Q. One $kg$ of water, at ${20}^{o}C$, is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20\Omega$. The rms voltage in the mains is $200V$. Ignoring heat loss from the kettle. time taken for water to evaporate folly. is close to:
[Specific heat of water $=4200J/kg{}^{o}C$), Latent heat of water $=2260kJ/kg$]

1. $3$ minutes
2. $22$ minutes
3. $10$ minutes
4. $16$ minutes

Q. A tuning fork of frequency $480Hz$ is used in an experiment for measuring speed of sound $\left(v\right)$ in air by resonance tube method. resonance is observed to occur at two successive lengths of the air column, $l_1=30cm$ and $l_2=70cm$. Then $v$ is equal to:

1. $332m{s}^{-1}$
2. $379m{s}^{-1}$
3. $338m{s}^{-1}$
4. $384m{s}^{-1}$

Q. Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency $660Hz$. A listener is moving from source $S_1$ towards $S_2$ with a constant speed $um/s$ and he hears $10beats/s$. The velocity of sound is $330m/s$. Then, $u$ equals:

1. $2.5m/s$
2. $15.0m/s$
3. $5.5m/s$
4. $10.0m/s$

Q. Consider an electron in a hydrogen atom, revolving in its second excited state (having radius $4.65\mathring{A}$). The de-Broglie wavelength of this electron is:

1. $6.6\mathring{A}$
2. $12.9\mathring{A}$
3. $9.7\mathring{A}$
4. $3.5\mathring{A}$

Q. A small speaker delivers $2W$ of audio output. At what distance from the speaker will one detect $120dB$ intensity sound ? [Given reference intensity of sound as ${10}^{-12}W/m^2$]

1. $10cm$
2. $30cm$
3. $20cm$
4. $40cm$

Q. A Carnot engine has an efficiency of $1/6$. When the temperature of the sink is reduced by ${62}^{o}C$, its efficiency is doubled. The temperatures of the source and the sink are, respectively

1. ${124}^{o}C,{62}^{o}C$
2. ${37}^{o}C,{99}^{o}C$
3. ${62}^{o}C,{124}^{o}C$
4. ${99}^{o}C,{37}^{o}C$

Q. A diatomic gas with rigid molecules does $10J$ of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ?

1. $35J$
2. $40J$
3. $25J$
4. $30J$

Q. A particle is moving with speed $v=b\sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t=\tau$ (assume that the particle is at origin at $t=0$)

1. $\frac{b^2\tau }{4}$
2. $\frac{b^2\tau }{2}$
3. $b^2\tau$
4. $\frac{b^2\tau }{\sqrt{2}}$

Q. The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, ${\lambda }_1/{\lambda }_2$ of the photons emitted in this process is:

1. $\frac{9}{7}$
2. $\frac{7}{5}$
3. $\frac{20}{7}$
4. $\frac{27}{5}$

Q. A moving coil galvanometer, having a resistance $G$, produces full scale deflection when a current $I_g$ flows through it. This galvanometer can be converted into (i) an ammeter of range $0$ to $I_0(I_0>I_g)$ by connecting a shunt resistance $R_A$ to it and (ii) into a voltmeter of range $0$ to $V(V=G{I}_0)$ by connecting a series resistance $R_V$ to it. Then

Q. The number density of molecules of a gas depends on their distance $r$ from the origin as, $n\left(r\right)=n_0{e}^{-\alpha r^4}$. Then the total number of molecules is proportional to:

Q. A smooth wire of length $2\pi$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter $AB$, as shown in figure, the bead is at rest with respect to the circular ring at position $P$ as shown. Then the value of ${\omega }^2$ is equal to:

Q. Find the magnetic field at point $P$ due to a straight line segment $AB$ of length $6cm$ carrying a current of $5A$. (See figure)
$({\mu }_0=4\pi \times {10}^{-7}N-A^{-2})$

Q. A transparent cube of side $d$, made of a material of refractive index ${\mu }_2$, is immersed in a liquid of refractive index ${\mu }_1({\mu }_1<{\mu }_2)$. A ray is incident on the face $AB$ at an angle $\theta$ (shown in the figure). Total internal reflection takes place at point $E$ on the face $BC$.
The $\theta$ must satisfy:

Q. Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $\rho \left(r\right)=kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, a form the centre. If $A$ and $B$ do not experience any force, then:

Q. Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct?

Q. A spring whose unstretched length is $l$ has a force constant $k$. The spring is cute into two pieces of unstretched lengths $l_1$ and $l_2$ where, $l_1=n{l}_2$ and $n$ is an integer. The ratio $\frac{k_1}{k_2}$ of the corresponding force constants, $k_1$ and $k_2$ will be:

Q. A block of mass $5kg$ is (i) pushed in case (A) and (ii) pulled in case (B), by force $F=20N$, making an angle of ${30}^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu =0.2$. The difference between the accelerations of the block, in case (B) and case (A) will be:
$(g=10m{s}^{-2})$

Q. Consider the $LR$ circuit shown in the figure. If the switch $S$ is closed at $t=0$ then the amount of charge that passes through the battery between $t=0$ and $t=\frac{L}{R}$ is:

Q. A system of three polarizers $P_1,P_2,P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$. The pass axis of $P_2$ is inclined at ${60}^o$ to the pass axis of $P_3$. When a beam of unpolarized light of intensity lo is incident on $P_1$ the in of light transmitted by the three polarizers $I$. The ratio $\left(I_0/I\right)$ equals (nearly):

Q. Half lives of two radioactive nuclei $A$ and $B$ are $10$ minutes and $20$ minutes, respectively. If, initially a sample has equal number of nuclei, then after $60$ minutes, the ratio of decayed numbers of nuclei A and B will be:

Q. A solid sphere, of radius R acquires a terminal velocity $v_1$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into $27$ identical solid spheres. If each of these spheres acquires a terminal velocity, $v_2$, when falling through the same fluid. the ratio $\left(v_1/v_2\right)$ equals :

Q. The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9:4$. The mass of the planet is $\frac{1}{9}th$ of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ?
(Take the planets to have the same mass density)

Q. Figure shown a DC voltage regulator circuit, with a Zener diode of breakdown voltage = $6V$. If the unregulated input voltage varies between $10V$ to $16V$, then what is the maximum Zener current ?

Q. A uniform cylindrical rod of length L and radius r, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to :

Q. Three particles of masses $50g,100g$ and $150g$ are placed at the vertices of an equilateral triangle of side $1m$ (as shown in the figure). The (x, y) coordinates of the centre of mass will be :

Q. An electron, moving along the x-axis with an initial energy of $100eV$, enters a region of magnetic field $\overrightarrow{B}=(1.5\times {10}^{-3}T)\hat{k}$ at S (See figure). The field extends between $x=0$ and $x=2cm$. The electron is detected at the point Q on a screen placed $8cm$ away from the point S. The distance d between P and Q (on the screen) is :
(electron's charge = $1.6\times {10}^{-19}C$, mass of electron = $9.1\times {10}^{-31}kg$)

Q. A plane electromagnetic wave having a frequency $v=23.9GHz$ propagates along the positive z-direction in free space. The peak value of the electric field is $60V/m$. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

Q. In an amplitude modulator circuit, the carrier wave is given by,
$C\left(t\right)=4\sin \left(2000\pi t\right)$ while modulating signal is given by, $m\left(t\right)=2\sin \left(200\pi t\right)$. the values of modulation index and lower side band frequency are :

Q. In the given circuit, the charge on $4\mu F$ capacitor will be :