Q. 1 kg of water is converted into steam at the same temperature and at 1 atm (100 kPa). The density of water and steam are 1000 kgm${}^{-3}$ and 0.6 kgm${}^{-3}$ respectively. The latent heat of vaporisation of water is $2.25\times {10}^{6}Jk{g}^{-1}$. What will be increase in energy?

1. $3\times {10}^{5}J$
2. $4\times {10}^{6}J$
3. $2.08\times {10}^{6}J$
4. None of these

Q. The lower end of capillary tube is immersed in mercury. The level of mercury in the tube is found to be 2 cm below the outer level. If the same tube is immersed in water, upto what height(in cm) will the water rise in the capillary?

1. 5.9
2. 4.9
3. 2.9
4. 1.9

Q. Find the increase in pressure required to decrease the volume of water sample by 0.01%. Bulk modulus of water $=2.1\times {10}^{9}N{m}^{-2}$.

1. $4.3\times {10}^{4}N/m^2$
2. $1.8\times {10}^{7}N/m^2$
3. $2.1\times {10}^{5}N/m^2$
4. $3.7\times {10}^{4}N/m^2$

Q. A block slides down on an incline of angle 30${}^o$ with an acceleration $\frac{g}{4}$. Find the coefficient of kinetic friction .

1. $\frac{1}{2\sqrt{2}}$
2. 0.6
3. $\frac{1}{2\sqrt{3}}$
4. $\frac{1}{\sqrt{2}}$

Q. The earth receives solar radiation at a rate of 8.2 J cm${}^{-2}$ min${}^{-1}$. If the sun radiates as the black bodies, the temperature at the surface of the sun will be (the angle subtended by sun on the earth in suppose 0.53${}^o$ and Stefan constant is $\sigma =5.67\times {10}^{-8}W{m}^{-2}{K}^4$)

1. 5800 K
2. 8000 K
3. 6700 K
4. 7800 K

Q. A wire of resistance 10$\Omega$ is bent to form a complete circle. Find its resistance between two diametrically opposite point.

1. $2.5\Omega$
2. $1.25\Omega$
3. $5\Omega$
4. $\frac{10}{3}\Omega$

Q. A particle is subjected to two simple harmonic motions along X-axis while other is along a line making angle 45${}^o$ with the X-axis. The two motions are given by $x=x_{0}sin\omega t$ and $s=s_{0}sin\omega t$.
The amplitude of resultant motion is

1. $\sqrt{x_0^2-s_0^2+2x_0{s}_0}$
2. $x_0+s_0+2x_0{s}_0$
3. $[x_0^2+s_0^2+\sqrt{2}{x}_0{s}_0{]}^{1/2}$
4. $\sqrt{x_0^2+s_0^2}$

Q. A uniform ring of mass $m$ and radius $a$ is placed directly above a uniform sphere of mass ($M$) and of equal radius. The centre of the ring is at a distance $\sqrt{3}$a from the centre of the sphere. The gravitational force (F) exerted by the sphere on the ring is

1. $\frac{2GMm}{3a^2}$
2. $\frac{7GMm}{\sqrt{2}{a}^2}$
3. $\frac{3GMm}{a^2}$
4. $\frac{\sqrt{3}GMm}{8a^2}$

Q. Figure shows spring + block + pulley system which are light. The time period of mass would be

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

Q. A copper rod of length 20 cm and cross-sectional area 2 mm${}^2$ is joined with a similar aluminium rod as shown below
The resistance of pair of rods is (${\rho }_{Al}=2.6\times {10}^{-8}\Omega -m$ and ${\rho }_{Cu}=1.7\times {10}^{-8}\Omega -m$)

1. 1.0 m $\Omega$
2. 3.0 m $\Omega$
3. 2.0 m $\Omega$
4. None of these

Q. Find the resistance of a hollow cylindrical conductor of length $1m$ with inner radius 1.0 mm and outer radius 2.0 mm respectively. The resistivity of the material is $2.0\times {10}^{-8}\Omega m$.

1. $2.1\times {10}^{-3}\Omega$
2. $1.3\times {10}^{-4}\Omega$
3. $3.2\times {10}^{-4}\Omega$
4. $4.6\times {10}^{-2}\Omega$

Q. The distance x (in $\mu$m) covered by a molecule starting from point A at time t = 0 and stopping at another point B is given by the equation
$x=t^2(2-\frac{t}{3})$
The distance between A and B (in $\mu$m) is closed to

1. 10.7
2. 20.7
3. 40.7
4. 50.7

Q. Water level is maintained in a cylindrical vessel upto a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?

1. $h=\frac{H}{2}$
2. $h=\frac{3H}{2}$
3. $h=\frac{2H}{3}$
4. $h=\frac{3}{4}H$

Q. The density of a rod having length $l$ varies as $\rho =c+dx$, where $x$ is the distance from the left end. The centre of mass is:

1. $\frac{3cl+2D{l}^2}{3(2c+Dl)}$
2. $\frac{2cl+3D{l}^2}{2(4c+8l)}$
3. $\frac{2cl+3D{l}^2}{3(2c+l)}$
4. $\frac{cl+D{l}^2}{3(2c+Dl)}$

Q. A 4 kg block is suspended from the ceiling of an elevator through a spring having a linear mass density of $19.2\times {10}^{-3}kg{m}^{-3}$. Find the speed with respect to spring with which a wave pulse can proceed on the spring if the elevator accelerates up at the rate of 2.0 ms${}^{-2}$ Take g = 10 ms${}^{-2}$

1. 30 m/s
2. 42 m/s
3. 46 m/s
4. 50 m/s

Q. A diatomic gas $(\gamma =1.4)$ does 200 J of work when it is expanded isobarically. Find the heat given to the gas in the process.

