{-1}$ versus time $t$ in seconds?

1. 
   
2. 
   
3. 
   
4. 
   

Q. The water flows from a tap of diameter $1.25cm$ with a rate of $5\times {10}^{-5}{m}^3{s}^{-1}$. The density and coefficient of viscosity of water are ${10}^{3}kg{m}^{-3}$ and ${10}^{-3}Pas$ respectively. The flow of water is

1. Steady with Reynold's number $5100$
2. Turbulent with Reynold's number $5100$
3. Turbulent with Reynold's number $3900$
4. Steady with Reynold's number $3900$

Q. The escape velocity of $10g$ body from the earth is $11.2km{s}^{-1}$. Ignoring air resistance, the escape velocity of $10kg$ of the iron ball from the earth will be

1. $0.0112km{s}^{-1}$
2. $0.56km{s}^{-1}$
3. $11.2km{s}^{-1}$
4. $0.112km{s}^{-1}$

Q. In a thermocouple, the neutral temperature is ${270}^{o}C$ and the temperature of inversion is ${525}^{o}C$. The temperature of cold junction would be

1. ${30}^{o}C$
2. ${255}^{o}C$
3. ${15}^{o}C$
4. ${25}^{o}C$

Q. The acceleration $a$ of particle starting from rest varies with time according to relation $a=\alpha t+\beta$. The velocity of the particle after a time $t$ will be

1. $\frac{\alpha t^2}{2}+\beta$
2. $\frac{\alpha t^2}{2}+\beta t$
3. $\alpha t^2+\frac{1}{2}\beta t$
4. $\frac{\left(\alpha t^2\right)+\beta }{2}$

Q. A particle is projected with certain velocity at two different angles of projections with respect to horizontal plane so as to have same range $R$ on a horizontal plane. If $t_1$ and $t_2$ are the time taken for the two paths, then which one of the following relations is correct?

1. $t_1{t}_2=\frac{R}{g}$
2. $t_1{t}_2=\frac{2R}{g}$
3. $t_1{t}_2=\frac{R}{2g}$
4. $t_1{t}_2=\frac{4R}{g}$

Q. Moment of inertia of a ring of mass $M$ and radius $R$ about an axis passing through the centre and perpendicular to the plane is $I$. What is the moment of inertia about its diameter?

1. $I$
2. $\frac{I}{2}$
3. $I+{MR}^2$
4. $\frac{I}{\sqrt{2}}$

Q. A body is tied with a string and is given a circular motion with velocity $v$ in radius $r$. The magnitude of the acceleration is

1. $v/r$
2. $v^2/r^2$
3. $v^2/r$
4. $v/r^2$

Q. A ball is thrown vertically upward, Ignoring the air resistance, which one of the following plot represent the velocity time plot for the period ball remains in air?

1. 
   
2. 
   
3. 
   
4. 
   

Q. A Carnot engine working between $450K$ and $600K$ has a work output of $300J$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is

1. $400J$
2. $3200J$
3. $1600J$
4. None of the given option is correct
5. $800J$

Q. A plane e.m wave of frequency $30MHz$ travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time $E=6V/m$ along $y$-direction. Its magnetic field component $B$ at this point would be

1. $2\times {10}^{-8}T$ along $z$-direction
2. $2\times {10}^{-8}T$ along $y$-direction
3. $6\times {10}^{-8}T$ along $x$-direction
4. $6\times {10}^{-8}T$ along $z$-direction

Q. Which one of the following pair of quantities has same dimension?

1. Force and work done
2. Momentum and impulse
3. Pressure and force
4. Surface tension and stress

Q. A body travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance(s) travelled with time ($t$)?

1. 
   
2. 
   
3. 
   
4. 
   

Q. Two masses of $M$ and $4M$ are moving with equal kinetic energy. The ratio of their linear momenta is

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

Q. The excess pressure inside a spherical drop of radius $r$ of a liquid of surface tension $T$ is

1. Directly proportional to $r$ and inversely proportional to $T$
2. Directly proportional to the product of $T$ and $r$
3. Directly proportional to $T$ and inversely proportional to $r$
4. Inversely proportional to the product of $T$ and $r$

Q. It two parallel wires carry current in opposite directions

1. The wires attract each other
2. The wires repel each other
3. The wires experience neither attraction nor repulsion
4. The forces of attraction or repulsion do not depend on current direction

Q. The equivalent resistance between the terminals $A$ and $D$ in the following circuit is

1. $10\Omega$
2. $5\Omega$
3. $20\Omega$
4. $30\Omega$

Q. A bullet hits and gets embedded in a solid block resting on a frictionless surface. In this process which one of the following is correct?

1. Only kinetic energy is conserved
2. Both momentum and kinetic energy are conserved
3. Neither momentum nor kinetic energy is conserved
4. Only momentum is conserved

Q. A circular disc rolls down an inclined plane. The ratio of rotational kinetic energy to total kinetic energy is

1. $1/2$
2. $1/3$
3. $2/3$
4. $3/4$

Q. A steady electric current is flowing through a cylindrical conductor.

1. The magnetic field in the vicinity of the conductor is zero
2. The electric field in the vicinity of the conductor is non-zero
3. The magnetic field at the axis of the conductor is zero
4. The electric field at the axis of the conductor is zero