Q. The dimensions of $\frac{a}{b}$ in the equation $P=\frac{a-t^2}{bx}$ where $P$ is pressure, $x$ is distance and $t$ is time, are:

1. $\left[M^2{LT}^{-3}\right]$
2. $\left[{MT}^{-2}\right]$
3. $\left[{LT}^{-3}\right]$
4. $\left[M{L}^3{T}^{-1}\right]$

Q. Two wires are fixed in a sonometer. Their tensions are in the ratio $8:1$. The lengths are in the ratio $36:35$. The diameters are in the ratio $4:1$. Densities of the materials are in the ratio $1:2$. If the higher frequency in the setting is $360Hz$, the beat frequency when the two wires are sounded together, is:

1. 8
2. 5
3. 10
4. 6

Q.

A bucket full of hot water cools from ${75}^{\circ }C$ to ${70}^{\circ }C$ in time $T_1$, from ${70}^{\circ }C$ to ${65}^{\circ }C$ in time $T_2$ and from ${65}^{\circ }C$ to ${60}^{\circ }C$ in time $T_3$. Then

1. $T_1>T_2<T_3$
2. $T_1=T_2=T_3$
3. $T_1>T_2>T_3$
4. $T_1<T_2<T_3$

Q. A fish, looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $4/3$ and the fish is $12cm$ below the surface of water, the radius of the circle in centimetre is:

1. $\frac{12\times 3}{\sqrt{5}}$
2. $\frac{12\times 3}{\sqrt{7}}$
3. $12\times 3\times \sqrt{5}$
4. $12\times 3\times \sqrt{7}$

Q. As a result of interference of two coherent sources of light, energy is:

1. increased
2. redistributed and the distribution does not vary with time
3. redistributed and that distribution changes with time
4. decreased

Q. The displacement time graph of a particle executing S.H.M. is as shown in the figure. The corresponding force-time graph of the particle is:

1. 
   
2. 
   
3. 
   
4. 
   

Q. If $v_m$ is the velocity of sound in moist air, $v_d$ is the velocity of sound in dry air, under identical conditions of pressure and temperature:

1. $v_m<v_d$
2. $v_m>v_d$
3. $v_m{v}_d=1$
4. $v_m{=v}_d$

Q. A sound source is moving towards stationary listener with $\frac{1}{10}$th of the speed of sound. The ratio of apparent to real frequency is:

1. ${\left(\frac{9}{10}\right)}^2$
2. $\frac{10}{9}$
3. $\frac{11}{10}$
4. ${\left(\frac{11}{10}\right)}^2$

Q. Young's modulus of perfectly rigid body material is:

1. Zero
2. Infinite
3. $10\times {10}^{10}N/m^2$
4. $1\times {10}^{10}N/m^2$

Q. Weight of a body of mass m decreases by $1\%$ when it is raised to height $h$ above the earth's surface. If the body is taken to a depth $h$ in a mine, change in its weight is:

1. by $0.5\%$ decrease
2. by $2\%$ decrease
3. by $0.5\%$ increase
4. by $1\%$ increase

Q. A lamp hanging $4$ metres above the table is lowered by $1$ metre. The illumination on the table:

1. decreased by 25%
2. increased by 25%
3. decreased by 66.7%
4. increased by 77.7%

Q. In Young's double slit experiment, the fringe width is $\beta$, If the entire arrangement is placed in a liquid of refractive index $n$, the fringe width becomes:

1. $n\beta$
2. $\frac{\beta }{n+1}$
3. $\frac{\beta }{n-1}$
4. $\frac{\beta }{n}$

Q. Yellow light is used in single slit diffraction experiment with slit width $0.6mm$. If yellow light is replaced by X-rays, then the pattern will reveal:

1. no diffraction pattern
2. that the central maxima narrower
3. more number of fringes
4. less number of fringes

Q. The aperture of the objective lens of a telescope is made large so as to:

1. to focus on distant objects
2. increase the magnifying power of the telescope
3. increase the resolving power of the telescope
4. make image aberration less