1. 500 J
2. 700 J
3. 600 J
4. 900 J

Q. A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as showing in figure
If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

1. $\frac{F}{2m}$
2. $\frac{3F}{7m}$
3. $\frac{10F}{7m}$
4. $\frac{7F}{2m}$

Q. A horizontal tube of length $l$ closed at both ends, contains an ideal gas of molecular weight M. The tube is rotated at a constant angular velocity $\omega$ about a vertical axis passing through an end. Assuming the temperature to be uniform and constant. If ${\rho }_1$ and ${\rho }_2$ denote the pressure at free and the fixed end respectively, then choose the correct relation.

1. $\frac{{\rho }_2}{{\rho }_1}=e^{\frac{M{\omega }^2{l}^2}{2RT}}$
2. $\frac{{\rho }_1}{{\rho }_2}=e^{\frac{M\omega l^2}{RT}}$
3. $\frac{{\rho }_1}{{\rho }_2}=e^{\frac{\omega lM}{3RT}}$
4. $\frac{{\rho }_2}{{\rho }_1}=e^{\frac{M^2{\omega }^2{l}^2}{3RT}}$

Q. An inductor (L = 20 H), a resistor (R = 100 $\Omega$) and a battery (E = 10 V) are connected in series. After a long time, the circuit is short-circuited and then the battery is disconnected. Find the current in the circuit at 1 ms after short circuiting.

1. $4.5\times {10}^{5}A$
2. $3.2\times {10}^{-5}A$
3. $9.9\times {10}^{-2}A$
4. $6.7\times {10}^{-4}A$

Q. The angle between two linear transmembrane domain is defined by following vectors $a=\hat{i}+\hat{j}-\hat{k}$ and $b=\hat{i}-\hat{j}+\hat{k}$

1. $co{s}^{-1}\left(\frac{1}{3}\right)$
2. $co{s}^{-1}\left(\frac{-1}{3}\right)$
3. $si{n}^{-1}\left(\frac{1}{3}\right)$
4. $si{n}^{-1}\left(\frac{-1}{3}\right)$

Q. The rms speed (in m/s) of oxygen molecules of the gas at temperature $300K$, is

1. $483$
2. $504$
3. $377$
4. $346$

Q. Two charges of +10 $\mu$C and +20 $\mu$C are separated by a distance of $2cm$. The net potential (electric) due to the pair at the middle point of the line joining the two charges, is :

1. $27MV$
2. $18MV$
3. $20MV$
4. $23MV$

Q. A lead ball at 30${}^o$C is dropped from a height of 6.2 km. The ball is heated due to the air resistance and it completely melts just before reaching the ground. The molten substance falls slowly on the ground. If the specific heat of lead = 126 Jkg${}^{-1}$${}^o$C${}^{-1}$ and melting point of lead = 130${}^o$C and suppose that any mechanical energy lost is used to heat the ball, then the latent heat of fusion of lead is

1. $7.6\times {10}^{2}Jk{g}^{-1}$
2. $2.4\times {10}^{4}Jk{g}^{-1}$
3. $3.6\times {10}^{4}Jk{g}^{-1}$
4. $4.9\times {10}^{4}Jk{g}^{-1}$
5. $7.9\times {10}^{4}Jk{g}^{-1}$

Q. What is the change in the volume of 1.0 L kerosene, when it is subjected to an extra pressure of $2.0\times {10}^{5}N{m}^{-2}$ from the following data? Density of kerosene = 800 kg m${}^{-3}$ and speed of sound in kerosene = 1330 ms${}^{-1}$

1. 0.97 cm${}^{-3}$
2. 0.66 cm${}^{-3}$
3. 0.59 cm${}^{-3}$
4. 0.15 cm${}^{-3}$

Q. Two long straight wires, each carrying an electric current of 5 A, are kept parallel to each other at a separation of 2.5 cm. Find the magnitude of the magnetic force experienced by 10 cm of a wire.

1. $4.0\times {10}^{-4}N$
2. $2.0\times {10}^{-5}N$
3. $3.5\times {10}^{-6}N$
4. $2.0\times {10}^{-9}N$

Q. Three equal charges, each having a magnitude of $2.0\times {10}^{-6}C$ are placed at the three corners of a right angled triangle of sides $3cm,$ $4cm$ and $5cm.$ The force (in magnitude) on the charge at the right angled corner is :

1. $50N$
2. $26N$
3. $29N$
4. $45.9N$

Q. One end of a massless spring of constant 100 N/m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the mass is made to rotate at angular velocity of 2 rad/s, then elongation of spring is

1. 0.1 m
2. 10 cm
3. 1 cm
4. 0.01 cm

Q. A projectile is fired with a velocity $u$ at angle $\theta$ with the ground surface. During the motion at any time it is making an angle $\alpha$ with the ground surface. The speed of particle at this time will be

1. $ucos\theta sec\alpha$
2. $u^{2}co{s}^2\alpha si{n}^2\alpha$
3. $ucos\theta .tan\alpha$
4. $usin\theta .sin\alpha$

Q. The ammeter shown in figure consists of a 480 $\Omega$ coil connected in parallel to a 20 $\Omega$ shunt. The reading of ammeter is

1. 0.125 A
2. 1.67 A
3. 0.13 A
4. 0.67 A

Q. The parts of two concentric circular arcs joined by two radial lines and carries current $i$. The arcs subtend an angle $\theta$ at the center of the circle. The magnetic field at the centre O, is

1. $\frac{{\mu }_{0}i(b-a)\theta }{4\pi ab}$
2. $\frac{{\mu }_{0}i(b-a)}{\pi -\theta }$
3. $\frac{{\mu }_{0}i(a-b)}{2\pi ab}$
4. $\frac{{\mu }_{0}i(b-a)\theta }{\pi ab}$