Q. The supply voltage to a room is 120 $V$. The resistance of the lead wires is 6 $\Omega$. A $60W,120V$ bulb is already switched on. What is the decrease of voltage (in Volts ) across the bulb, when a $240W,120V$ heater is switched on in parallel to the bulb?

1. 2.9
2. 13.3
3. 0
4. 10.4

Q. A beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of ${45}^o$ relative to that of $A$. The intensity of the emergent light is:

1. $I_0/4$
2. $I_0/8$
3. $I_0/2$
4. $I_0$

Q. Two capacitors $C_1$ and $C_2$ are charged to 120 $V$ and 200 $V$ respectively. It is found that by connecting them together the potential on each one can be made zero. Then,

1. $3C_1=5C_2$
2. $9C_1=4C_2$
3. $5C_1=3C_2$
4. $3C_1+5C_2=0$

Q. A hoop of radius $r$ and mass $m$ rotating with an angular velocity ${\omega }_o$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

1. $\frac{r{\omega }_0}{3}$
2. $\frac{r{\omega }_0}{2}$
3. $r{\omega }_0$
4. $\frac{r{\omega }_0}{4}$

Q. In a hydrogen-like atom, an electron makes a transition from an energy level with the quantum number $n$ to another with the quantum number $(n-1)$. If $n>>1$, the frequency of radiation emitted is approximately proportional to:

1. $\frac{1}{n}$
2. $\frac{1}{n^2}$
3. $\frac{1}{n^{3/2}}$
4. $\frac{1}{n^3}$

Q. A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium, is

1. $\frac{Mg}{k}(1-\frac{LA\sigma }{M})$
2. $\frac{Mg}{k}(1-\frac{LA\sigma }{2M})$
3. $\frac{Mg}{k}(1+\frac{LA\sigma }{M})$
4. $\frac{Mg}{k}$

Q. The graph between angle of deviation $\left(\delta \right)$ and angle of incidence (i) for a triangular prism is represented by:

1. 
   
2. 
   
3. 
   
4. 
   

Q. Two charges, each equal to $q$, are kept at $x=-a$ and $x=a$ on the $x$-axis. A particle of mass $m$ and charge $q_0=\frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y<<a)$ along the $y$-axis, the net force acting on the particle is proportional to:

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

Q. The magnetic field in a travelling electromagnetic wave has a peak value of 20 $nT$. The peak value of electric field strength is

1. 6 V/m
2. 9 V/m
3. 12 V/m
4. 3 V/m

Q. A projectile is given an initial velocity of $(\hat{i}+2\hat{j})m/s$, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g=10m/s^2$, the equation of its trajectory is:

1. $y=x-5x^2$
2. $4y=2x-25x^2$
3. $y=2x-5x^2$
4. $4y=2x-5x^2$

Q. A metallic rod of length $l$' is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ` $B$' in the region, the e.m.f. induced across the ends of the rod is:

1. $\frac{4B\omega l^2}{2}$
2. $\frac{3B\omega l^2}{2}$
3. $\frac{5B\omega l^2}{2}$
4. $\frac{2B\omega l^2}{2}$

Q. A circular loop of radius $0.3cm$ lies parallel to a much bigger circular loop of radius $20cm$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15cm$. If a current of $2.0A$ flows through the smaller loop, then the flux linked with bigger loop is

1. $9.1\times {10}^{-11}Wb$
2. $6\times {10}^{-11}Wb$
3. $3.3\times {10}^{-11}Wb$
4. $6.6\times {10}^{-9}Wb$

Q. Two coherent point sources $S_1$ and $S_2$ are separated by a small distance `d' as shown. The fringes obtained on the screen will be:

1. straight lines
2. semi-circles
3. concentric circles
4. points

Q. What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$?

1. $\frac{GmM}{2R}$
2. $\frac{2GmM}{3R}$
3. $\frac{GmM}{3R}$
4. $\frac{5GmM}{6R}$

Q. This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I: A point particle of mass $m$ moving with speed $v$ collides with stationary point particle of mass $M.$ If the maximum energy loss possible is given as $f\left(\frac{1}{2}m{v}^2\right)$ then $f=\left(\frac{m}{M+m}\right)$.
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

1. Statement I is true, Statement II is true, Statement II is not a correct explanation of Statement I.
2. Statement I is true, Statement II is true, Statement II is a correct explanation of Statement I.
3. Statement I is false, Statement II is true
4. Statement I is true, Statement II is false.

