A thin lens made of glass (refractive index $= 1.5$) of focal length $f = 16 \mathrm {~cm}$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f _ { l }$, then the ratio $f _ { l } / f$ is closest to the integer:
(1) 1
(2) 9
(3) 5
(4) 17

In a Young's double slit experiment, the separation between the slits is 0.15 mm. In the experiment, a source of light of wavelength 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is:
(1) 6.9 mm
(2) 3.9 mm
(3) 5.9 mm
(4) 4.9 mm

An electron (of mass $m$) and a photon have the same energy $E$ in the range of a few eV. The ratio of the de Broglie wavelength associated with the electron and the wavelength of the photon is ($c =$ speed of light in vacuum)
(1) $\frac { 1 } { c } \left( \frac { 2 E } { m } \right) ^ { 1 / 2 }$
(2) $c ( 2 m E ) ^ { 1 / 2 }$
(3) $\frac { 1 } { c } \left( \frac { E } { 2 m } \right) ^ { 1 / 2 }$
(4) $\left( \frac { E } { 2 m } \right) ^ { 1 / 2 }$

The activity of a radioactive sample falls from $700 \mathrm {~s} ^ { - 1 }$ to $500 \mathrm {~s} ^ { - 1 }$ in 30 minutes. Its half life is close to:
(1) 72 min
(2) 62 min
(3) 66 min
(4) 52 min

$ABC$ is a plane lamina of the shape of an equilateral triangle. $D , E$ are mid-points of $AB , AC$ and $G$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and perpendicular to the plane $ABC$ is $I _ { 0 }$. If part $ADE$ is removed, the moment of inertia of the remaining part about the same axis is $\frac { N I _ { 0 } } { 16 }$ where $N$ is an integer. Value of $N$ is:

A non-isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10 ^ { - 5 } / { } ^ { \circ } \mathrm { C }$ along the x-axis and $5 \times 10 ^ { - 6 } / { } ^ { \circ } \mathrm { C }$ along the y and the z-axis. If the coefficient of volume expansion of the solid is $\mathrm { C } \times 10 ^ { - 6 } / { } ^ { \circ } \mathrm { C }$ then the value of $\mathbf { C }$ is $\_\_\_\_$

An asteroid is moving directly towards the centre of the earth. When at a distance of $10R$ ($R$ is the radius of the earth) from the centre of the earth, it has a speed of $12\,\mathrm{km\,s^{-1}}$. Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is $11.2\,\mathrm{km\,s^{-1}}$)? Give your answer to the nearest integer in $\mathrm{km\,s^{-1}}$ $\underline{\hspace{1cm}}$.

One end of a straight uniform $1 m$ long bar is pivoted on horizontal table. It is released from rest when it makes an angle $30 ^ { \circ }$ from the horizontal (see figure). Its angular speed when it hits the table is given as $\sqrt { n } \mathrm { rad } s ^ { - 1 }$, where $n$ is an integer. The value of $n$ is $\_\_\_\_$

A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre?

A circular disc of mass M and radius R is rotating about its axis with angular speed $\omega _ { 1 }$. If another stationary disc having radius $\frac { \mathrm { R } } { 2 }$ and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega _ { 2 }$. The energy lost in the process is $p \%$ of the initial energy. Value of $p$ is $\_\_\_\_$

The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta \mathrm { P }$ is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $\Delta \mathrm { T }$ at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm respectively. If $| \Delta \mathrm { T } | = \mathrm { C } | \Delta \mathrm { P } |$ then value of C in (K/atm) is $\_\_\_\_$

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is $\_\_\_\_$

Three containers $C_{1}$, $C_{2}$ and $C_{3}$ have water at different temperatures. The table below shows the final temperature $T$ when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process)

$C_{1}$	$C_{2}$	$C_{3}$	$T$
$1l$	$2l$	--	$60^{\circ}\mathrm{C}$
--	$1l$	$2l$	$30^{\circ}\mathrm{C}$
$2l$	--	$1l$	$60^{\circ}\mathrm{C}$
$1l$	$1l$	$1l$	$\theta$

The value of $\theta$ (in ${}^{\circ}\mathrm{C}$ to the nearest integer) is $\underline{\hspace{1cm}}$

Nitrogen gas is at $300^\circ\mathrm{C}$ temperature. The temperature (in K) at which the rms speed of a $\mathrm{H_2}$ molecule would be equal to the rms speed of a nitrogen molecule, is $\_\_\_\_$ (Molar mass of $\mathrm{N_2}$ gas 28 g).

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300 \mathrm {~m} / \mathrm { s }$, the frequency difference between the fundamental and second harmonic of this pipe is $\_\_\_\_$ Hz.

A loop $ABCDEFA$ of straight edges has six corner points $A(0,0,0), B(5,0,0), C(5,5,0), D(0,5,0), E(0,5,5)$ and $F(0,0,5)$. The magnetic field in this region is $\vec { B } = (3 \hat { i } + 4 \hat { k }) T$. The quantity of flux through the loop $ABCDEFA$ (in Wb) is $\_\_\_\_$

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) $\_\_\_\_$

The series combination of two batteries, both of the same emf 10 V, but different internal resistance of $20\,\Omega$ and $5\,\Omega$, is connected to the parallel combination of two resistors $30\,\Omega$ and $x\,\Omega$. The voltage difference across the battery of internal resistance $20\,\Omega$ is zero, the value of $x$ (in $\Omega$) is $\underline{\hspace{1cm}}$

The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is 40 cm. If the power of the lens is close to $\left( \frac { \mathrm { N } } { 100 } \right) \mathrm { D }$ where N is an integer, the value of N is $\_\_\_\_$

A prism of angle $A = 1^\circ$, $\mu = 1.5$. A good estimate for the minimum angle of deviation (in degrees) is close to $\frac{N}{10}$. Value of N is $\_\_\_\_$

Four resistances of $15 \Omega , 12 \Omega , 4 \Omega$ and $10 \Omega$ respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of $10 \Omega$ to balance the network is $\_\_\_\_$ $\Omega$.

A beam of electromagnetic radiation of intensity $6.4 \times 10 ^ { - 5 } \mathrm {~W} / \mathrm { cm } ^ { 2 }$ is comprised of wavelength, $\lambda = 310 \mathrm {~nm}$. It falls normally on a metal (work function $\varphi = 2 e V$) of surface area of $1 \mathrm {~cm} ^ { 2 }$. If one in $10 ^ { 3 }$ photons ejects an electron, total number of electrons ejected in 1 s is $10 ^ { x }$. ($h c = 1240 \mathrm { eVnm } , 1 \mathrm { eV } = 1.6 \times 10 ^ { - 19 } J$), then $x$ is $\_\_\_\_$

The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of $10 \Omega$ is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the cell is $\frac { \mathrm { n } } { 10 } \Omega$, where n is an integer then value of n is $\_\_\_\_$

Orange light of wavelength $6000 \times 10 ^ { - 10 }$ m illuminates a single slit of width $0.6 \times 10 ^ { - 4 }$ m. The maximum possible number of diffraction minima produced on both sides of the central maximum is $\_\_\_\_$

The surface of a metal is illuminated alternately with photons of energies $E_1 = 4\,\mathrm{eV}$ and $E_2 = 2.5\,\mathrm{eV}$ respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is $\_\_\_\_$