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Find the angle of incidence of ray for which after reflection, it passes through pole of concave mirror.

A point charge is moving along a straight line with a constant velocity $v$. Consider a small area $A$ perpendicular to the direction of motion of the charge. Calculate the displacement current through the area when its distance from the charge is $x$. The value of $x$ is not large so that the electric field at any instant is essentially given by Coulomb's law.

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 $\hat{j}$ towards north. Ship $B$ is at a distance of $80km$ east and $150km$ north of Ship $A$ and is sailing towards west at $10km/hr$. Time in which $A$ will be at minimum distance from $B$ is

A body traveling along a straight line traversed one third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 2 m/s for half of the time and with velocity 4 m/s for the other half of time. The mean velocity averaged over the whole time of motion is

The condition for a body having density ${\rho }_b$ to float completely immersed in the liquid having density ${\rho }_L$ is

The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${37}^{\circ }$.If $|\overrightarrow{A}|=15$ and $|\overrightarrow{B}|=12$. Then $|\overrightarrow{A}\times \overrightarrow{B}|$ is

A bus starts moving with acceleration $2{\text{ms}}^{-2}$. A cyclist $96\text{m}$ behind the bus starts simultaneously toward the bus at a constant speed of $20\text{m/s}$. After some time, the bus will be left behind. If the bus continues moving with the same acceleration, after what time from the beginning, the bus will overtake the cyclist?

A cubical block of ice of mass 'm' and edge 'L' is placed in a large tray of mass 'M'. If the ice melts, how far does the centre of mass of the system "ice plus tray” come down with reference to the point O as shown in figure

Find the components of force $\text{F}$ along and perpendicular to the incline if the direction of $\text{F}$ is parallel to the horizontal axis.

The acceleration versus velocity graph of a particle moving in a straight line starting from rest is as shown in the figure.



The corresponding velocity-time graph may be

In a cyclotron , The Magnetic field is ___ and Electric field is ___.

The period of revolution of an earth satellite close to surface of earth is 90 min. The time period of another satellite in an orbit at a distance of three times the radius of earth from its surface will be

The horizontal and vertical components of the velocity of projection of a projectile are $10{\text{ms}}^{-1}$ and $20{\text{ms}}^{-1}$ respectively. Find the horizontal range of projectile. ($g=10{\text{ms}}^{-2}$).

X-rays are in nature similar to

A boy of $45kg$ weight is standing on the piston of cross sectional area $900c{m}^2$. Find the difference in the levels of water in the two tubes.

In a guitar, two strings $A$ and $B$ made up of the same material produce beats of frequency $4\text{Hz}$. When the tension in $B$ is slightly decreased, the beat frequency increases to $6\text{Hz}$. If the frequency of $A$ is $530\text{Hz}$ then the original frequency of $B$ will be

Work function of a metal is 2.1 eV. Which of the waves of the following wavelengths will be able to emit photoelectrons from its surface

A block of mass 2 kg slides down the face of a smooth ${45}^{\circ }$ wedge of mass 9kg as shown in figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge.

PN-junction diode works as a insulator, if connected :

Three particles of masses $2\text{kg},3\text{kg}$ and $5\text{kg}$ are situated at the vertices of a right angled triangle $\Delta ABC$ as shown in figure. Find the moment of inertia of the system about line $PQ$ perpendicular to the $BC$ and in the plane of $\Delta ABC$.

A sample of an ideal gas has volume V, pressure P and temperature T. The mass of each molecule of the gas is m. The density of the gas is (k is the Boltzmann's constant )

In the pulley arrangement shown, the pulley $P_2$ is movable. Assuming coefficient of friction between $m$ and surface to be $\mu$, the minimum value of $M$ for which $m$ is at rest is

System is released from rest. Find speed of the blocks after 2 seconds.

