Q. A train is moving on a straight track with speed $20m{s}^{-1}$. It is blowing its whistle at the frequency of $1000Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $=320m{s}^{-1}$) close to :

1. $18\%$
2. $6\%$
3. $12\%$
4. $24\%$

Q. A red LED emits light at $0.1W$ uniformly around it. The amplitude of the electric filed of the light at a distance of $1m$ form the diode is:

1. $1.73V/m$
2. $2.45V/m$
3. $5.48V/m$
4. $7.75V/m$

Q. Consider a spherical shell of radius $R$ at temperature $T$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u=\frac{U}{V}\propto T^4$ and pressure $P=\frac{1}{3}\left(\frac{U}{V}\right)$ . If the shell now undergoes an adiabatic expansion the relation between T and R is :

1. $T\propto \frac{1}{R}$
2. $T\propto e^{-R}$
3. $T\propto e^{-3R}$
4. $T\propto \frac{1}{R^3}$

Q. An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit the capacitor is charged to $Q_0$ and then connected to the $L$ and $R$ as shown above. If a student plots graphs of the square of maximum charge $\left(Q_{Max}^2\right)$ on the capacitor with time (t) for two different values $L_1$ and $L_2(L_1>L_2)$ of L then which of the following represents this graph correctly? (plots schematic and not drawn to scale)

Q. A solid body of constant heat capacity $1J{/}^{\circ }C$ is being heated by keeping it in contact with reservoirs in two ways :
(i) Sequentially keeping in contact with $2$ reservoirs such that each reservoir supplies same amount of heat.
(ii) Sequentially keeping in contact with $8$ reservoirs such that each reservoir supplies same amount of heat.
In both the cases body is brought from initial temperature of ${100}^{\circ }C$ to a final temperature of ${200}^{\circ }C$ . Entropy change of the body in two cases respectively is :

1. $\ln 2,4\ln 2$
2. $\ln 2,\ln 2$
3. $\ln 2,2\ln 2$
4. $2\ln 2,8\ln 2$

Q. For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly ?
(graphs are schematic and not drawn to scale)

1. 
   
2. 
   
3. 
   
4. 
   

Q. From a solid sphere of mass $M$ and radius $R$, a spherical portion of radius $\frac{R}{2}$ is removed, as shown in the figure. Taking gravitational potential $V=0$ at $r=\infty$ , the potential at the centre of the cavity thus formed is :
($G=$ gravitational constant)

1. $\frac{-GM}{R}$
2. $\frac{-2GM}{3R}$
3. $\frac{-GM}{2R}$
4. $\frac{-2GM}{R}$

Q. On a hot summer night, the refractive index of air is smallest near the ground and increase with height from the ground. When a light beam is directed horizontally, the Huygen's principle leads us to conclude that as it travels, the light beam

1. bends upwards
2. becomes narrower
3. goes horizontally without any deflection
4. bends downwards

Q. A rectangular loop of sides 10 cm and 5 cm carrying a current I and 12 A is placed in different orientations as shown in the figures above.
If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?

1. (A) and (B), respectively
2. (A) and (C), respectively
3. (B) and (D), respectively
4. (B) and (C), respectively

Q. Distance of the center of mass of a solid uniform cone from its vertex is $z_0$ . If the radius of its base is $R$ and its height is h then $z_0$ is equal to :

1. $\frac{h^2}{4R}$
2. $\frac{3h}{4}$
3. $\frac{5h}{8}$
4. $\frac{3h^2}{8R}$

Q. Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is :

1. $1\mu m$
2. $30\mu m$
3. $300\mu m$
4. $100\mu m$

Q. A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3V_0}{2},\frac{5V_0}{4},\frac{3V_0}{4}$ and $\frac{V_0}{4}$ have radius $R_1,R_2,R_3$ and $R_4$ respectively. Then :

1. $R_1=0$ and $R_2>(R_4-R_3)$
2. $R_1\ne 0$ and $(R_2-R_1)>(R_4-R_3)$
3. $2R<R_4$
4. None of the above

Q.

1. 
   
2. 
   
3. 
   
4. 
   

Q. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes adiabatic expansion, the average time of collision between molecules increases as $V^q$, where V is the volume of the gas. The value of q is :
$(\gamma =\frac{C_p}{C_v})$

1. $\frac{3\gamma +5}{6}$
2. $\frac{3\gamma -5}{6}$
3. $\frac{\gamma +1}{2}$
4. $\frac{\gamma -1}{2}$

Q. Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$, a ray incident at an angle $\theta$, on the face AB would get transmitted through the face AC of the prism provided

1. $\theta >si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
2. $\theta <si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
3. $\theta >co{s}^{-1}\left[\mu sin(A+si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
4. $\theta <co{s}^{-1}\left[\mu sin(A+si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$

Q. Two coaxial solenoids of different radii carry current I in the same direction. Let $\overrightarrow{F_1}$ be the magnetic force on the inner solenoid due to the outer one and $\overrightarrow{F_2}$ be the magnetic force on the outer solenoid due to the inner one. Then

