Q. A mixture of light, consisting of wavelength $590nm$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the $4^{th}$ bright fringe of the unknown light. From this data, the wavelength of the unknown light is:

1. $393.4nm$
2. $885.0nm$
3. $442.5nm$
4. $776.8nm$

Q. The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g=$ the acceleration due to gravity on the surface of the earth) in terms of $R$, the radius of the earth, is:

1. $2R$
2. $R/2$
3. $\frac{R}{\sqrt{2}}$
4. $\sqrt{2}R$

Q. The surface of a metal is illuminated with the light of $400nm$. The kinetic energy of the ejected photoelectrons was found to be 1.68 $eV$. The work function of the metal is :

1. $1.41$ $eV$
2. $3.09$ $eV$
3. $1.51$ $eV$
4. $1.68$ $eV$

Q. If $x$, $v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T$, then, which of the following does not change with time?

1. $a^2{T}^2+4{\pi }^2{v}^2$
2. $\frac{aT}{x}$
3. $aT+2\pi v$
4. $\frac{aT}{v}$

Q. A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is -

1. ${\sin }^{-1}\left(\frac{1}{2}\right)$
2. ${\sin }^{-1}\left(\frac{2}{\sqrt{3}}\right)$
3. ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$.
4. ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Q. An inductor of inductance $L=400mH$ and resistors of resistances $R_1=2\Omega$ and $R_2=2\Omega$ are connected to a battery of emf $12$ $V$ as shown in the figure. The intemal resistance of the battery is negligible. The switch $S$ is closed at $t=0$. The potential drop across $L$ as a function of time is :

1. $\frac{12}{t}{e}^{-3t}V$
2. $6$ $e^{-5t}V$
3. $12$ $e^{-5t}$ $V$
4. $6(1-e^{-t/0.2})V$

Q. A charge $Q$ is placed at each of the opposite comers of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q/q$ equals:

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

Q. Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area $A$ and wire 2 has cross- sectional area $3A$. If the length of wire 1 increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire 2 by the same amount ?

1. $F$
2. $4F$
3. $6F$
4. $9F$

Q. Two moles of Helium gas are taken over the cycle ABCDA as shown in the P-T diagram. Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is :

1. $200$ $R$
2. $300$ $R$
3. $400$ $R$
4. $500$ $R$

Q. Two moles of Helium gas are taken over the cycle ABCDA as shown in the P-T diagram. The net work done on the gas in the cycle $ABCDA$ is :

1. $0$
2. $276$ $R$
3. $1076$ $R$
4. $1094$ $R$

Q. A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of :

1. $\frac{l^2{\omega }^2}{8g}$
2. $\frac{l^2{\omega }^2}{3g}$
3. $\frac{l^2{\omega }^2}{2g}$
4. $\frac{l^2{\omega }^2}{6g}$

Q. A p-n junction diode shown in the figure can act as a rectifier. An alternating current source $\left(V\right)$ is connected in the circuit. The current $\left(I\right)$ in the resistor $\left(R\right)$ can be shown by :

1. 
   
2. 
   
3. 
   
4. 
   

Q. A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius = $b$) and $DA$ (radius = $a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is ${30}^o$. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field due to the loop $ABCD$ at the origin $\left(O\right)$ is:

1. $zero$
2. $\frac{{\mu }_{0}I}{4\pi }\left[\frac{b-a}{ab}\right]$
3. $\frac{{\mu }_{0}I(b-a)}{24ab}$
4. $\frac{{\mu }_{0}I}{4\pi }\left[2\right(b-a)+\frac{\pi }{3}(a+b\left)\right]$.

Q. Three sound waves of equal amplitudes have frequencies $(v-1),v,(v+1)$. They superpose to give beats. The number of beats produced per second will be

1. $4$
2. $3$
3. $2$
4. $1$

Q. A long metallic bar is carrying heat from one of its ends to the other end under steady state. The variation of temperature $q$ along the length $x$ of the bar from its hot end is best described by which of the following figures ?

1. 
   
2. 
   
3. 
   
4. 
   

Q. A motor cycle starts from rest and accelerates along a straight path at $2$ $m/s^2$. At the starting point of the motor cycle, there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\%$ of its value when the motor cycle was at rest?

