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What is the resultant of three coplanar forces $300\text{N}$ at $0^o$, $400\text{N}$ at ${30}^{\circ }$ and $400\text{N}$ at ${150}^{\circ }$ with $x-$ axis?

A tuning fork $A$ of unknown frequency produces $4$ beats per second when sounded with another tuning fork $B$ of frequency $254\text{Hz}$. When tuning fork $A$ is loaded with wax, it still gives $4$ beats per second with tuning fork $B$. The initial unknown frequency of tuning fork $A$ is

Iterative function for calculating $(N{)}^{1/2N}$ by Newton-Raphson method is

In the shown figure two beads slide along a smooth horizontal rod as shown in the figure. The relation between $v$ and $v_0$ in the shown position will be

If a chain is lowered at a constant speed of $v=1.2\text{m/s}$, determine the normal reaction exerted on the floor as a function of time. The chain has a mass of $80\text{kg}$ and a total length of $6\text{m}$. [Take $g=10{\text{m/s}}^2$]

A body started with a velocity of $20m{s}^{-1}$ and moving with an acceleration of $2m{s}^{-2}$. The distance (in $\text{m})$ travelled by the body in the $8^{th}$ second is

A rectangular loop with a sliding connector of length l = 1.0 m is situated in a uniform magnetic field B = 2T perpendicular to the plane of loop. Resistance of connector is r = 2

$\Omega$. Two resistances of 6$\Omega$ and 3$\Omega$ are connected as shown in figure. The external force required to keep the connector moving with a constant velocity v = 2m/s is

A wooden plank of mass $20\text{kg}$ and length $10\text{m}$ is resting on a smooth horizontal floor. A man of mass $60\text{kg}$ starts moving from one end of the plank to the other end. Find the magnitude of displacement of the plank over the floor when the man reaches the other end of the plank.

A bob of mass $M$ is suspended through a massless string of length $L$. The horizontal velocity at position $A$ is sufficient enough to make it reach at point $B$. The angle at which the speed of bob is half of that at $A$, satisfies

A ball is thrown vertically downwards from a height of $20m$ with an initial velocity ${\upsilon }_0$. It collides with the ground, loses $50$ percent of its energy in collision and rebounds to the same height. The initial velocity ${\upsilon }_0$ is (Take $g=10m{s}^{-2}$)

By what distance do the wedges move if horizontal plank moves by $x\text{cm}$ downwards?

Surface area is

A ring of mass $2\pi \text{kg}$ and radius $0.25\text{m}$ is making $300\text{rpm}$ about an axis perpendicular to its plane. The tension (in newtons) developed in the ring is, approximately

In the arrangement shown in figure, slits $S_1$ and $S_4$ are having a variable separation Z. Point O on the screen is at the common perpendicular bisector of $S_1{S}_2$ and $S_3{S}_4$.

When $Z=\frac{\lambda D}{2d^{\prime }}$ the intensity measured at O is $I_0$. The intensity at O when $Z=\frac{2\lambda D}{d}$ is

A spherical ball rolls on an inclined plane without slipping. Ratio of total kinetic energy to rotational kinetic energy is

Magnetic field inside long solenoid changes from $2\times {10}^{-3}T$ to $1T$ when it is filled with some ferromagnetic material. Susceptibility of this material is

Two identical pulses whose centres are initially $16\text{cm}$ apart are moving towards each other on a stretched string with same speed as shown in the figure. After $4$ seconds, if the vertical displacement for resultant pulse is zero then the speed of pulses are

In which radioactive disintegration, neutron dissociates into proton and electron

A rigid body of mass 'M' and radius R is rolling without sliding, along with bock of radius of gyration K, and mass $m_1$, then find the minimum value of friction coefficient $\mu$?

The ball is thrown vertically up (taken $+z-$ axis) from the ground. The correct momentum-height $(p-h)$ diagram is:

Find the displacement of a particle in time $0$ to $10\text{s}$ whose velocity versus time graph is shown below.

