Q. A bat moving at $10m{s}^{-1}$ towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound $=320m{s}^{-1}$)

1. 8258
2. 8000
3. 8516
4. 8424

Q. You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :

1. 60 cm
2. 30 cm
3. -24 cm
4. 24 cm

Q. If a body moving in a circular path maintains constant speed of $410m{s}^{-1}$, then which of the following correctly describes relation between acceleration and radius?

1. 
   
2. 
   
3. 
   
4. 
   

Q. A simple harmonic oscillator of angular frequency $2rad{s}^{-1}$ is acted upon by an external force $F=\left(sint\right)N$. If the oscillator is at rest in its equilibrium position at $t=0$, its position at later times is proportional to :

1. $cost-\frac{1}{2}sin2t$
2. $sint-\frac{1}{2}sin2t$
3. $sint+\frac{1}{2}sin2t$
4. $sint+\frac{1}{2}cos2t$

Q. If the capacitance of a nano capacitor is measured in terms of a unit ${}^{\prime }{\mu }^{\prime }$ made by combining the electronic charge 'e', bohr radius '$a_0$', Planck's constant '$h$' and speed of light '$c$' then which of the following relation is possible?

1. $\mu =\frac{e^{2}h}{c{a}_0}$
2. $\mu =\frac{hc}{e^2{a}_0}$
3. $\mu =\frac{e^{2}c}{h{a}_0}$
4. $\mu =\frac{e^2{a}_0}{hc}$

Q. Suppose the drift velocity $v_d$ in a material varied with the applied electric field $E$ as: $v_d\propto \sqrt{E}$. Then V - I graph for a wire made of such a material is best given by

1. 
   
2. 
   
3. 
   
4. 
   

Q. x and y displacements of a particle are given as x(t)=a sin $\omega t$ and y(t)=a sin 2$\omega$t.
Its trajectory will look like.

1. 
   
2. 
   
3. 
   
4. 
   

Q. Consideration a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about of its diagonals, then

1. $I=\frac{m{a}^2}{12}$
2. $I=\frac{m{a}^2}{24}$
3. $I>\frac{m{a}^2}{12}$
4. $\frac{m{a}^2}{24}<I<\frac{m{a}^2}{12}$

Q. A block of a mass of $10$ kg rests on a horizontal table. The coefficient of friction between the block and the table is $0.05$. When hit by a bullet of mass $50$ g moving with speed $v$, that gets embedded in it, the block moves and comes to rest after moving a distance of $2$ m on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height H, then neglecting energy losses and taking $g=10m{s}^{-2}$, the value of H is close to:

1. $0.04km$
2. $0.05km$
3. $0.02km$
4. $0.03km$

Q. Show in the figure are two point charges +Q and -Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If ${\sigma }_1$ is the surface charge on the inner surface and $Q_1$ net charge on it and ${\sigma }_2$ the surface charge on the outer surface and $Q_2$ net charge on it then :

1. ${\sigma }_1\ne 0,Q_1=0{\sigma }_2\ne 0,Q_2=0$
2. ${\sigma }_1\ne 0,Q_1\ne 0{\sigma }_2=0,Q_2\ne 0$
3. ${\sigma }_1\ne 0,Q_1=0{\sigma }_2=0,Q_2=0$
4. ${\sigma }_1=0,Q_1=0{\sigma }_2=0,Q_2=0$

Q. A 10V battery with internal resistance 1 $\Omega$ and a 15V battery with internal resistance $0.6\Omega$ are connected in parallel to a voltmeter. The reading in the voltmeter will be close to.

1. 11.9 V
2. 13.1 V
3. 24.5 V
4. 12.5 V

Q. When current is coil changes from 5 A to 2 A in 0.1 s, an average of 50 V is produced. The self-inductance of the coil is.

1. 6 H
2. 0.67 H
3. 1.67 H
4. 3 H

Q. A proton (mas m) accelerated by a potential difference V files through a uniform transverse magnetic field B. The field occupies a region of space by width 'd'. If '$\alpha$' be the angle of deviation of proton from initial direction of motion (see figure), the value of $\sin \alpha$ will be:

1. $Bd\sqrt{\frac{q}{2mV}}$
2. $qV\sqrt{\frac{Bd}{2m}}$
3. $\frac{B}{d}\sqrt{\frac{q}{2mV}}$
4. $\frac{B}{d}\sqrt{\frac{qd}{mV}}$

Q. A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is

1. $ma$
2. $\frac{5}{3}ma$
3. $2ma$
4. $\frac{3}{2}ma$

Q. Diameter of a steel ball is measured using a Vernier cllipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurement for a ball are given as.

S. No.	MS(cm)	VS divisions
1.	0.5	8
2.	0.5	4
3.	0.5	6

If the zero error is -0.03 cm, then mean corrected diameter is.

1. 0.56
2. 0.53
3. 0.52
4. 0.59

Q. A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to magnet of the same size and magnetization $\overrightarrow{M}$ Magnetic moment / vloume), then $\overrightarrow{|M|}$ is.

