Q. In amplitude modulation, sinusoidal carrier frequency used is denoted by ${\omega }_c$ and the signal frequency is denoted by ${\omega }_m$. The bandwidth $\left(△{\omega }_m\right)$ of the signal is such that $△{\omega }_m<<{\omega }_c$. Which of the following frequencies is not contained in the modulated wave?

1. ${\omega }_c-{\omega }_m$
2. ${\omega }_m$
3. ${\omega }_c$
4. ${\omega }_m+{\omega }_c$

Q. A particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths ${\lambda }_A$ to ${\lambda }_B$ after the collision is :

1. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{1}{3}$
2. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{1}{2}$
3. $\frac{{\lambda }_A}{{\lambda }_B}=2$
4. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{2}{3}$

Q. In a Young's double slit experiment, slits are separated by $0.5mm$, and the screen is placed $150cm$ away. A beam of light consisting of two wavelengths, $650nm$ and $520nm$, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is :

1. $15.6mm$
2. $1.56mm$
3. $7.8mm$
4. $9.75mm$

Q. In the above circuit the current in each resistance is :

1. $1A$
2. $0.5A$
3. $0.25A$
4. $0A$

Q. $C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that
$C_p-C_v=a$ for hydrogen gas
$C_p-C_v=b$ for nitrogen gas
The correct relation between a and b is :

1. $a=28b$
2. $a=\frac{1}{14}b$
3. $a=b$
4. $a=14b$

Q. A slender uniform rod of mass M and length $l$ is pivoted at one end so that it can rotate in a vertical pane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is :

1. $\frac{2g}{3l}\cos \theta$
2. $\frac{2g}{3l}\sin \theta$
3. $\frac{3g}{2l}\sin \theta$
4. $\frac{3g}{2l}\cos \theta$

Q. In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance $C$ will be :

1. $CE\frac{r_1}{(r_1+r)}$
2. $CE$
3. $CE\frac{r_1}{(r_2+r)}$
4. $CE\frac{r_2}{(r+r_2)}$

Q. The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $l/R$ such that the moment of inertia is minimum ?

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

Q. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10GHz$. What is the frequency of the microwave measured by the observer?
(speed of light $=3\times {10}^{8}m{s}^{-1}$)

1. $15.3GHz$
2. $10.1GHz$
3. $17.3GHz$
4. $12.1GHz$

Q. A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity vs time?

1. 
   
2. 
   
3. 
   
4. 
   

Q. A copper ball of mass $100gm$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100gm$, filled with $170gm$ of water at room temperature. Subsequently, the temperature of the system is found to be ${75}^{o}C$. $T$ is given by :
(Given : room temperature $={30}^{o}C$, specific heat of copper $=0.1cal/g{m}^{o}C$)

1. ${800}^{o}C$
2. ${885}^{o}C$
3. ${825}^{o}C$
4. ${1250}^{o}C$

Q. The temperature of an open room of volume $30m^3$ increases form ${17}^{o}C$ to ${27}^{o}C$ due to the sunshine. The atmospheric pressure in the room remains $1\times {10}^5$ Pa. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f-n_i$ will be :

1. $2.5\times {10}^{25}$
2. $-1.61\times {10}^{23}$
3. $-2.5\times {10}^{25}$
4. $1.38\times {10}^{23}$

Q. A capacitance of $2\mu F$ is required in an electrical circuit across a potential difference of $1.0kV$. A large number of $1\mu F$ capacitors are available which can withstand a potential difference of not more than $300V$. The minimum number of capacitors required to achieve this is :

1. $2$
2. $32$
3. $16$
4. $24$

Q. A man grows into a giant such that his linear dimensions increase by a factor of $9$. Assuming that his density remains same, the stress in the leg will change by a factor of :

1. $\frac{1}{9}$
2. $81$
3. $\frac{1}{81}$
4. $9$

Q. A time dependent force $F=6t$ acts on a particle of mass $1kg$. If the particle starts from rest, the work done by the force during the first 1 sec. will be :

1. $18J$
2. $4.5J$
3. $22J$
4. $9J$

Q. A diverging lens with magnitude of focal length $25cm$ is placed at a distance of $15cm$ from a converging lens of magnitude of focal length $20cm$. A beam of parallel light falls on the diverging lens. The final image formed is :

1. Real and at a distance of $40cm$ from convergent lens.
2. Virtual and at a distance of $40cm$ from convergent lens.
3. Real and at a distance of $6cm$ from the convergent lens.
4. Real and at a distance of $40cm$ from the divergent lens.

