Q. The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used ?

1. $\frac{b^{2}c}{a}$
2. $\frac{b^2}{ac}$
3. $\frac{a}{c}$
4. $\frac{b}{c}$

Q. The elastic limit of brass is $379MPa$. What should be the Minimum diameter of a brass rod if it is to support a $400N$ load without exceeding its elastic limit ?

1. $1.16mm$
2. $1.00mm$
3. $0.90mm$
4. $1.36mm$

Q. Water from a tap emerges vertically downwards with an initial speed of $1.0m{s}^{-1}$. The cross-sectional area of the tap is ${10}^{-4}{m}^2$. Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream $0.15m$ below the tap is ($g=10m{s}^{-2}$)

1. $5.0\times {10}^{-4}{m}^2$
2. $5.0\times {10}^{-5}{m}^2$
3. $2.0\times {10}^{-5}{m}^2$
4. $1.0\times {10}^{-5}{m}^2$

Q. A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet ?
[Given : Mass of planet = $8\times {10}^{22}kg$;
Radius of planet = $2\times {10}^{6}m$,
Gravitational constant $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$]

1. $9$
2. $11$
3. $13$
4. $17$

Q. The time dependence of the position of a particle of mass $m=2$ is given by $\overrightarrow{r}\left(t\right)=2t\hat{i}-3t^2\hat{j}$. Its angular momentum, with respect to the origin at time $t=2$ is :

1. $36\hat{k}$
2. $-34(\hat{k}-\hat{i})$
3. $48(\hat{i}+\hat{j})$
4. $-48\hat{k}$

Q. The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6V and the load resistance is $R_L=4k\Omega$. The series resistance of the circuit is $R_i=1k\Omega$. If the battery voltage $V_B$ varies from $8V$ to $16V$, what are the minimum and maximum values of the current through Zener diode ?

1. $0.5mA;6mA$
2. $0.5mA;8.5mA$
3. $1.5mA;8.5mA$
4. $1mA;8.5mA$

Q. The magnitude of the magnetic field at the center of an equilateral triangular loop of side $1m$ which is carrying a current of 10 A is :
[Take ${\mu }_0=4\pi \times {10}^{-7}N{A}^{-2}$]

1. $18\mu T$
2. $1\mu T$
3. $4\mu T$
4. $9\mu T$

Q. A cubical block of side $0.5m$ floats on water with $30\%$ of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water ?
(Take density of water = ${10}^{3}kg/m^3$)

1. $65.4kg$
2. $87.5kg$
3. $46.3kg$
4. $30.1kg$

Q. A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :

1. $2\pi \sqrt{\frac{L}{\sqrt{g^2-\frac{q^2{E}^2}{m^2}}}}$
2. $2\pi \sqrt{\frac{L}{(g-\frac{qE}{m})}}$
3. $2\pi \sqrt{\frac{L}{\sqrt{g^2+{\left(\frac{qE}{m}\right)}^2}}}$
4. $2\pi \sqrt{\frac{L}{(g+\frac{qE}{m})}}$

Q. A submarine experience a pressure of $5.05\times {10}^6$ Pa at a depth of $d_1$ in a sea. When it goes further to a depth of $d_2$, it experiences a pressure of $8.08\times {10}^{6}Pa$., Then $d_2-d_1$ is approximately (density of water = ${10}^{3}kg/m^3$ and acceleration due to gravity = $10m{s}^{-2}$)

1. $500m$
2. $400m$
3. $300m$
4. $600m$

Q. A plane is inclined at an angle $\alpha ={30}^o$ with a respect to the horizontal. A particle is projected with a speed $u=2m{s}^{-1}$ from the base of the plane, making an angle $\theta ={15}^o$ with respect to the plane as shown in the figure.The distance from the base, at which the particle hits the plane is close to :
(Take $g=10m{s}^{-2}$)

1. $14cm$
2. $20cm$
3. $18cm$
4. $26cm$

Q. Two radioactive substances A and B have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$ they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ${\left(\frac{1}{e}\right)}^2$ after a time interval