The surface mass density $\left(\frac{mass}{area}\right)$ of a circular disc of radius a depends on the distance from the centre as $\rho \left(r\right)$ = $A+Br$. Find its moment of inertia about the line perpendicular to the plane of the disc and passing through its centre

A particle of mass $0.2\text{kg}$ (initially at rest) starts moving in one dimension under a force that delivers a constant power $0.5W$ to the particle. Then the speed after $5\text{seconds}$ is

A ball is projected from the ground with a speed $u$ making an angle $\theta$ with the horizontal. Which of the following graphs correctly represents the variation of angle between the velocity and acceleration vectors with time.

[If $T$ is the time of flight]

Consider the situation given in the diagram two cars are moving along road '1' and road '2'. Draw the direction of the motion of car 'B' as seen from car 'A'

An infinite number of charges of equal magnitude q, but of opposite sign are placed alternately starting with positive charge along x- axis at x = 1 m; x = 2 m,x = 4 m, x= 8 m and so on. The electric potential at the point x = 0 due to these charges will be (in S.I units and k = $\frac{1}{4\pi {ϵ}_0}$

The energy of a photon emitted in a Bohr atom due to electronic transitions from one orbit to the other is:

A boy standing on the viewing platform of the Qutub Minar. He then throws a ball vertically downwards at $2\text{m/s}$. If the platform is $72\text{m}$ above ground, the speed with which the ball hits the ground in $\left(\text{m/s}\right)$ is

Speed of a longitudinal wave in air is $300\text{m/s}$ and in steel is $3000\text{m/s}$. If wavelength in air is $0.5\text{m}$ , then its wavelength in steel is

In the figure shown, string $AB$ and $BC$ have masses $m$ and $2m$ respectively. Both are of the same length $l$. Mass of each string is uniformly distributed on its length. The string is suspended vertically from the ceiling of a room. A small jerk wave pulse is given at the end ${}^{\prime }{C}^{\prime }$. It goes up to upper end ${}^{\prime }{A}^{\prime }$ in time ${}^{\prime }{t}^{\prime }$. If $m=2\text{kg},l=\frac{9610}{1681}\text{m},g=10{\text{m/s}}^2,\sqrt{2}=1.4,\sqrt{3}=1.7$, then the value of ${}^{\prime }{t}^{\prime }$ is :-

The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate can NOT be given by :





where, $I_1,I_2,I_3,I_4$ are the moments of inertia of the plates about axes 1,2,3,4 respectively.

Two masses $m$ and $M$ are connected by a light string passing over a smooth pulley. When set free, $m$ moves up by $1.4\text{m}$ in $2\text{s}$. The ratio $\frac{m}{M}$ is $(g=9.8{\text{ms}}^{-2})$

Two balls at same temperature collide. What is conserved?

Three identical sperical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is:

A block is placed on a rough horizontal plane. A time dependent horizontal force $F=kt$ acts on the block. Here $k$ is a positive constant. Acceleration-time graph of the block is

10kg block is kept on a horizontal surface and Ram is trying to pull it with a force of 5N, Given coefficient of static friction is 0.2 and coefficient of Kinetic friction n(μK) = 0.1 Which of these statements is/are correct.

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

In the following figure, the p.d. between the points $M$ and $N$ is balanced at $50\text{cm}$. length. The length in $\text{cm}$, balancing for the potential difference between points $N$ and $C$ will be –

A steel wire of mass 4.0 g and length 80 cm is fixed at the two ends. The tension in the wire is 50N. The frequency of the fourth harmonic of the fundamental is

A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total distance covered by the body before it comes to rest is

Match the block diagrams of block of mass, m, with their corresponding free body diagram.

(Bodies are at rest with respect to ground)

A cylindrical container is divided in two equal parts by a diathermic piston. Different ideal gases are filled in the two parts. Find the ratio of the mass of the molecules of the gas in the lower part to that of the upper part, if the root mean square velocity of molecules in the lower part is equal to the mean velocity of molecules in the upper part.

At what angle, the two forces 3F and F$\sqrt{3}$ should act, so that the resultant force is F$\sqrt{21}$.

The majority charge carriers in P-type semiconductor are

A stone tied to a string of length $l$ is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest point and has a speed $u$. The magnitude of change in velocity as it reaches its highest point of the circle is