Q. White light is used to illuminate two slits in Young's double slit experiment. The separation between the slits is b and the screen is at a distance $d(>>b)$ from the slits. At a point on the screen directly in front of one of the slits, which wavelengths are missing?

1. $\frac{b}{d},\frac{b}{3d},\frac{b}{5d}$
2. $\frac{b^2}{d},\frac{b^2}{3d},\frac{b^2}{5d}$
3. $\frac{b}{2d},\frac{b}{4d},\frac{b}{6d}$
4. $\frac{b^2}{2d},\frac{b^2}{4d},\frac{b^2}{6d}$

Q. A graph between pressure P(along y-axis) and absolute temperature, T(along x-axis) for equal moles of two gases has been drawn. Given that volume of second gas is more than volume of first gas. Which of the following statement is correct?

1. Slope of gas $1$ is less than gas $2$
2. Both have some slopes
3. None of the above
4. Slope of gas $1$ is more than gas $2$

Q. A wide hose pipe is held horizontally by a fireman. It delivers water through a nozzle at one litre per second. On increasing the pressure, this increases to two litres per second. The fireman has now to.

1. Push backward twice as hard
2. Push forward twice as hard
3. Push backward four times as hard
4. Push forward four times as hard

Q. The wavelength $\lambda$ of a photon and the de-Broglie wavelength of an electron have the same value. Find the ratio of energy of photon of the kinetic energy of electron in terms of mass m, speed of light c and planck constant.

1. $\frac{hmc}{\lambda }$
2. $\frac{2hmc}{\lambda }$
3. $\frac{\lambda mc}{h}$
4. $\frac{2\lambda mc}{h}$

Q. A skier starts from rest at point A and slides down the hill without turning or breaking. The friction coefficient is $\mu$. When he stops at point B, his horizontal displacement is S. What is the height difference between points A and B? (The velocity of the skier is small so that the additional pressure on the snow due to the curvature can be neglected. Neglect also the friction of air and the dependence of $\mu$ on the velocity of the skier.)

1. $h=2\mu S$
2. $h=\mu S$
3. $h=\mu S^2$
4. $h=\frac{\mu }{S}$

Q. Two $20$g flatworms climb over a very thin wall, $10$cm high. One of the worm is $20$cm long, the other is wider and only $10$cm long. Which of the following statement is correct regarding them?

1. $20$cm worm has done more work against gravity
2. Both worms have done equal work against gravity
3. Ratio of work done by both the worms is $4:5$
4. $10$cm worm has done more work against gravity

Q. When the radioactive isotope ${}_{88}R{a}^{226}$ decays in a series by emission of three alpha$\left(\alpha \right)$ and a beta $\left(\beta \right)$ particle, the isotope X which remains undecay is?

1. ${}_{83}{X}^{214}$
2. ${}_{84}{X}^{220}$
3. ${}_{84}{X}^{218}$
4. ${}_{87}{X}^{223}$

Q. A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are $t_1$ and $t_2$, respectively. Then, the velocity of projection will be(take g as acceleration due to gravity).

1. $\frac{g\sqrt{t_1{t}_2}}{2}$
2. $g\sqrt{t_1{t}_2}$
3. $\frac{g(t_1+t_2)}{2}$
4. $g\frac{t_1{t}_2}{(t_1+t_2)}$

Q. The turns of a solenoid, designed to provide a given magnetic flux density along its axis, are wound to fill the space between two concentric cylinders of fixed radii. How should the diameter d of the wire used by chosen so as to minimize the heat dissipated in the windings?

1. Wire should be multiple of $5$d
2. Wire is independent of d
3. Can't say
4. Wire should be multiple of $d/3$

Q. A particle of mass m is executing oscillation about the origin on X-axis. Its potential energy is $V\left(x\right)=K|x{|}^3$. Where K is a positive constant. If the amplitude of oscillation is a, then its time period T is proportional to.

1. $1/\sqrt{a}$
2. a
3. $\sqrt{a}$
4. $a^{3/2}$

Q. Two identical glass spheres filled with air are connected by a horizontal glass tube. The glass tube contains a pellet of mercury at its mid-point. Air in one sphere is at $0^o$C and the other is at ${20}^o$C. If both the vessels are heated through ${10}^o$C, then neglecting the expansions of the bulbs and the tube.

