Q. A black body has a wavelength of $\lambda$ at temperature $2000K$. Its corresponding wavelength at temperature $3000K$ will be :

1. $\frac{2\lambda }{3}$
2. $\frac{4\lambda }{9}$
3. $\frac{3\lambda }{2}$
4. $\frac{9\lambda }{4}$

Q. A uniform wire of resistance $R$ and length $L$ is cut into four equal parts, each of length $\frac{L}{4}$, which are then connected in parallel combination. The effective resistance of the combination will be

1. $R$
2. $4R$
3. $\frac{R}{16}$
4. $\frac{R}{4}$

Q. A capacitor of capacitance $5\mu F$ is connected as shown in the figure. The internal resistance of the cell is $0.5\Omega$. The amount of charge on the capacitor plates is:

1. $80\mu C$
2. $20\mu C$
3. $12.5\mu C$
4. $40\mu C$

Q. A square wire frame of size $L$ is dipped in a liquid. On taking out a membrane is formed. If the surface tension of liquid is $T$, then force acting on the frame will be

1. $2TL$
2. $4TL$
3. $8TL$
4. $16TL$

Q. A wire can be broken by applying load of $200N$. The force required to break another wire of the same length and same material, but double in diameter is

1. $400N$
2. $200N$
3. $600N$
4. $800N$

Q. The potential energy of a particle varies with distance $x$ from fixed a origin as $U=\left(\frac{A\sqrt{x}}{x+B}\right)$; where, $A$ and $B$ are constants. The dimensions of $AB$ are

1. $\left[M{L}^{5/2}{T}^{-2}\right]$
2. $\left[M{L}^2{T}^{-2}\right]$
3. $\left[M^{3/2}{L}^{3/2}{T}^{-2}\right]$
4. $\left[M{L}^{7/2}{T}^{-2}\right]$

Q. A plane mirror produces a magnification of:

1. Zero
2. $-1$
3. $+1$
4. Between $0$ and $+1$

Q. Two spherical bodies of masses $M$ and $5M$ and radii $R$ and $2R$ respectively are released in free space with initial separation between their centres equal to $12R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision, is:

1. $1.5R$
2. $7.5R$
3. $2.5R$
4. $4.5R$

Q. A cube of side $40mm$ has its upper face displaced by $0.1mm$ by a tangential force of $8kN$. The shearing modulus of cube is

1. $2\times {10}^{9}N{m}^{-2}$
2. $4\times {10}^{9}N{m}^{-2}$
3. $8\times {10}^{9}N{m}^{-2}$
4. $16\times {10}^{9}N{m}^{-2}$

Q. Three capacitors of capacitances $1\mu F$, $2\mu F$ and $4\mu F$ are connected first in a series combination, and then in a parallel combination. The ratio of their equivalent capacitances will be:

1. $49:2$
2. $4:49$
3. $2:49$
4. $49:4$

Q. The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis passing from the edge of the disc and normal to the disc is

1. $M{R}^2$
2. $\frac{1}{2}M{R}^2$
3. $\frac{3}{2}M{R}^2$
4. $\frac{7}{2}M{R}^2$

Q. At room temperature, copper has free electron density of $8.4\times {10}^{28}{m}^{-3}$. The electron drift velocity in a copper conductor of cross-sectional area of ${10}^{-6}{m}^2$ and carrying a current of $5.4A$, will be

1. $0.4{ms}^{-1}$
2. $4cm{s}^{-1}$
3. $0.4mm{s}^{-1}$
4. $4{ms}^{-1}$

Q. An electron of mass $m$ and charge $q$ is travelling with a speed $v$ along a circular path of radius $r$ at right angles to a uniform magnetic field $B$. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

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

Q. A galvanometer acting as a voltmeter should have:

1. Low resistance in parallel with its coil
2. Low resistance in series with its coil
3. High resistance in parallel with its coil
4. High resistance in series with its coil

Q. The neck and bottom of a bottle are $3cm$ and $15cm$ in radius respectively. If the cork is pressed with a force $12N$ in the neck of the bottle, then force exerted on the bottom of the bottle is

