Q. When a particle executing SHM oscillates with a frequency $\nu$, then the kinetic energy of the particle:

1. changes periodically with a frequency of $\nu$
2. changes periodically with a frequency of $2\nu$
3. remains constant
4. changes periodically with a frequency of $\frac{\nu }{2}$

Q. In which of the following phenomena, the heat waves travel along straight lines with the speed of light?

1. Thermal conduction
2. Natural convection
3. Thermal radiation
4. Forced convection

Q. The intensity of magnetization of a bar magnet is $5.0\times {10}^4{Am}^{-1}$. The magnetic length and the area of cross-section of the magnet are $12cm$ and $1{cm}^2$ respectively. The magnitude of magnetic moment of this bar magnet is (in SI unit):

1. $0.6$
2. $1.24$
3. $2.4$
4. $1.3$

Q. In which of the following pairs, the two physical quantities have different dimensions?

1. Planck's constant and angular momentum
2. Energy and torque
3. Moment of inertia and moment of a force
4. Impulse and linear momentum

Q. A particle is moving uniformly in a circular path of radius $r$. When it moves through an angular displacement $\theta$, then the magnitude of the corresponding linear displacement will be:

1. $2r\cos \left(\frac{\theta }{2}\right)$
2. $2r\cot \left(\frac{\theta }{2}\right)$
3. $2r\tan \left(\frac{\theta }{2}\right)$
4. $2r\sin \left(\frac{\theta }{2}\right)$

Q. An artificial satellite moves in a circular orbit around the earth. Total energy of the satellite is given by $E$. The potential energy of the satellite is:

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

Q. A luminous object is separated from a screen by distance $d$. A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is:

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

Q. A scientist proposes a new temperature scale in which the ice point is $25X$ ($X$ is the new unit of temperature) and the steam point is $305X$. The specific heat capacity of water in this new scale is (in $J{kg}^{-1}{X}^{-1}$):

1. $4.2\times {10}^3$
2. $3.0\times {10}^3$
3. $1.2\times {10}^3$
4. $1.5\times {10}^3$

Q. A very small circular loop of radius $a$ is initially (at $t=0$) coplanar and concentric with a much larger fixed circular loop of radius $b$. A constant current $I$ flows in the larger loop. The smaller loop is rotated with a constant angular speed $\omega$ about the common diameter. The emf induced in the smaller loop as a function of time $t$ is:

1. $\frac{\pi a^2{\mu }_{0}I}{2b}\omega \cos \left(\omega t\right)$
2. $\frac{\pi a^2{\mu }_{0}I}{2b}\omega \sin \left({\omega }^2{t}^2\right)$
3. $\frac{\pi a^2{\mu }_{0}I}{2b}\omega \sin \left(\omega t\right)$
4. $\frac{\pi a^2{\mu }_{0}I}{2b}\omega {\sin }^2\left(\omega t\right)$

Q. To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at ${45}^0$ and the block is released from rest. The block takes a time $t$ in moving a distance $d$. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time $t/2$ in moving down the same distance $d$. The coefficient of friction is:

1. $3/4$
2. $5/4$
3. $1/2$
4. $1/\sqrt{2}$

Q. Three capacitors $3\mu F,6\mu F$ and $6\mu F$ are connected in series to a source of $120V$. The potential difference, in volt, across the $3\mu F$ capacitor will be:

1. 24
2. 30
3. 40
4. 60

Q. The output $Y$ of the logic circuit given above is:

1. $\overline{A}+B$
2. $\overline{(\overline{A}+B)}\cdot A$
3. $\overline{A}$
4. $\overline{(\overline{A}+B)}\cdot \overline{A}$

Q. One mole of a vander Waal's gas obeying the equation
$(p+\frac{a}{V^2})(V-b)=RT$
undergoes the quasi-static cyclic process which is shown in the p-V diagram. The net heat absorbed by the gas in this process is:

1. $\frac{1}{2}(p_1-p_2)(V_1-V_2)$
2. $\frac{1}{2}(p_1+p_2)(V_1-V_2)$
3. $\frac{1}{2}(p_1+\frac{a}{V_1^2}-p_2-\frac{a}{V_2^2})(V_1-V_2)$
4. $\frac{1}{2}(p_1+\frac{a}{V_1^2}+p_2+\frac{a}{V_2^2})(V_1-V_2)$

Q. A galvanometer having internal resistance $10\Omega$ requires $0.01A$ for a full scale deflection. To convert this galvanometer to a voltmeter of full-scale deflection at $120V$, we need to connect a resistance of:

1. $11990\Omega$ in parallel
2. $11990\Omega$ in series
3. $12010\Omega$ in series
4. $12010\Omega$ in parallel

Q. A uniform rod is suspended horizontally from its mid-point. A piece of metal whose weight is $w$ is suspended at a distance $l$ from the mid-point. Another weight $W_1$ is suspended on the other side at a distance $l_1$ from the mid-point to bring the rod to a horizontal position. When $w$ is completely immersed in water, $w_1$ needs to be kept at a distance $l_2$ from the mid-point to get the rod back into horizontal position. The specific gravity of the metal piece is

1. $\frac{w{l}_1}{wl-w_1{l}_2}$
2. $\frac{w}{w_1}$
3. $\frac{l_1}{l_1-l_2}$
4. $\frac{l_1}{l_2}$