1. The mercury pellet gets displaced towards the sphere at higher temperature
2. The temperature rise causes the pellet to expand without any displacement
3. The mercury pellet gets displaced towards the sphere at lower temperature
4. The mercury pellet does not get displaced at all

Q. A non-conducting ring of radius $0.5$m carries a total charge of $1.11\times {10}^{-10}$C distributed non-uniformly on its circumference producing on its circumference on electric field E, everywhere in space. The value of the line integral ${\int }_{l=\infty }^{l=0}(-E\cdot dl)$ ($l=0$ being centre of ring) in volts is?

1. $+2$
2. $-1$
3. $-2$
4. Zero

Q. Mercury boils at ${367}^o$. However, mercury thermometers are made such that they can measure temperature upto ${500}^o$C. This is done by.

1. Filling nitrogen gas at high pressure above the mercury column
2. Maintaining vacuum above mercury column in the stem of the thermometer
3. Filling oxygen gas at high pressure above the mercury column
4. Filling nitrogen gas at low pressure above the mercury column

Q. A bicycle wheel rolls without slipping on a horizontal floor. Which one of the following is true about the motion of points on the rim of the wheel, relative to the axis at the wheel's centre?

1. Points near the top move faster than points near the bottom
2. All points on the rim move with the same speed
3. Points near the bottom move faster than points near the top
4. All points have the velocity vectors that are pointing in the radial direction towards the centre of the wheel

Q. The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by.

1. $\mu =\tan \theta$
2. $\mu =2\tan \theta$
3. $\mu =1/\tan \theta$
4. $\mu =2/\left(\tan \theta \right)$

Q. A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little less than the amount that is necessary and an auxiliary engine (only capable of operating for a short time) has to be used as well. When is it best to switch on the auxiliary engine?

1. When the rocket has nearly stopped with respect to the Earth
2. It doesn't matter
3. At take-off
4. Can't say

Q. A solid cylinder is attached to a horizontal massless spring as shown in figure. If the cylinder rolls without slipping, the time period of oscillation of the cylinder is?

1. $2\pi \sqrt{\frac{x}{g}}$
2. $2\pi \sqrt{\frac{2M}{3K}}$
3. $2\pi \sqrt{\frac{3M}{8K}}$
4. $2\pi \sqrt{\frac{3M}{2K}}$

Q. The displacement of a particle along the x-axis is given by $x=a{\sin }^2\omega t$. The motion of the particle corresponds to.

1. Simple harmonic motion of frequency $3\omega /2\pi$
2. Simple harmonic motion of frequency $\omega /2\pi$
3. Non simple harmonic motion
4. Simple harmonic motion of frequency $\omega /\pi$

Q. A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are.

1. Up the incline while ascending as well as descending
2. Up the incline while ascending and down the incline while descending
3. Down the incline while ascending and up the incline while descending
4. Down the incline while ascending as well as descending

Q. A long straight wire is carrying current I in $+z$ direction. The x-y pkane contains a closed circular loop carrying current $I_2$ and not encircling the straight wire. The force on the loop will be.

1. ${\mu }_0{I}_1{I}_2/4\pi$
2. ${\mu }_0{I}_2{I}_0/2\pi$
3. Zero
4. Depends on the distance of the circle of the loop from the wire

Q. The planets with radii $R_1$ and $R_2$ have densities ${\rho }_1$, ${\rho }_2$ respectively. Their atmospheric pressures are $p_1$ and $p_2$ respectively. Therefore, the ratio of masses of their atmospheres, neglecting variation of g within the limits of atmosphere is?

