Q. Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is $I_o$ as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, and F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

1. $\frac{15}{16}{I}_o$
2. $\frac{7}{8}{I}_o$
3. $\frac{3I_o}{4}$
4. $\frac{31I_o}{32}$

Q. A 9 V battery with internal resistance of 0.5 $\Omega$ is connected across an infinite network as shown in the figure. All ammeters $A_1,A_2,A_3$ and voltmeter V are ideal.
Choose correct statement.

1. Reading of $A_1$ is 2 A.
2. Reading of V is 7 V.
3. Reading of V is 9 V.
4. Reading of $A_1$ is 18 A.

Q. Let the refractive index of a denser medium with respect to a rare medium be $N_{12}$ and its critical angle ${\theta }_C$ . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is ${90}^o$. Angle A is given by :

1. ${\tan }^{-1}\left(\sin {\theta }_C\right)$
2. $\frac{1}{{\tan }^{-1}\left(\sin {\theta }_C\right)}$
3. $\frac{1}{{\cos }^{-1}\left(\sin {\theta }_C\right)}$
4. ${\cos }^{-1}\left(\sin {\theta }_C\right)$

Q. Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron $=1.1MeV$ and for helium $=7.0MeV$)

1. $30.2MeV$
2. $23.6MeV$
3. $25.8MeV$
4. $32.4MeV$

Q. Two wires $W_1$ and $W_2$ have the same radius r and respective densities ${\rho }_2=4{\rho }_1$ . They are joined together at the point O, shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of anti nodes formed in $W_1$ to $W_2$ is :

1. 4 : 1
2. 1 : 3
3. 1 : 1
4. 1 : 2

Q. A single of frequency 20 kHz and peak voltage of 5 Vlt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 volts. Choose the correct statement.

1. Modulation index = 5, side frequency bands are at 1400 kHz and 1000 kHz.
2. Modulation index = 5 , side frequency bands are at 21.2 kHz and 18.8 kHz.
3. Modulation index = 0.8, side frequency bands are at 1180 kHz and 1220 kHz.
4. Modulation index = 0.2, side frequency bands are at 1220 kHz and 1180 kHz.

Q. Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

1. 
   
2. 
   
3. 
   
4. 
   

Q. A potentiometer PQ is set up to compare two resistance as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key $K_3$ is open. The balance point is at a length $l_1$ cm from P when two way key $K_3$ is plugged between 2 and 1, while the balance point is at a length $l_2$ cm from P when key $K_3$ is plugged between 3 and 1. The ratio of two resistances $\frac{R_1}{R_2}$ , is found to be

1. $\frac{l_2}{l_2-l_1}$
2. $\frac{l_1}{l_1+l_2}$
3. $\frac{l_1}{l_1-l_2}$
4. $\frac{l_1}{l_2-l_1}$

Q. There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$, in the region, is found to vary between the limits $589.0V$ to $589.8V$. What is the potential at a point on the sphere whose radius vector makes an angle of ${60}^o$ with the direction of the field?

1. $589.2V$
2. $589.5V$
3. $589.6V$
4. $589.4V$

Q. An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :
(Take $C_v$ = 1.5 R, where R is gas constant )

1. 0.24
2. 0.15
3. 0.08
4. 0.32

Q. Time $\left(T\right)$ , Velocity $\left(C\right)$ and angular momentum $\left(H\right)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, dimension of mass would be:

1. $\left[M\right]=\left[T^{-1}{C}^{-2}{h}^{-1}\right]$
2. $\left[M\right]=\left[T^{-1}{C}^{2}h\right]$
3. $\left[M\right]=\left[T{C}^{-2}h\right]$
4. $\left[M\right]=\left[T^{-1}{C}^{-2}h\right]$

Q. A magnetic dipole in a constant magnetic field has ;

1. Minimum potential energy when the torque is maximum.
2. Zero potential energy when the torque is minimum.
3. Maximum potential energy when the torque is maximum.
4. Zero potential energy when the torque is maximum.

Q. The maximum velocity of the photoelectrons emitted from the surface is $v$ when light of frequency $n$ falls on a metal surface. If the incident frequency is increased in $3n$, the maximum velocity of the ejected photoelectrons will be :

1. Equal to $\sqrt{3}v$
2. Equal to $2v$
3. Less than $\sqrt{3}v$
4. More than $\sqrt{3}v$

Q. In a physical balance working on the principle of moments, when 5 mg weight is placed on the left plan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

1. Every object that is weighed using this balance appears lighter than its actual weight.
2. Left arm is longer than the right arm.
3. Both the arms are of same length.
4. Left arm is shorter than the right arm.

Q. The energy stored in magnetic field produced by a metal sphere is $4.5J$. If the sphere contains $4\mu C$ charge, its radius will be :
[Take : $\frac{1}{4\pi {ϵ}_0}=9\times {10}^{9}N-m^2/C^2$ ]

1. $28mm$
2. $32mm$
3. $16mm$
4. $20mm$

Q. The ratio of maximum acceleration to maximum velocity in a simple harmonic motion 10 $S^{-1}$ . At, t = 0 the displacement is 5 m. What is the maximum acceleration? The initial phase is $\frac{\pi }{4}$ .