1. $300A{m}^{-1}$
2. $30000A{m}^{-1}$
3. $30000\pi A{m}^{-1}$
4. $3\pi A{m}^{-1}$

Q. An ideal gas goes through a reversible cycle $a\to b\to c\to d$ has the V- T diagram shown below. Process $d\to a$ and $b\to c$ are adiabatic.
The corresponding P-V diagram for the process is ( all figure are schematic and not drawn to scale).

1. 
   
2. 
   
3. 
   
4. 
   

Q. A very long (length $L$) cylindrical galaxy is made of uniformly distributed mass and has radius $R(R<<L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is $t$ and its distance from the galaxy's axis is $r$, then

1. $T\propto r^2$
2. $T\propto r$
3. $T\propto \sqrt{r}$
4. $T^2\propto r^3$

Q. If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that give rise to lower pressure in the water in comparison to the atmosphere. If the radius of the cylindrical surface is $R$ and surface tension of water is $T$ then the pressure in water between the plates is lower by :

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

Q. De-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to: $(|e|=1.6\times {10}^{-19}C,m_e=9.1\times {10}^{-31}kg,h=6.6\times {10}^{-34}Js).$

1. $0.5\mathring{A}$
2. $1.7\mathring{A}$
3. $2.4\mathring{A}$
4. $1.2\mathring{A}$

Q. A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is $\theta$, then $\theta$ close to.

1. ${60}^o$
2. $1^o$
3. ${30}^o$
4. ${15}^o$

Q. If one were to apply Bohr model to a particle '$m$' and charge '$q$' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the $n^{th}$ level will be.

1. $n\left(\frac{hqB}{4\pi m}\right)$
2. $n\left(\frac{hqB}{8\pi m}\right)$
3. $n\left(\frac{hqB}{2\pi m}\right)$
4. $n\left(\frac{hqB}{\pi m}\right)$

Q. In the circuit (a) and (b) switches $S_1$ and $S_2$ are closed at t-0 and are kept closed for a long time. The variation of currents in the two circuits for $t\ge 0$ are roughly shown by(figures are schematic and not drawn to scale).

1. 
   
2. 
   
3. 
   
4. 
   

Q. In an unbiased n-p junction electrons diffuse from n-region to p- region because

1. electrons concentration in n region is more as compared to that in p-region.
2. holes in p-region attract them.
3. electrons travel across the junction due to potential difference.
4. only electrons move from n- to p- region and not the vice-versa.

Q. A block of mass $m=0.1kg$ is connected to a spring of unknown spring constant $k$. It is compressed to a distance $x$ from its equilibrium position and released from rest.
After approaching half the distance $\left(\frac{x}{2}\right)$ from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3m{s}^{-1}$. The total initial energy of the spring is :

1. 0.8 J
2. 1.5 J
3. 0.3 J
4. 0.6 J
5. 0.7 J

Q. An electromagnetic wave travelling in the x-direction has frequency of $2\times {10}^{14}Hz$ and electric field amplitude of 27 $V{m}^{-1}$. From the options given below, which one describes the magnetic field for this wave?

1. $\overrightarrow{B}(x,t)=(3\times {10}^{-8}T)\hat{j}$ $sin\left[2\pi \right(1.5\times {10}^{-8}x-2\times {10}^{14}t\left)\right]$
2. $\overrightarrow{B}(x,t)=(9\times {10}^{-8}T)\hat{j}$ $sin\left[\right(1.5\times {10}^{-6}x-2\times {10}^{14}t\left)\right]$
3. $\overrightarrow{B}(x,t)=(9\times {10}^{-8}T)\hat{k}$ $sin\left[2\pi \right(1.5\times {10}^{-6}x-2\times {10}^{14}t\left)\right]$
4. $\overrightarrow{B}(x,t)=(9\times {10}^{-8}T)\hat{i}$ $sin\left[2\pi \right(1.5\times {10}^{-8}x-2\times {10}^{14}t\left)\right]$

Q. A parallel beam of electrons travelling in x-direction falls on a slit of width d. If after passing the slit, an electron acquires momentum $p_y$ in the y direction, then for a majority of electrons passing through the slit (h is Planck's constant).

1. $|P_y|d<h$
2. $|P_y|d\simeq h$
3. $|P_y|d>h$
4. $|P_y|d>>h$

Q. A thin disc of radius b=2a has a concentric hole of radius 'a' is in it. It carries uniform surface charge ${}^{\prime }{\sigma }^{\prime }$ on it. If the electric field on its axis at height 'h' (h<<a) from its centre is given as 'Ch' the value of 'C' is.

1. $\frac{\sigma }{a{ϵ}_0}$
2. $\frac{\sigma }{2a{ϵ}_0}$
3. $\frac{\sigma }{8a{ϵ}_0}$
4. $\frac{\sigma }{4a{ϵ}_0}$

Q. If it takes $5$ minutes to fill a $15L$ bucket from a water tap of diameter $\frac{2}{\sqrt{\pi }}$ cm then the Reynolds number for the flow is (density of water = ${10}^{3}kg/m^3$ and visocsity of water =${10}^{-3}Pa.s$) close to.

1. $11,000$
2. $550$
3. $1100$
4. $5500$

Q. In an ideal gas at temperature T, the average force that a molecules applies on the walls of a closed container depends on T as $T^q$. As good estimate for q is.

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