Q. A charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at a distance $L$ from the end $A$ is:

1. $\frac{3Q}{4\pi {\epsilon }_{0}L}$
2. $\frac{Q\ln 2}{4\pi {\epsilon }_{0}L}$
3. $\frac{Q}{4\pi {\epsilon }_{0}L\ln 2}$
4. $\frac{Q}{8\pi {\epsilon }_{0}L}$

Q. Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is $2\times {10}^{8}m/s$, the focal length of the lens is:

1. 15 cm
2. 10 cm
3. 20 cm
4. 30 cm

Q. This question has statement $I$ and statement $II$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement- $I$: Higher the range, greater is the resistance of ammeter.
Statement- $II$: To increase the range of ammeter, additional shunt needs to be used across it.

1. Statement I is false, Statement II is true
2. Statement I is true, Statement II is true, Statement II is the correct explanation of statement- I .
3. Statement I is true, statement II is false.
4. Statement I is true, Statement II is true, Statement II is not the correct explanation of StatementI.

Q. Two short bar magnets of length 1 cm each have magnetic moments $1.20A{m}^2$ and $1.00A{m}^2$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0cm$. The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to
(Horizontal component of earth's magnetic induction is $3.6\times {10}^{-5}Wb/m^2$)

1. $2.56\times {10}^{-4}Wb/m^2$
2. $3.50\times {10}^{-4}Wb/m^2$
3. $5.80\times {10}^{-4}Wb/m^2$
4. $3.6\times {10}^{-5}Wb/m^2$

Q. If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature ${\theta }_0$, the graph between the temperature $T$ of the metal and time $t$ will be closest to :

1. 
   
2. 
   
3. 
   
4. 
   

Q. A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250pF in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.

1. 10.62 $kHz$
2. 5.31 MHz
3. 5.31 $kHz$
4. 10.62 MHz

Q. Let $\left[{\epsilon }_0\right]$ denote the dimensional formula of the permittivity of vacuum. If $M=$ mass, $L=$ length, $T=$ time and $A=$ electric current, then:

1. $\left[{\epsilon }_0\right]=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$
2. $\left[{\epsilon }_0\right]=\left[M^{-1}{L}^2{T}^{-1}{A}^{-2}\right]$
3. $\left[{\epsilon }_0\right]=\left[M^{-1}{L}^2{T}^{-1}A\right]$
4. $\left[{\epsilon }_0\right]=\left[M^{-1}{L}^{-3}{T}^{2}A\right]$

Q. In an LCR circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. ( $q$ is charge on the capacitor and $\tau =RC$ is capacitive time constant). Which of the following statement is correct?

1. At $t=2\tau ,q=CV(1-e^{-2})$
2. At $t=\tau ,q=CV/2$
3. At $t=\frac{T}{2},q=CV(1-e^{-1})$
4. Work done by the battery is half of the energy dissipated in the resistor.

Q. The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude is $5s$. In another $10s$ it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals.

1. $0.81$
2. $0.7$
3. $0.6$
4. $0.729$

Q. An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

1. $\frac{1}{2\pi }\frac{V_{0}M(P_0+\frac{Mg}{A})}{A^2\gamma }$
2. $\frac{1}{2\pi }\sqrt{\frac{A^2\gamma (P_0+\frac{Mg}{A})}{M{V}_0}}$
3. $\frac{1}{2\pi }\frac{A\gamma (P_0+\frac{Mg}{A})}{V_{0}M}$
4. $\frac{1}{2\pi }\sqrt{\frac{M{V}_0}{A\gamma (P_0+\frac{Mg}{A})}}$

Q. The above P-V diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

1. $4P_o{V}_0$
2. $\left(\frac{11}{2}\right)P_o{V}_0$
3. $P_o{V}_0$
4. $\left(\frac{13}{2}\right)P_o{V}_0$

Q. Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is $T$, density of liquid is $\rho$ and $L$ is its latent heat of vaporization.

1. $T/\rho L$
2. $\sqrt{T/\rho L}$
3. $2T/\rho L$
4. $\rho L/T$

Q. The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows:

1. 
   
2. 
   
3. 
   
4. 
   

Q. The $I-V$ characteristic of an LED is

1. 
   
2. 
   
3. 
   
4. 
   

Q. A sonometer wire of length $1.5m$ is made of steel. The tension in it produces an elastic strain of $1\%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times {10}^{3}kg/m^3$ and $2.2\times {10}^{11}N/m^2$ respectively?

1. $178.2Hz$
2. $200.5Hz$
3. $770Hz$
4. $188.5Hz$