1. $\overrightarrow{F_1}$ is radially inwards and $\overrightarrow{F_2}$ is radially outwards
2. $\overrightarrow{F_1}$ = $\overrightarrow{F_2}$ = 0
3. $\overrightarrow{F_1}$ radially outwards and $\overrightarrow{F_2}$ = 0
4. $\overrightarrow{F_1}$ is radially inwards $\overrightarrow{F_2}$ = 0

Q. An inductor (L=0.03H) and a resistor (R=0.15 K$\Omega$) are connected in series to a battery of 15V EMF in a circuit shown below. The key $K_1$ has been kept closed for a long time. Then at t=0, $K_1$ is opened and key $K_2$ is closed simultaneously. At t=1ms, the current in the circuit will be : $(e^5\cong 150)$

1. 100mA
2. 67mA
3. 6.7mA
4. 0.67mA

Q. A pendulum of a uniform wire of cross-sectional area $A$ has time period $T.$ When an additional mass $M$ is added to its bob, the time period changes to $T_M$ . If the Young's modulus of the material of the wire is $Y$ then $\frac{1}{Y}$ is equal to :
($g$ = gravitational acceleration)

1. $[1-{\left(\frac{T_M}{T}\right)}^2]\frac{Mg}{A}$
2. $[{\left(\frac{T}{T_M}\right)}^2-1]\frac{Mg}{A}$
3. $[1-{\left(\frac{T_M}{T}\right)}^2]\frac{A}{Mg}$
4. $[{\left(\frac{T_M}{T}\right)}^2-1]\frac{A}{Mg}$

Q. A signal of $5kHz$ frequency is amplitude modulated on a carrier wave of frequency $2MHz$. Frequencies of the resultant signal is/are

1. $2MHz$ only
2. $2005kHz$, $2000kHz$ and $1995kHz$
3. $2005kHz$ and $1995kHz$
4. $2000kHz$ and $1995kHz$

Q.

The period of oscillation of a simple pendulum is $T=2\pi \sqrt{\frac{L}{g}}$. Measure of $L$ is $20.0cm$ known to $1mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90s$ using a wrist watch of $1s$ resolution. The accuracy in the determination of $g$?

1. $2.7\%$
2. $2.5\%$
3. $2\%$
4. $3\%$

Q. Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list

	List I		List II
(A)	Franck-Hertz Experiment	(i)	Particle nature of light
(B)	Photo-electric experiment	(ii)	Discrete energy level of atom
(C)	Davison-Germer Experiment	(iii)	Wave nature of electron
		(iv)	Structure of atom

1. (A)- (i), (B)-(iv), (C)-(iii)
2. (A)- (ii), (B)-(iv), (C)-(iii)
3. (A)- (ii), (B)-(i), (C)-(iii)
4. (A)- (iv), (B)-(iii), (C)-(ii)

Q. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

1. $\frac{M{R}^2}{32\sqrt{2}\pi }$
2. $\frac{M{R}^2}{16\sqrt{2}\pi }$
3. $\frac{4M{R}^2}{9\sqrt{3}\pi }$
4. $\frac{4M{R}^2}{3\sqrt{3}\pi }$

Q. A particle of mass m moving in the direction $x$ with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v$ . If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

1. $44\%$
2. $50\%$
3. $62\%$
4. $56\%$

Q. A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in :
(figures are schematic and not drawn to scale)

1. 
   
2. 
   
3. 
   
4. 
   

Q. Given in the figure are two blocks A and B of weight $20$N and $100$N, respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between block B and the wall is $0.15$, the frictional force applied by the wall on block B is

1. 80 N
2. 100 N
3. 120 N
4. 150 N

Q. When $5V$ potential difference is applied across a wire length $0.1m$, the drift speed of electron is 2.5 $\times {10}^{-4}m{s}^{-1}$. If the electron density in the wire is 8 $\times {10}^{28}{m}^{-3}$, the resistivity of the material is close to

1. $1.6\times {10}^{-8}\Omega$m
2. $1.6\times {10}^{-7}\Omega$m
3. $1.6\times {10}^{-6}\Omega$m
4. $1.6\times {10}^{-5}\Omega$m

Q. As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom ion

1. its kinetic energy increases but potential energy and total energy decrease
2. kinetic energy, potential energy and total energy decrease
3. kinetic energy decreases, potential energy increases but total energy remains same
4. kinetic energy and total energy decreases but potential energy increase

Q. Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle '$\theta$' with the vertical. If wires have mass $\lambda$ per unit length then the value of I is :
(g = gravitational acceleration)

1. 2sin$\theta \sqrt{\frac{\pi \lambda gL}{{\mu }_{0}cos\theta }}$
2. sin$\theta \sqrt{\frac{\pi \lambda gL}{{\mu }_{0}cos\theta }}$
3. 2$\sqrt{\frac{\pi gL}{{\mu }_0}tan\theta }$
4. $\sqrt{\frac{\pi \lambda gL}{{\mu }_0}tan\theta }$

Q. Two stones are thrown up simultaneously from the edge of a cliff $240m$ high with initial speed $10m/s$ and $40m/s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ?
(Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10m/s^2$)
(The figures are schematic and not drawn to scale.)

1. 
   
2. 
   
3. 
   
4. 
   

Q. In the circuit shown, the current in the 1$\Omega$ resistor is :

1. 1.3 A, from P to Q
2. 0 A
3. 0.13 A, from Q to P
4. 0.13 A, from P to Q