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Block A and B have masses of 2kg and 3kg respectively. The ground is smooth. Pis an external force of 10N.The force exerted by B on A is

A car is moving on a plane inclined at ${30}^{\circ }$ to the horizontal with an acceleration of $9.8m/s^2$ parallel to the plane upward. A bob is suspended by a string from the roof. The angle in degrees which the string makes with the vertical is: (Assume that the bob does not move relative to car and $g=9.8m/s^2$)

When one centimeter thick surface is illuminated with light of wavelength $\lambda$, the stopping potential is $V$. When the same surface is illuminated by light of wavelength $2\lambda$, the stopping potential is $\frac{V}{3}$. Threshold wavelength for metallic surface is

The degree of the polynomial $f(x,y)=3x^{2}y-2\sqrt{x}{y}^3+4xy-8x$ is

The plate separation in a parallel plate condenser is d and plate area is A. If it is charged to V volt and battery is disconnected then the work done in increasing the plate separation to 2d will be

In a long straight solenoid with number of turns per unit length $n$, current varies as $I\text{A/s}$. Find the magnitude of induced electric field strength inside the solenoid as a function of distance $r$ from the axis of the solenoid.

The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the frequency is $10\text{kHz}$. When the container is filled with a gas, the frequency changes by $50\text{Hz}$. The dielectric constant of the gas is

Figure (6-E6) shows two blocks in contact sliding down an inclined surface of inclination ${30}^{\circ }$ The friction coefficient between the block of mass 2.0 kg and the incline is ${\mu }_1$ and that between the block of mass 4.0 kg

The value of $\int \frac{3\cos x+2}{\sin x+2\cos x+3}dx$ is

(where $C$ is integration constant)

If velocity of a particle is $v\left(t\right)=t^2-3t\text{m/s}$, the average speed and magnitude of average velocity of the particle in $6\text{sec}$ respectively are

A uniform plank of mass $m=1\text{kg}$ and of sufficient length , which is free to move only in the horizontal direction is placed upon the top of a solid cylinder of mass $2m$ and radius $R$. The plank is attached to a fixed wall by means of a light spring of spring constant $k=7\text{N/m}$. Assuming , there is no slipping between cylinder and the plane system, and between cylinder and the ground. Find the Angular frequency of small oscillations of the system.

In the figure shown, if a ball of mass $m$ is at rest relative to the wedge moving to the left with an acceleration $a=g\sqrt{3}$, find the force exerted by the vertical face of the wedge on mass $m$.

The angular velocity of earth about its axis of rotation is

Four balls are dropped from the top of a tower at intervals of one second. The first ball reaches the ground after four seconds of dropping. What are the distances between first and second, second and third, third and fourth balls at this instant?

The equation of a transverse wave travelling on a rope is given by $y=10sin\pi (0.001x-2.00t)$ where y and x are in centimeters and t in seconds. The maximum transverse speed of a particle in the rope is about.

A conducting liquid bubble of inner radius $a$ and thickness $t$ where $a$ = $81\text{cm}$ and $t$ = $0.001\text{cm}$ is charged to potential $\text{V}$. If the bubble collapses to a droplet, find the potential on the droplet in terms of $\text{V}$.

A swimmer can swim with a speed $v$ in still water


If the swimmer crosses a swimming pool of width ${}^{\prime }{d}^{\prime }$ from $A$ to directly opposite point $B$ on other side in time $t_1$ as shown in figure and in a flowing river (river velocity $u$) of same width ${}^{\prime }{d}^{\prime }$ from $A^{\prime }$ to directly opposite point $B^{\prime }$ on other bank in time $t_2$, then $\left(\frac{t_1}{t_2}\right)$ is equal to: (Assume $v>u$)

The wave number of the first balmer line of $L{i}^{2+}$ ions is 1,36,800 $c{m}^{-1}$. The wavelenght of the first line of Balmer series of hydrogen atom is (in $c{m}^{-1}$)

A photon of wavelength $\lambda$ incident on a free electron and is scattered in the backward direction. The fractional shift in its wavelength in terms of the Compton wavelength ${\lambda }_c$ of the electron is-

When a ball is thrown vertically upwards with velocity $v_0$, it reaches a maximum height of $h$. With what velocity should the ball be thrown to reach half the maximum height.

A block is placed on the top of a plane inclined at ${30}^{\circ }$ with horizontal. The length of the plane is $10\text{m}$. The block slides down the plane and reaches the bottom. If the surface is frictionless, the speed of the block at the bottom of the inclined plane is

A boy of mass $M$ stands on a platform of radius $R$ capable to rotate about its axis. The moment of inertia of the platform is $I$. The system is at rest. The friend of the boy throws a ball of mass $m$ with a velocity $v$ horizontally. The boy on the platform catches it. Find the angular velocity of the system in the process.

A gas at temperature $250\text{K}$ is contained in a closed vessel. If the gas is heated and the temperature rises by $1^{\circ }\text{C},$ the percentage increase in its pressure is nearly

A fly wheel of mass $140\text{kg}$ and radius $3\text{m}$ is rotating at $240\text{rpm}$. The angular acceleration of flywheel if it comes to rest, after $7$ rotations is (Assume constant angular acceleration)

Represent graphically a displacement of 40 km, ${30}^{\circ }$ east of north.

An iron cored transducer is excited with a frequency of $15kHz.$ The maximum value of frequency of displacement to be measured with this transducer should not exceed ____.

A thin wire of length l is carrying a constant current. The wire is bent to form a circular coil. If radius of the coil, thus formed, is equal to R and number of turns in it is equal to n, then which of the following graphs represent(s) variation of magnetic field induction (B) at centre of the coil?