1. $500\sqrt{2}m/s^2$
2. $750\sqrt{2}m/s^2$
3. $500m/s^2$
4. $750m/s^2$

Q. A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. Then the acceleration of the body is :

1. $\frac{2mg}{2m+M}$
2. $\frac{2Mg}{2M+m}$
3. $\frac{2mg}{2M+m}$
4. $\frac{2Mg}{2m+M}$

Q. According to Bohr's theory, the time averaged magnetic field at the centre (i.e nucleus) of a bydrogen atom due to the motion of electrons in the $n^{th}$ orbit is propotional to : $(n=$ principal quantum number$)$

1. $n^{-3}$
2. $n^{-5}$
3. $n^{-2}$
4. $n^{-4}$

Q. What is the conductivity of a semiconductor sample having electron concentration of $5\times {10}^{18}{m}^{-3}$ , hole concentration of $5\times {10}^{19}{m}^{-3}$ , electron mobility of 2.0 $m^2{v}^{-1}{s}^{-1}$ and hole mobility of 0.01 $m^2{v}^{-1}{s}^{-1}$ ?
(Take charge of electron as $1.6\times {10}^{-19}C$ )

1. $1.68(\Omega -m{)}^{-1}$
2. $0.59(\Omega -m{)}^{-1}$
3. $1.20(\Omega -m{)}^{-1}$
4. $1.83(\Omega -m{)}^{-1}$

Q. A $1kg$ block attached to a spring vibrates with a frequency of $1Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in a parallel to an $8kg$ block placed on the same table. So, the frequency of vibration of the $8kg$ block is ;

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

Q. Magnetic field in a plane electromagnetic wave is given by
$\overrightarrow{B}=B_{0}sin(kx+\omega t)\hat{j}T$
Expression for corresponding electric field will be :
Where c is speed of light.

1. $\overrightarrow{E}=B_{0}c\sin (kx+\omega t)\hat{k}V/m$
2. $\overrightarrow{E}=-B_{0}c\sin (kx+\omega t)\hat{k}V/m$
3. $\overrightarrow{E}=\frac{B_0}{c}\sin (kx+\omega t)\hat{k}V/m$
4. $\overrightarrow{E}=B_{0}c\sin (kx-\omega t)\hat{k}V/m$

Q. In a certain region static electric and magnetic fields exist. The magnetic feild is given by $\overrightarrow{B}=B_0(\hat{i}+2\hat{j}-4\hat{k})$ . If a test charge is given by $\overrightarrow{v}=v_0(3\hat{i}+\hat{j}-2\hat{k})$ experiences no force in that region, then the electric field in the region, in SI units, is :

1. $\overrightarrow{E}=-v_0{B}_0(\hat{i}+\hat{j}-7\hat{k})$
2. $\overrightarrow{E}=-v_0{B}_0(14\hat{j}+7\hat{k})$
3. $\overrightarrow{E}=v_0{B}_0(14\hat{j}+7\hat{k})$
4. $\overrightarrow{E}=-v_0{B}_0(3\hat{i}-2\hat{j}-4\hat{k})$

Q. An object is dropped from height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as $t\to \infty$ is :

1. $\frac{5}{3}h$
2. 3h
3. $\infty$
4. $\frac{8}{3}h$

Q. An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure $\left(C_p\right)$ and at constant volume $\left(C_v\right)$ is

1. $\frac{7}{5}$
2. $6$
3. $\frac{5}{2}$
4. $\frac{7}{2}$

Q. A small circle loop of wire of radius a is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I+I_{o}cos\left(\omega t\right)$ . The emf induced in the smaller inner loop is nearly :

1. $\frac{\pi {\mu }_o{I}_o{b}^2}{a}\omega cos\left(\omega t\right)$
2. $\frac{\pi {\mu }_o{I}_o}{2}.\frac{a^2}{b}\omega sin\left(\omega t\right)$
3. $\pi {\mu }_o{I}_o\frac{a^2}{b}\omega sin\left(\omega t\right)$
4. $\frac{\pi {\mu }_o{I}_o}{2}.\frac{a^2}{b}\omega cos\left(\omega t\right)$

Q. A compressive force, F is applied at the two ends of a long thin steel rod. It is hated, simultaneously, such that its temperature increases by $△T$ . The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young, s modulus, and $\alpha$ its coefficient of linear expansion. Then, F is equal to :

1. $l^{2}Y\alpha △T$
2. $lAY\alpha △T$
3. $\frac{AY}{\alpha △T}$
4. $AY\alpha △T$

Q. The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is :

1. $100$
2. ${10}^{-6}$
3. $10$
4. ${10}^6$

Q. In an experiment a sphere of aluminium of mass $0.20kg$ is heated upto ${150}^{o}C$. Immediately, it is put into water of volume $150cc$ at ${27}^{o}C$ kept in a calorimeter of water equivalent of $0.025kg$. Final temperature of the system is ${40}^{o}C$. The specific heat of aluminium is :
(take $4.2$ Joule $=1$ calorie)

1. $434J/kg{-}^{o}C$
2. $476J/kg{-}^{o}C$
3. $378J/kg{-}^{o}C$
4. $315J/kg{-}^{o}C$

Q. If the Earth has no rational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh $\frac{3}{4}$ W. radius of the Earth is 6400 km and g = 10 $m/s^2$ .

1. $1.1\times {10}^{-3}rad/s$
2. $0.28\times {10}^{-3}rad/s$
3. $0.83\times {10}^{-3}rad/s$
4. $0.63\times {10}^{-3}rad/s$

Q. A single slit of width b is illuminated by a coherent monochromatic light of wavelength $\lambda$ . If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at $3$ cm and $6$ cm respectively from the central maximum, what is the width of the central maximum? (i.e. distance between first minimum on either side of the central maximum)

1. $6.0cm$
2. $4.5cm$
3. $1.5cm$
4. $3.0cm$