Q. A magnetic needle of magnetic moment $6.7\times {10}^{-2}A{m}^2$ and moment of inertia $7.5\times {10}^{-6}kg{m}^2$ is performing simple harmonic oscillations in a magnetic field of $0.01T$. Time taken for $10$ complete oscillations is :

1. $8.89s$
2. $6.65s$
3. $8.76s$
4. $6.98s$

Q. An electric dipole has fixed dipole moment $\overrightarrow{p}$, which makes angle $\theta$ with respect to x-axis. When subjected to an electric field $\overrightarrow{E_1}=E\hat{i}$, it experiences a torque $\overrightarrow{T_1}=\tau \hat{k}$. When subjected to another electric field $\overrightarrow{E_2}=\sqrt{3}{E}_1\hat{j}$ it experiences a torque $\overrightarrow{T_2}=-\overrightarrow{T_1}$. The angle $\theta$ is :

1. ${60}^o$
2. ${90}^o$
3. ${30}^o$
4. ${45}^o$

Q. The following observations were taken for determining surface tension $T$ of water by capillary method :
diameter of capillary, $D=1.25\times {10}^{-2}m$
rise of water, $h=1.45\times {10}^{-2}m$.
Using $g=9.80m/s^2$ and the simplified relation. $T=\frac{rhg}{2}\times {10}^{3}N/m$, the possible error in surface tension is closest to :

1. $1.5\%$
2. $0.15\%$
3. $10\%$
4. $2.4\%$

Q. A particle is executing simple harmonic motion with a time period $T$. At time $t=0$, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like :

1. 
   
2. 
   
3. 
   
4. 
   

Q. In a coil of resistance $100\Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is :

1. $275Wb$
2. $200Wb$
3. $250Wb$
4. $225Wb$

Q. An electron beam is accelerated by a potential difference $V$ to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If ${\lambda }_{min}$ is the smallest possible wavelength of X-rays in the spectrum, the variation of $\log {\lambda }_{min}$ with log $V$ is correctly represented in :

1. 
   
2. 
   
3. 
   
4. 
   

Q. A body of mass $m={10}^{-2}kg$ is moving in medium and experiences a frictional force $F=-k{v}^2$. Its initial speed is $v_0=10m{s}^{-1}$. If, after $10s$, its energy is $\frac{1}{8}m{v}_0^2$, the value of $k$ will be :

1. ${10}^{-4}kg{m}^{-1}$
2. ${10}^{-1}kg{m}^{-1}{s}^{-1}$
3. ${10}^{-3}kg{m}^{-1}$
4. ${10}^{-3}kg{s}^{-1}$

Q. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r={\lambda }_1/{\lambda }_2$, is given by :

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

Q. An external pressure $P$ is applied on a cube at $0^{o}C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by :

1. $3PK\alpha$
2. $\frac{P}{3\alpha K}$
3. $\frac{3\alpha }{PK}$
4. $\frac{P}{\alpha K}$

Q. The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by (R=Earth's radius) :

1. 
   
2. 
   
3. 
   
4. 
   

Q. A radioactive nucleus $A$ with a half life $T$, decays into a nucleus $B$. At $t=0$, there is no nucleus $B$. At sometime $t$, the ratio of the number of $B$ to that of $A$ is $0.3$. Then, $t$ is given by :

1. $t=\frac{T}{\log \left(1.3\right)}$
2. $t=T\frac{\log 1.3}{\log 2}$
3. $t=\frac{T}{2}\frac{\log 2}{\log 1.3}$
4. $t=T\log \left(1.3\right)$

Q. In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be :

1. ${45}^o$
2. ${180}^o$
3. ${90}^o$
4. ${135}^o$

Q. When a current of $5mA$ is passed through a galvanometer having a coil of resistance $15\Omega$, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range $0-10V$ is:

1. $1.985\times {10}^3\Omega$
2. $4.005\times {10}^3\Omega$
3. $2.045\times {10}^3\Omega$
4. $2.535\times {10}^3\Omega$

Q. Which of the following statements is false?

1. Kirchhoff's second law represents energy conservation.
2. Wheatstone bridge is the most sensitive when all the four resistance are of the same order of magnitude.
3. In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed.
4. A rheostat can be used as a potential divider.