1. ${\rho }_1{R}_2{p}_1/{\rho }_2{R}_1{p}_2$
2. $p_1{R}_1{\rho }_1/p_2{R}_2{\rho }_2$
3. $p_1{R}_2{\rho }_2/p{P}_2{R}_2{\rho }_1$
4. $p_1{R}_1{\rho }_2/p_2{R}_2{\rho }_1$

Q. Radioactive decay will occur as follows.
${}_{86}^{220}Rn\to {}_{84}^{216}PO+{}_2^{4}He$ Hald life $=55$s
${}_{84}^{216}Po\to {}_{82}^{212}Pb+{}_2^{4}He$ Half life$=0.66$s
${}_{82}^{822}Pb\to {}_{82}^{212}BL+{\lambda }^o$e Half life $=10.6$h
If a certain mass of radon(Rn$=220$) is allowed to decay in a certain container; then after $5$ minutes the element with the greater mass will be.

1. Radon
2. Polonium
3. Lead
4. Bismuth

Q. Two soap bubbles coalesce. It is noticed that, whilst joined together, the radii of the two bubbles are a and b where $a>b$. Then the radius of curvature of interface between the two bubbles will be.

1. $a+b$
2. $ab/(a-b)$
3. $ab/(a+b)$
4. $a-b$

Q. A liquid is allowed into a tube of truncated cone shape. Identify the correct statement from the following.

1. The speed is high at the wider end and low at the narrow end
2. The speed is low at the wider end and high at the narrow end
3. The liquid flows with uniform velocity in the tube
4. The speed is same at both ends in a streamline flow

Q. A stream of a liquid of density $\rho$ flowing horizontally with speed v rushes out of a tube of radius r and hits a vertical wall nearly normally. Assuming that the liquid does not rebound from the wall, the force exerted on the wall by the impact of the liquid is given by.

1. $\pi r\rho v^2$
2. $\pi r^2\rho v^2$
3. $\pi r^2\rho v$
4. $\pi r\rho v$

Q. A cylindrical tube of uniform cross-sectional area A is filled with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is $p_o$ and temperature is $T_o$, atmospheric pressure is also $p_o$$.Now,thetemperatureofthegasisincreasedto$2T_0$, the tension of wire will be.

1. $p_{o}A$
2. $2p_{o}A$
3. $\frac{p_{o}A}{2}$
4. $4p_{o}A$

Q. N lamps each of resistance r, are fed by a machine of resistance R. If light emitted by any lamp is proportional to the square of the heat produced, prove that the most efficient way of arranging them is to place them in parallel arcs, each containing n lamps, where n is the integer nearest to.

1. ${\left(\frac{NR}{r}\right)}^{1/2}$
2. $(NRr{)}^{3/2}$
3. $(NRr{)}^{1/2}$
4. ${\left(\frac{r}{NR}\right)}^{3/2}$

Q. A nucleus ${}_Z^{A}X$ has mass represented by $m(A,Z)$. If $m_p$ and $m_n$ denote the mass of proton and neutron respectively and BE the binding energy(in MeV) then.

1. $BE=\left[m\right(A_{1}Z)-Z{m}_p-(A-Z\left)m_n\right]C^2$
2. $BE=[Z{m}_p+(A-Z)m_n-m(A,Z\left)\right]C^2$
3. $BE=[Z{m}_p+A{m}_n-m(A,Z\left)\right]C^2$
4. $BE=m\left(A_{1}Z\right)-Z{m}_p-(A-Z)m_N$

Q. The x and y coordinates of a particle moving in a plane are given by $x\left(t\right)=a\cos \left(pt\right)$ and $y\left(t\right)=b\sin \left(pt\right)$ where a, b$(<a)$ and p are positive constants of appropriate dimensions and t is time. Then, which of the following is not true?

1. The path of the particle is an ellipse
2. Velocity and acceleration of the particle are perpendicular to each other at $t=\frac{\pi }{2\rho }$
3. Acceleration of the particle is always directed towards a fixed point
4. Distance travelled by the particle in time interval between $t=0$ and $t=\frac{\pi }{2P}$ is a

Q. A thin symmetrical double convex lens of refractive index ${\mu }_2=1.5$ is placed between a medium of refractive index ${\mu }_1=1.4$ to the left and another medium of refractive index ${\mu }_3=1.6$ to the right. Then, the system behaves as.

1. A convex lens
2. A concave lens
3. A glass plate
4. A convo concave lens