1. $196$ $m$
2. $147$ $m$
3. $98$ $m$
4. $49$ $m$

Q. Statement 1: The temperature dependence of resistance is usually given as $R=R_0(1+\alpha \Delta t)$. The resistance of a wire changes from 100 $\Omega$ to 150 $\Omega$ when its temperature is increased from ${27}^{o}C$ to ${227}^{o}C$. This implies that $\alpha =2.5\times {10}^{-3}{/}^{o}C$.
Statement 2: $R=R_0(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=(R-R_0)<<R_0$.

1. Statement 1 is True, Statement 2 is False.
2. Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1.
3. Statement 1 is False, Statement 2 is True.
4. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1.

Q. The logic circuit shown below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform.

1. 
   
2. 
   
3. 
   
4. 
   

Q. A particle has an initial velocity of $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after $10s$ is:

1. $10$ units
2. $7\sqrt{2}$ units
3. $7$ units
4. $8.5$ units

Q. The transition from the state $n=4$ to $n=3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

1. $2\to 1$
2. $4\to 2$
3. $5\to 4$.
4. $3\to 2$

Q. In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v$, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of ${45}^o$ with the $x$-axis meets the experimental curve at P. The coordinates of $P$ will be

1. $(2f,2f)$
2. $(\frac{f}{2},\frac{f}{2})$
3. $(f,f)$
4. $(4f,4f)$.

Q. In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree$(={0.5}^o)$, then the least count of the instrument is:

1. One minute
2. One degree
3. Half degree
4. Half minute

Q. Consider a rubber ball freely falling from a height $h=4.9m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be :

1. 
   
2. 
   
3. 
   
4. 
   

Q. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I isflowing in the loop. Angle made by AB and CD at the origin O is ${30}^o$. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin.Due to the presence of the current $I_1$ at the origin :

1. the forces on AB and DC are zero
2. the magnitude of the net force on the loop is given by $\frac{{\mu }_{0}I{I}_1}{24ab}(b-a)$
3. the magnitude of the net force on the loop is given by $\frac{I_{1}I}{4\pi }{\mu }_0\left[2\right(b-a)+\frac{\pi }{3}(a+b\left)\right]$
4. the forces on AD and BC are zero

Q. The above is a plot of binding energy per nucleon $E_b$, against the nuclear mass $M;A,B,C,D,E,F$ correspond to different nuclei. Consider four reactions :
(i) $A+B\to C+ϵ$
(ii) $C\to A+B+ϵ$
(iii) $D+E\to F+ϵ$
(iv) $F\to D+E+ϵ$
where $ϵ$ is the energy released ? In which reaction is $ϵ$ positive ?

1. (i) and (iv)
2. (i) and (iii)
3. (ii) and (iv)
4. (ii) and (iii).

Q. Let $P\left(r\right)=\frac{Q}{\pi R^4}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge Q. For a point $p_1$ inside the sphere at distance $r_1$ from the centre of sphere, the magnitude of electric field is

1. $\frac{Q}{4\pi {ϵ}_0{r}_1^2}$
2. $\frac{Q{r}_1^2}{4\pi {ϵ}_0{R}^4}$
3. $\frac{Q{r}_1^2}{3\pi {ϵ}_0{R}^4}$
4. $0$

Q. Statement 1: For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connected point $P$ to point Q.
Statement 2: The net work done by a conservative force on an object moving along a closed loop is zero.

1. Statement 1 is True, Statement 2 is False.
2. Statement 1 is False, Statement 2 is True.
3. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1.
4. Statement 1 is True, Statement 2 is True; Statement 2 is not the correct explanation for Statement 1.

Q. One $kg$ of a diatomic gas is at a pressure of $8\times {10}^{4}N/m^2$. The density of the gas is $4$ $kg/m^3$. What is the energy of the gas due to its thermal motion ?

1. $3\times {10}^{4}J$
2. $7\times {10}^{4}J$
3. $5\times {10}^{4}J$
4. $6\times {10}^{4}J$

Q. Two points $P$ and $Q$ are maintained at the potentials of $10V$ and $-4V$, respectively. The work done in moving 100 electrons from $P$ to $Q$ is :

1. $2.24\times {10}^{-16}J$
2. $-2.24\times {10}^{-16}J$
3. $9.60\times {10}^{-17}J$
4. $-9.60\times {10}^{-17}J$

Q. Two moles of Helium gas are taken over the cycle ABCDA as shown in the P-T diagram. Assuming the gas to be ideal the work done on the gas in taking it from $D$ to $A$ is :

1. $+414$ $R$
2. $-414$ $R$
3. $-690$ $R$
4. $+690$ $R$