Q. Which of the following sets of concurrent forces may be in equilibrium?

1. $F_1=3N,F_2=5N,F_3=1N$
2. $F_1=3N,F_2=5N,F_3=6N$
3. $F_1=3N,F_2=5N,F_3=15N$
4. $F_1=3N,F_2=5N,F_3=9N$

Q. The equation of a transverse wave travelling along positive X axis with amplitude $0.2m$, velocity $360m/s$ and wavelength $60m$ can be written as:

1. $y=0.2\sin \pi [6t+\frac{x}{60}]$
2. $y=0.2\sin \pi [6t-\frac{x}{60}]$
3. $y=0.2\sin 2\pi [6t-\frac{x}{60}]$
4. $y=0.2\sin 2\pi [6t+\frac{x}{60}]$

Q. Three vectors satisfy the relation $\overrightarrow{A}.\overrightarrow{B}=0$ and $\overrightarrow{A}.\overrightarrow{C}=0$, then $\overrightarrow{A}$ is parallel to:

1. $\overrightarrow{B}$
2. $\overrightarrow{C}$
3. $\overrightarrow{B}\times \overrightarrow{C}$
4. $\overrightarrow{B}.\overrightarrow{C}$

Q. A sample of ideal monoatomic gas is taken round the cycle ABCA as shown in the figure. The work done during the cycle is:

1. Zero
2. $3PV$
3. $9PV$
4. $6PV$

Q. Waves that can not be polarised are:

1. Electromagnetic waves
2. Light waves
3. Longitudinal waves
4. Transverse waves

Q. A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and material are now added to P, as shown in the figure. The ray will suffer:

1. same deviation
2. greater deviation
3. total internal reflection
4. no deviation

Q. An ideal monoatomic gas at ${27}^{\circ }C$ is compressed adiabatically to $8/27$ times of its present volume. The increase in temperature of the gas is:

1. ${375}^{\circ }C$
2. ${402}^{\circ }C$
3. ${475}^{\circ }C$
4. ${175}^{\circ }C$

Q. In an interference experiment, third bright fringe is obtained at a point on the screen with a light of $700nm$. What should be the wavelength of the light source in order to obtain $5$th bright fringe at the same point?

1. $420nm$
2. $500nm$
3. $630nm$
4. $750nm$

Q. A student is standing at a distance of $50$ metre from the bus. As soon as the bus begins its motion with an acceleration of $1{ms}^{-2}$, the students starts running towards the bus with a uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is:

1. $5{ms}^{-1}$
2. $12{ms}^{-1}$
3. $8{ms}^{-1}$
4. $10{ms}^{-1}$

Q. For a given velocity, a projectile has the same range $R$ for two angles of projection. If $t_1$ and $t_2$ are the time of flight in the two cases, then:

1. $t_1{t}_2\propto R^2$
2. $t_1{t}_2\propto R$
3. $t_1{t}_2\propto \frac{1}{R^2}$
4. $t_1{t}_2\propto \frac{1}{R}$

Q. If $T$ is the reverberation time of an auditorium of volume $V$, then:

1. $T\propto V^2$
2. $T\propto V$
3. $T=\frac{1}{V^2}$
4. $T\propto \frac{1}{V}$

Q. The phenomenon of rotation of plane polarized light is called:

1. Kerr effect
2. Double refraction
3. Optical activity
4. Dichroism

Q. A group of $N$ cells whose emf varies directly with the internal resistance as per the equation $E_N=1.5r_N$ are connected as shown in the figure above. The current $I$ in the circuit is:

1. $5.1A$
2. $0.51A$
3. $1.5A$
4. $0.15A$

Q. If $v$ is the speed of sound in air then the shortest length of the closed pipe which resonates to a frequency $n$, is:

1. $\frac{v}{2n}$
2. $\frac{v}{4n}$
3. $\frac{4n}{v}$
4. $\frac{2n}{v}$

Q. Cavitation is a special application property exhibited only by:

1. Ultrasonics
2. Electromagnetic waves
3. Audible sound
4. Infrasonics

Q. If a ray of light in a denser medium enters into a rarer medium at an angle of incidence $i$, the angle of reflection and refraction are respectively $r$ and $r^{\prime }$. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is:

1. ${\sin }^{-1}\left(\tan r^{\prime }\right)$
2. ${\sin }^{-1}\left(\tan r\right)$
3. ${\tan }^{-1}\left(\sin i\right)$
4. $\cot \left(\tan i\right)$