1. $\frac{1}{4\lambda }$
2. $4\lambda$
3. $2\lambda$
4. $\frac{1}{2\lambda }$

Q. A bullet of mass $20g$ has an initial speed of $1m{s}^{-1}$, just before it starts penetrating a mud wall of thickness $20cm$. if the wall offers a mean resistance of $2.5\times {10}^{-2}N$, the speed of the bullet after emerging from the other side of the wall is close to :

1. $0.4m{s}^{-1}$
2. $0.1m{s}^{-1}$
3. $0.3m{s}^{-1}$
4. $0.7m{s}^{-1}$

Q. Light is incident normally on a completely absorbing surface with an energy flux of $25Wc{m}^{-2}$. if the surface has an area of $25c{m}^{-2}$, the momentum transferred to the surface in 40 min time duration will be :

1. $6.3\times {10}^{-4}Ns$
2. $3.5\times {10}^{-6}Ns$
3. $1.4\times {10}^{-6}Ns$
4. $5.0\times {10}^{-3}Ns$

Q. A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be :

1. $\frac{3m}{\pi }$
2. $\frac{2m}{\pi }$
3. $\frac{4m}{\pi }$
4. $\frac{m}{\pi }$

Q. A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him ?
(Take velocity of sound in air is $350m/s$)

1. $857Hz$
2. $807Hz$
3. $1143Hz$
4. $750Hz$

Q. In $L{i}^{++}$, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda$. when the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of $\lambda$ ?
(Given : $h=6.63\times {10}^{34}Js$; $c=3\times {10}^{8}m{s}^{-1}$)

1. $9.4nm$
2. $12.3nm$
3. $10.8nm$
4. $11.4nm$

Q. In free space, a particle A of charge $1\mu C$ is held fixed at a point P. Another particle B of the same charge and mass $4\mu g$ is kept at a distance of $1mm$ from P. if B is released, then its velocity at a distance of $9mm$ from P is :
[Take $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N{m}^2{C}^{-2}$]

1. $3.0\times {10}^{4}m/s$
2. $1.5\times {10}^{2}m/s$
3. $2.0\times {10}^{3}m/s$
4. $1.0m/s$

Q. Space between two concentric conducting spheres of radii a and $b(b>a)$ is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be :

Q. A coil of self inductance $10mH$ and resistance $0.1\Omega$ is connected through a switch to a battery of internal resistance $0.9\Omega$ After the switch is closed, the time taken for the current to attain $80\%$ of the saturation value is : (Take $ln5=1.6$)

Q. In the formula $X=5Y{Z}^2$, X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units ?

Q. A $2mW$ laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is :
[Given Planck's constant $h=6.6\times {10}^{-34}Js$,
speed of light $c=3.0\times {10}^{8}m/s$]

Q. When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $\Delta T$. The heat required to produce the same change in temperature, at a constant pressure is :

Q. A metal coin of mass $5g$ and radius $1cm$ is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at $25$ rotations per second in $5s$, is close to :

Q. In an experiment, bras and steel wires of length lm each with areas of cross section $1m{m}^2$ are used. the wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of $0.2mm$ is :
(Given, the Young's Modulus for steel and brass are respectively, $120\times {10}^{9}N/m^2$ and $60\times {10}^{9}N/m^2$)

Q. Two blocks A and B of masses $m_A=1kg$ and $m_B=3kg$ are kept on the table as shown in figure. The coefficient of friction between A and B is $0.2$ and between B and the surface of the table is also $0.2$. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is :
(Take $g=10m/s^2$)

Q. In a Young's doubble slit experiment, the ratio of the slit's width is $4:1$. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :

1. $(\sqrt{3}+1{)}^4:16$
2. $9:1$
3. $4:1$
4. $25:9$

Q. A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R$. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about its axis and $I_2$ be the moment of inertia of the new sphere about its axis. The ratio $I_1/I_2$ is given by :

Q. The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies $9Hz$ and $11Hz$ is :

Q. One mole of an ideal gas passes through a process where pressure and volume obey the relation $P=P_0[1-\frac{1}{2}{\left(\frac{V_0}{V}\right)}^2]$. Here $P_0$ and $V_0$ are constants . Calculate the change in the temperature of the gas if its volume change from $V_o$ to $2V_o$.