Q. A light ray is incident on a prism in minimum deviation position and suffers a deviation of ${34}^o$. If the shaded half of the prism is removed off, then the same ray will suffer a deviation of :

1. $0^o$
2. ${65}^o$
3. ${17}^o$
4. ${34}^o$

Q. A circular railway track of radius r is banked at angle so that a train moving with speed v can safely go round the track. A student writes: $\tan \theta =\frac{rg}{v^2}$. Why this relation is not correct?
(i) Equality of dimensions does not guarantee correctness of the relation.
(ii) Dimensionally correct relation may not be numerically correct
(iii) The relation is dimensionally incorrect.

1. (ii) and (iii)
2. (i), (ii) and (iii)
3. (i) and (ii)
4. (iii) and (i)

Q. $\frac{1}{\alpha }-\frac{1}{\beta }$ is equal to.

1. $\alpha \beta$
2. $2$
3. $\alpha -\beta$
4. $1$

Q. The magnification of the image when an object is placed at a distance x from the principle focus of a mirror of focal length f is?

1. $\frac{x}{f}$
2. $1+f/x$
3. $\frac{f}{x}$
4. $1-\frac{f}{x}$

Q. An electromagnetic wave passing through vacuum is described by the equations. $E=E_0\sin (kx-\omega t)$ and $B=B_0\sin (kx-\omega t)$. Then.

1. $E_{0}k=B_0\omega$
2. $E_0=B_0$
3. $E_0{B}_0=\omega k$
4. $E_0\omega =B_{0}k$

Q. Rise in capillary tube __________ with addition of detergent in pure water.

1. Decreases
2. None of these
3. Remains same
4. Increases

Q. A batsman deflects a ball by an angle of ${45}^o$ without changing its initial speed which is equal to $54$km/hr. Mass of the ball is $0.15$kg. What is the impulse imparted to the ball?

1. $4.2$kg m/s in the direction of the final velocity
2. $4.2$kg m/s in the direction of the initial velocity
3. $4.2$kg m/s in the direction opposite to the initial velocity
4. $4.2$kg m/s directed along the bisector of the initial and the final directions of the velocity

Q. A satellite in a force-free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt}=\beta v$. The acceleration of satellite is?

1. $-M\beta /v^2$
2. $-\beta v^2/2M$
3. $-\beta v^2$
4. $-\beta v^2/M$

Q. In the diagram, vector C is equivalent to.

1. $\overline{D}-\overline{A}+\overline{B}$
2. $\overline{A}+\overline{B}-\overline{D}$
3. $\overline{D}-\overline{A}-\overline{B}$
4. $\overline{D}+\overline{A}-\overline{B}$

Q. For an optical communication system, operating at $\lambda =800$nm, only $1\%$ of the optical source frequency is the available channel band width. How many channels can be accommodated for transmitting video T.V. signal requiring an approximate band width of $4.5$MHz?

1. $8.3\times {10}^7$
2. $1.71\times {10}^{22}$
3. $8.3\times {10}^5$
4. $1.71\times {10}^{20}$

Q. Which one of the following curves represents variation of current i with frequency f in series LCR circuit?

1. 
   
2. 
   
3. 
   
4. 
   

Q. Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance d, by what distance should be second particle be moved, so as to keep the centre of mass at the same position?

1. $\frac{m_1}{m_2}d$
2. d
3. $\frac{m_2}{m_1}d$
4. $\frac{m_1}{m_2+m_1}d$

Q. An element with atomic number $Z=11$ emits $K_a$ X-ray of wavelength $\lambda$, then the atomic number of the element which emits $K_a$. X-ray of wavelength $4\lambda$ is?

1. $11$
2. $6$
3. $44$
4. $5$

Q. A Nicol prism is based on the principle of.

1. Refraction
2. Scattering
3. Dichroism
4. Double refraction

Q. Thomson coefficient $\sigma$, temperature T(in kelvin) and Seeback coefficient S are mutually related as.

1. $\sigma =\frac{ds}{T\cdot dt}$
2. $T=\sigma \cdot \frac{dS}{dt}$
3. $S=T\cdot \frac{d\sigma }{dT}$
4. $\sigma =T\cdot \frac{dS}{dt}$

Q. Two radioactive materials $X_1$ and $X_2$ have decay constants $10\lambda$ and $\lambda$ respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $1/e$ after a time.

1. $\frac{1}{10\lambda }$
2. $\frac{1}{9\lambda }$
3. $\frac{1}{11\lambda }$
4. $\frac{11}{10\lambda }$

Q. In Young's double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelength $\lambda$. In another experiment with the same set up the two slits are same of equal amplitude of wavelength $\lambda$ but are incoherent. The ratio of intensity of light at the mid point of the screen in the first to the second case is?