1. $30N$
2. $150N$
3. $300N$
4. $600N$

Q. A satellite orbiting the earth in a circular orbit of radius $R$ completes one revolution in $3h$. If orbital radius of geostationary satellite is $36000km$, orbital radius of satellite is

1. $9000km$
2. $15000km$
3. $12000km$
4. $6000km$

Q. $1mole$ of an ideal gas at an initial temperature of $TK$ does $6R$ joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5/3$, then final temperature of the gas will be

1. $(T-2.4)K$
2. $(T-4)K$
3. $(T+2.4)K$
4. $(T+4)K$

Q. A weightless thread can bear tension upto $37N$. A stone of mass $500g$ is tied to it and revolved in a circular path of radius $4m$ in a vertical plane. If $g=10{ms}^{-2}$, then the maximum angular velocity of the stone will be:

1. $16rad{s}^{-1}$
2. $2rad{s}^{-1}$
3. $4rad{s}^{-1}$
4. $8rad{s}^{-1}$

Q. Two coherent light beams of intensities $I$ and $4I$ are suspended. The maximum and minimum possible intensities in the resulting beam are

1. $5I$ and $I$
2. $5I$ and $3I$
3. $9I$ and $I$
4. $9I$ and $3I$

Q. Figure shows three spherical and equipotential surfaces $A$, $B$ and $C$ around a point charge $q$. The potential difference $V_A-V_B=V_B-V_C$. If $t_1$ and $t_2$ be the distances between them, then :

1. $t_1=t_2$
2. $t_1\le t_2$
3. $t_1<t_2$
4. $t_1>t_2$

Q. A charge $q$ is located at the centre of a cube. The electric flux through any face is :

1. $\frac{\pi q}{6\left(4\pi {\epsilon }_0\right)}$
2. $\frac{4\pi q}{6\left(4\pi {\epsilon }_0\right)}$
3. $\frac{q}{6\left(4\pi {\epsilon }_0\right)}$
4. $\frac{2\pi q}{6\left(4\pi {\epsilon }_0\right)}$

Q. The equation of a wave is $y=5\sin (\frac{t}{0.04}-\frac{x}{4})$; where $x$ is in $cm$ and $t$ is in second. The wave velocity of the wave will be

1. $2.5{ms}^{-1}$
2. $2{ms}^{-1}$
3. $1.5{ms}^{-1}$
4. $1{ms}^{-1}$

Q. If Young's double slit experiment is performed in water instead of air, then

1. Fringe width would increase
2. Fringe width would decrease
3. Fringe width would remain unchanged
4. No fringes would be seen

Q. Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency ${\nu }_1$ and the other with frequency ${\nu }_2$. The ratio $\frac{{\nu }_1}{{\nu }_2}$ is

1. 4
2. 8
3. 2
4. 1

Q. In $0.1s$, the current in a coil increases from $1A$ to $1.5A$. If inductance of coil is $60mH$, then induced current in external resistance of $3\Omega$ will be

1. $0.2A$
2. $1A$
3. $0.5A$
4. $0.1A$

Q. Consider a compound slab consisting of two different materials having equal lengths, thicknesses and thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is

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

Q. The magnetic flux linked with a coil at any instant $t$ is given by the equation $\varphi =5t^3-100t+300$. The magnitude of emf induced in the coil after $3s$ is

1. $10V$
2. $20V$
3. $35V$
4. $70V$

Q. $64$ spherical rain drops of equal size are falling vertically through air with a terminal velocity $1.5{ms}^{-1}$. If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is:

1. $8{ms}^{-1}$
2. $16{ms}^{-1}$
3. $24{ms}^{-1}$
4. $32{ms}^{-1}$

Q. A frog can be levitated in magnetic field produced by a current in a vertical solenoid placed below the frog. This is possible because the body of the frog behaves as

1. Ferromagnetic
2. Diamagnetic
3. Anti-ferromagnetic
4. Paramagnetic

Q. An electric current passes through a long straight copper wire. At a distance $5cm$ from the straight wire, the magnetic field is $B$. The magnetic field at $20cm$ from the straight wire would be

1. $\frac{B}{6}$
2. $\frac{B}{4}$
3. $\frac{B}{3}$
4. $\frac{B}{2}$