Q. In figure, the optical fibrer is $l=2n$ long and has a diameter of $d=20\mu m$. If a ray of light is incident on one end of the fiber at angle ${\theta }_1={40}^{\circ }$, the number of reflection it makes before emerging from the other end is close to: (refractive index of fibre is $1.31$ and $\sin {40}^{\circ }=0.64)$.

1. $55000$
2. $57000$
3. $66000$
4. $45000$

Q. The bob of a simple pendulum has mass $2g$ and a charge of $5.0\mu C$. It is at rest in a uniform horizontal electric field of intensity $2000V/m$. At equilibrium, the angle that the pendulum makes with the vertical is : (take $g=10m/s^2)$.

Q. Water from a pipe is coming at a rate of $100litres$ per minute. If the radius of the pipe is $5cm$, the Reynolds number for the flow is of the order of : (density of water $=1000kg/m^3$, coefficient of viscosity of water $=1mPas$).

Q. For the circuit shown, with $R_1=1.0\Omega ,R_2=2.0\Omega ,E_1=2V$ and $E_2=E_3=4V$, the potential difference between the points ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ is approximately (in $V$).

Q. A $200\Omega$ resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be

Q. A boy's catapult is made of rubber cord which is $42cm$ long, with $6mm$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02kg$ on it and stretches the cord by $20cm$ by applying a constant force. When released, the stone flies off with a velocity of $20m{s}^{-1}$. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to

Q. Two identical breakers $A$ and $B$ contain equal volumes of two different liquids at ${60}^{\circ }C$ each and left to cool down. Liquid in $A$ has density of $8\times {10}^{2}kg/m^3$ and specific heat of $2000Jk{g}^{-1}{K}^{-1}$ while liquid in $B$ has density of ${10}^{3}kg{m}^{-3}$ and specific heat of $4000Jk{g}^{-1}{K}^{-1}$. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same?

Q. Four particles $A,B,C$ and $D$ with masses $m_A=m,m_B=2m,m_C=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

Q. A circular coil having $N$ turns and radius $r$ carries a current $I$. It is held in the $XZ$ plane in a magnetic field $B\hat{i}$. The torque on the coil due to the magnetic field is

Q. Voltage rating of a parallel plate capacitor is $500V$. Its dielectric can withstand a maximum electric field of ${10}^{6}V/m$. The plate area is ${10}^{-4}{m}^2$. What is the dielectric constant is the capacitance is $15pF$?
(given ${ϵ}_0=8.86\times {10}^{-12}{C}^2/N{m}^2)$.

Q. The reverse breakdown voltage of a Zener diode is $5.6V$ in the given circuit.
The current $I_Z$ through the Zener is

Q. A $20$ Henry inductor coil is connected to a $10ohm$ resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is

Q. An upright object is placed at a distance of $40cm$ in front of a convergent lens of focal length $20cm$. A convergent mirror of focal length $10cm$ is placed at a distance of $60cm$ on the other side of the lens. The position and size of the final image will be

Q. A thin strip $10cm$ long is on a $U$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5N{m}^{-1}$ see figure. The assembly is kept in a uniform magnetic field of $0.1T$. If the strip is pulled from its equilibrium position and released, the number of oscillation it performs before its amplitude decreases by a factor of $e$ is $N$. If the mass of the strip is $50$ grams, its resistance $10\Omega$ and air drag negligible, $N$ will be close to

Q. A thin circular plate of mass $M$ and radius $R$ has its density varying as $\rho \left(r\right)={\rho }_{0}r$ with ${\rho }_0$ as constant and $r$ is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is $I=aM{R}^2$. The value of the coefficient $a$ is

Q. Ship $A$ is sailing towards north-east with velocity $\overrightarrow{v}=30\hat{i}+50\hat{j}km/hr$ where $\hat{i}$ points east and $\hat{j}$, north. Ship $B$ is at a distance of $80km$ east and $150km$ north of Ship $A$ and is sailing towards west at $10km/hr$. A will be at minimum distance from $B$ in

Q. A steel wire having a radius of $2.0mm$, carrying a load of $4kg$, is hanging from a ceiling. Given that $g=3.1\pi m{s}^{-2}$, what will be the tensile stress that would be developed in the wire?

Q. A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-4Q$, the new potential difference between the same two surfaces is

Q. A wire of length $2L$, is made by joining two wires $A$ and $B$ of some length but different radii $r$ and $2r$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $A$ is $p$ and that in $B$ is $q$ then the ratio $p:q$ is

Q. Four identical particles of mass $M$ are located at the corners of a square of side ${}^{\prime }{a}^{\prime }$. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?

Q. A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is $E=6V{m}^{-1}$ along y-direction. Its corresponding magnetic field component, $B$ would be

Q. A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled $3m$ is

Q. In $SI$ units, the dimensions of $\sqrt{\frac{{ϵ}_0}{{\mu }_0}}$ is

Q. Radiation coming from transitions $n=2$ to $n=1$ of hydrogen atoms fall on $H{e}^{+}$ ions in $n=1$ and $n=2$ states. The possible transition of helium ions as they absorb energy from the radiation is

Q. Two particles move at right angle to each other. Their de-Broglie wavelengths are ${\lambda }_1$ and ${\lambda }_2$ respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength $\lambda$, of the final particle, is given by

Q. A thermally insulated vessel contains $150g$ of water at $0^{\circ }C$. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at $0^{\circ }C$ itself. The mass of evaporated water will be closest to:
(Latent heat of vaporization of water $=2.10\times {10}^{6}Jk{g}^{-1}$ and Latent heat of Fusion of water $=3.36\times {10}^{5}Jk{g}^{-1})$

Q. An alternating voltage $v\left(t\right)=220\sin 100\pi tvolt$ is applied to a purely resistance load of $50\Omega$. The time taken for the current to rise from half of the peak value of the peak value is

Q. The wavelength of the carrier waves in a modern optical fiber communication network is close to

Q. In an interference experiment the ratio of amplitudes of coherent waves is $\frac{a_1}{a_2}=\frac{1}{3}$. The ratio of maximum and minimum intesities of fringes will be

Q. If ${10}^{22}$ gas molecules each of mass ${10}^{-26}kg$ collied with a surface (perpendicular to it) elastically per second over an area $1m^2$ with a speed ${10}^{4}m/s$, the pressure exerted by the gas molecules will be of the order of