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

Q. Two wires $AC$ and $BC$ are tied at $C$ of small sphere of mass $5kg$, which revolves at a constant speed $v$ in the horizontal circle of radius $1.6m$. The minimum value of $v$ is?

1. $3.01m/s$
2. $4.01m/s$
3. $8.2m/s$
4. $3.96m/s$

Q. Twelve resistors each of resistance $1$ $\Omega$ are connected in the circuit shown in figure. Net resistance between point A and H would be.

1. $\frac{5}{3}\Omega$
2. $1\Omega$
3. $\frac{3}{4}\Omega$
4. $\frac{7}{6}\Omega$

Q. A pendulum suspended from the roof of an elevator at rest has a time period $T_1$, when the elevator moves up with an acceleration a its time period becomes $T_2$, when the elevator moves down with an acceleration a, its time period becomes $T_1$, then.

1. $T_1=\sqrt{\left(T_2{T}_3\right)}$
2. $T_1=\frac{T_2{T}_3\sqrt{2}}{\sqrt{T_2^2+T_3^2}}$
3. $T_1=\sqrt{(T_2^2+T_3^2)}$
4. None of these

Q. A man of mass $60$kg and a boy of mass $30$kg are standing together on frictionless ice surface. If they push each other apart man moves away with a speed of $0.4$m/s relative to ice. After $5$sec they will be away from each other at a distance of.

1. $9.0$m
2. $3.0$m
3. $6.0$m
4. $30$,

Q. A condenser of capacity $1\mu F$ and a resistance $0.5$mega ohm are connected in series with a D.C. supply of $2$V. The time constant of the circuit is?

1. $0.25$sec
2. $0.5$sec
3. $1$sec
4. $2$sec

Q. Two parallel plate capacitors A and B having capacitances of $1\mu F$ and $5\mu F$ are charged separately to the same potential of $100$V. Now the positive plate of A is connected to the negative plate of B and the negative plate of A to the positive plate of B. The final charge on each capacitor is?

1. $\frac{200}{3}\mu C,\frac{1000}{3}\mu C$
2. $\frac{100}{3}\mu C,\frac{500}{3}\mu C$
3. $\frac{250}{3}\mu C,\frac{750}{3}\mu C$
4. None of these

Q. A car when passes through a convex bridge exerts a force on it which is equal to.

1. $Mg+\frac{M{v}^2}{r}$
2. $\frac{M{v}^2}{r}$
3. $Mg-\frac{M{v}^2}{r}$
4. None of these

Q. The spring constants of three springs connected to a mass M are shown in figure. When mass oscillates, what are the effective spring constant and the time period of vibration?

1. $2k,2\pi \sqrt{\frac{M}{2k}}$
2. $4k,2\pi \sqrt{\frac{M}{4k}}$
3. None of these
4. $3k,2\pi \sqrt{\frac{M}{3}}k$

Q. Graph of specific heat at constant volume for a monoatomic gas is?

1. 
   
2. 
   
3. 
   
4. 
   

Q. The hysteresis curve for the material suitable for making permanent magnet is?

1. Short and narrow
2. Tall and narrow
3. Short and wide
4. Tall and wide

Q. A body of density $\rho$ enters a tank of water of density ${\rho }^{\prime }$ after falling through a height h. The maximum depth to which it sinks in water is?

1. $\frac{h{\rho }^{\prime }}{(\rho -{\rho }^{\prime })}$
2. $\frac{h\rho }{(\rho -{\rho }^{\prime })}$
3. $\frac{h\rho }{{\rho }^{\prime }}$
4. $\frac{h{\rho }^{\prime }}{\rho }$

Q. Two rods of lengths $d_1$ and $d_2$ and coefficients of thermal conductivities $K_1$ and $K_2$ are kept in contact with each other end to end. Both have the same area of cross-section. The equivalent thermal conductivity is?

1. $K_1+K_2$
2. $\frac{d_1+d_2}{\left(\frac{d_1}{K_1}+\frac{d_2}{k_2}\right)}$
3. $\frac{K_1{d}_1+K_2{d}_2}{d_1+d_2}$
4. $K_1{d}_1+K_2{d}_2$

Q. What is the ratio of critical frequency for reflection of radiowaves from $E,F_1$ and $F_2$ layers in ionosphere if the electron densities are $2\times {10}^{11},3\times {10}^{11}$ and $8\times {10}^{11}{m}^{-3}$ respectively?

1. $1:1.5:3$
2. $1:2:3$
3. $1.41:1.73:2.83$
4. $1.52:1.52:1.89:2.60$