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that their circumferences coincide. The centre of mass of the new disc is at a distance of $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

A $10\text{kg}$ ball attached at the end of a rigid massless rod of length $1\text{m}$ rotates at a constant speed in a horizontal circle of radius $0.5\text{m}$ and with a period of $1.57\text{s}$, as shown in the figure. The force exerted by the rod on the ball is $(g=10{\text{ms}}^{-2})$

A mass $m$ is suspended from a spring of spring constant $K$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is

An iron transformer assumed to be $100\%$ efficient. The ration of the secondary truns to the primary truns is $1:20$. A $240V$ ac supply is connected to the primary coil. What is the current in the primary coil?

With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\overrightarrow{a}=4\hat{i}-\hat{j},\overrightarrow{b}=-3\hat{i}+2\hat{j}$ and

$\overrightarrow{c}=-\hat{k}$ where $\hat{i},\hat{j},\hat{k}$ are unit vectors, along the X, Y and Z-axis respectively. The unit vectors $\hat{r}$along the direction of sum of these vector is

Two masses $m$ and $2m$ are suspended together by a massless spring of force constant $K$. When the masses are in equilibrium, mass $m$ is removed without disturbing the system. Then, the amplitude of vibration of the system is:

Current gain in common base configuration is less than 1 because

The excess pressure inside a spherical drop of water is four times that of another water drop. Then the mass ratio of the two drops is

A stone with weight $W$ is thrown vertically upward into the air from ground level with initial speed $v_0$. If a constant force $f$ due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is

The acceleration-time graph of a body is shown below





The most probable velocity time graph of the body is

The cylindrical tube of spray pump has a cross-section of $10{\text{cm}}^2$, one end of which has $50$ fine holes each of area ${10}^{-8}{\text{m}}^2$. If liquid flows inside the tube with a speed of $0.3\text{m/min}$, find the speed with which the liquid is ejected through the holes.

A body is thrown with a velocity of 9.8 m/s making an angle of ${30}^{\circ }$ with the horizontal. It will hit the ground after a time

In a P-V graph if the initial state is further away from the y axis than the final state, which of these statements is true?

If the air on Earth's surface is replaced with water, then to what extent the water level must rise so as to maintain the same pressure $\left[{10}^5\frac{N}{m^2}\right]$ on Earth's surface? [Assume nothing above water surface. given g = 10 $m/s^2$, density of water = 1000 $kg/m^3$.

Find the maximum force $F$ to be applied on the system shown, so that the two blocks move together. Take $g=10{\text{m/s}}^2$.

A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is

Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is

For an object dropped under gravity, what is the ratio of displacement after equal subsequent time intervals starting from rest?

Two stones are thrown up simultaneously with initial speeds $u_1$ and $u_2(u_2>u_1)$. They hit the ground after $6\text{s}$ and $10\text{s}$ respectively. Which graph correctly represents the time variation of, $\Delta x=(x_2-x_1)$, the relative position of the second stone with respect to the first upto $t=10\text{s}$?

Assume that the stones do not rebound after hitting the ground.

A block of mass $m$ moving at a velocity $v$ collides head on with another block of mass $2m$ at rest. If the coefficient of restitution is $\frac{1}{2}$, find the velocities of the blocks after the collision.

What happens to the temperature of a gas in adiabatic expansion?

A wave pulse is generated in a string that lies along x-axis. At the points A and B, as shown in figure, if $R_{A}and{R}_B$ are ratios of magnitudes of particle speed to the wave speed, then

The displacement x of a particle moving in one dimension is related to time t by the equation $t=\sqrt{x}+3$ where x is in metres and t in seconds. The displacement of the particle when its velocity is zero is

In the circuit shown in figure, $X$ is joined to $Y$ for a long time and then $X$ is joined to $Z$. The total heat produced in $R_2$ is

A particle of mass $200\text{g}$ is projected from origin $O$ with speed $10\text{m/s}$ at an angle ${60}^{\circ }$ with positive $x-$ axis. Find the magnitude of angular momentum of particle after $1\text{sec}$ about the origin. (Take $g=10{\text{m/s}}^2$)