Q. A drop of some liquid of volume $0.04{cm}^3$ is placed on the surface of a glass slide. Then another glass slide is placed on it in such a way that the liquid forms a thin layer of area $20{cm}^2$ between the surfaces of the two slides. To separate the slides a force of $16\times {10}^{5}dyne$ has to be applied normal to the surfaces. The surface tension of the liquid is (in $dyne.{cm}^{-1}$):

1. 70
2. 60
3. 90
4. 80

Q. A wooden block is floating on water kept in beaker. 40% of the block is above the water surface. Now the beaker is kept inside a lift that starts going upward with acceleration equal to $g/2$. The block will then

1. float with 40% above the water surface
2. float with 70% above the water surface
3. sink
4. float with 10% above the water surface

Q. A cricket ball thrown across a field is at heights $h_1$ and $h_2$ from the point of projection at times $t_1$ and $t_2$ respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is:

1. $\frac{h_1{t}_2^2-h_2{t}_1^2}{h_1{t}_2-h_2{t}_1}$
2. $\frac{h_1{t}_1^2+h_2{t}_2^2}{h_2{t}_1+h_1{t}_2}$
3. $\frac{h_1{t}_2^2+h_2{t}_1^2}{h_1{t}_2+h_2{t}_1}$
4. $\frac{h_1{t}_1^2-h_2{t}_2^2}{h_1{t}_1-h_2{t}_2}$

Q. A smooth massless string passes over a smooth fixed pulley. Two masses $m_1$ and $m_2$, $(m_1>m_2)$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is:

1. $(m_1+m_2)g$
2. $\frac{{(m_1-m_2)}^2}{m_1+m_2}g$
3. $(m_1-m_2)g$
4. $\frac{{(m_1+m_2)}^2}{m_1-m_2}g$

Q. A whistle whose air column is open at both ends has a fundamental frequency of $5100Hz$. If the speed of sound in air is $340{ms}^{-1}$, the length of the whistle, in $cm$, is:

1. $10/3$
2. $20/3$
3. $5$
4. $5/3$

Q. A proton of mass $m$ and charge $q$ is moving in a plane with kinetic energy $E$. If there exists a uniform magnetic field $B$, perpendicular to the plane of the motion, the proton will move in a circular path of radius:

1. $\frac{2Em}{qB}$
2. $\frac{\sqrt{Em}}{2qB}$
3. $\frac{\sqrt{2Em}}{qB}$
4. $\sqrt{\frac{2Eq}{mB}}$

Q. A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved farther apart by pulling at them by means of insulating handles, then:

1. the capacitance of the capacitor increases
2. the energy stored in the capacitor decreases
3. the charge on the capacitor decreases
4. the voltage across the capacitor increases

Q. One mole of an ideal monoatomic gas is heated at a constant pressure from $0$ to $100$. Then the change in the internal energy of the gas is:

1. $2.08\times {10}^{3}J$
2. $0.83\times {10}^{3}J$
3. $1.25\times {10}^{3}J$
4. $4.6\times {10}^{3}J$

Q. A small metal sphere of radius $a$ is falling with a velocity $v$ through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is $\eta$, then the sphere encounters an opposing force of:

1. $\frac{\pi \eta v}{6a^3}$
2. $\frac{6\eta v}{\pi a}$
3. $6\pi \eta av$
4. $6\pi \eta a^{2}v$

Q. An infinite sheet carrying a uniform surface charge density $\sigma$ lies on the $xy$-plane. The work done to carry a charge $q$ from the point $A=a(\hat{i}+2\hat{j}+3\hat{k})$ to the point $B=a(\hat{i}-2\hat{j}+6\hat{k})$ (where $a$ is a constant with the dimension of length and ${\epsilon }_0$ is the permittivity of free space) is:

1. $\frac{3\sigma aq}{2{\epsilon }_0}$
2. $\frac{2\sigma aq}{{\epsilon }_0}$
3. $\frac{3\sigma aq}{{\epsilon }_0}$
4. $\frac{5\sigma aq}{2{\epsilon }_0}$

Q. An electron in a circular orbit of radius $0.05nm$ performs ${10}^{16}$ revolutions per second. The magnetic moment due to this rotation of electron is (in ${Am}^2$):

1. $2.16\times {10}^{-23}$
2. $3.21\times {10}^{-22}$
3. $3.21\times {10}^{-24}$
4. $1.26\times {10}^{-23}$

Q. The ionization energy of hydrogen is $13.6eV$. The energy of the photon released when an electron jumps from the first excited state $(n=2)$ to the ground state of a hydrogen atom is:

1. $10.2eV$
2. $3.4eV$
3. $4.53eV$
4. $13.6eV$

Q. Consider three vectors $\overrightarrow{A}=\hat{i}+\hat{j}-2\hat{k},\overrightarrow{B}=\hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{C}=2\hat{i}-3\hat{j}+4\hat{k}$. A vector $\overrightarrow{X}$ of the form $\alpha \overrightarrow{A}+\beta \overrightarrow{B}$ ($\alpha$ and $\beta$ are numbers) is perpendicular to $\overrightarrow{C}$. The ratio of $\alpha$ and $\beta$ is:

1. $1:1$
2. $3:1$
3. $-1:1$
4. $2:1$

Q. A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the 4th second compared to that in the 3rd second is:

1. 33%
2. 77%
3. 66%
4. 40%

Q. A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L,\alpha$ and $Y$ respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by $\Delta T$, the longitudinal stress developed in the rod is:

1. inversely proportional to $\alpha$
2. directly proportional to $\Delta T/Y$
3. inversely proportional to $Y$
4. independent of $L$