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A force $(4\hat{i}+\hat{j}-2\hat{k})\text{N}$ acting on a body maintains its velocity at $(2\hat{i}+3\hat{j}-\hat{k})\text{m/s}$. The power exerted is

In an EM wave Electric field vector and magnetic field vector are:

Volume of a cylinder increases by $6\%$ upon heating. The area of its curved surface will increase by

A body of mass $1kg$ is subjected to a force of $20N$ for $10$ seconds after which the force ceases to act. What distance would it travel in the next $10$ seconds? Assume that the body starts from rest.

A motorcycle starts from rest and accelerates along a straight line at $2.2m/s^2.$ The speed of sound is 330 m/s. A siren at the starting point remains stationary. When the driver hears the frequency of the siren at 90% of when the motorcycle is stationary, the distance travelled by the motorcyclist is

Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. Find the magnitude of the acceleration of the centre of mass of the two blocks.

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point ‘C’ starting from ‘A’. He swims with a speed of 5 km/hr at an angle $\theta$ w.r.t the river flow. If AB =BC =400 m, what is the value of $\theta$?

The $v-t$ plot of a moving object is shown in the figure. The average velocity of the object during the first $10\text{seconds}$ is

An aeroplane can fly at the rate of $500\text{km/h}$ in still atmosphere (when wind is not blowing). The pilot wishes to fly through the shortest path from $A$ to $B$. The wind is blowing at the rate of $300\text{km/h}$ perpendicular to line $AB$. Find the time taken by the aeroplane to reach the point $B$ which is at a distance of $2000\text{km}$ from $A$.

An alternating emf is applied across a parallel combination of a resistance $R$, capacitance $C$ and an inductance $L$. If $I_R,I_L,I_C$ are the currents through $R,L$ and $C$ respectively, then the diagram which correctly represents, the phase relationship among $I_R,I_L,I_C$ and source emf $E$, is given by

A body is moving in a circular path, unifomly with acceleration $a$. If the speed of the particle is two times that of initial one, what is the ratio of acceleration ?

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ (Kelvin) and mass $m$, is

Modulus of rigidity of a liquid

The $F-x$ graph is shown below. Find the change in potential energy from $x=0$ to $x=5\text{m}$

For continuous X-rays, produced wavelength is

The ratio of lengths of two rods A and B of same material is 1 : 2 and the ratio of their radii is 2 : 1, then the ratio of modulus of rigidity of A and B will be

A conductor has a reistance R, at $t_1^{0}C$ and R2 at $t_2^{0}C$. Find $\propto \left(i{n}^{\circ }{C}^{-1}\right)$

A rod of length $1\text{m}$ rotates in the $xy$ plane about the fixed point $\text{O}$ in the anticlockwise sense, as shown in figure, with angular velocity $\omega =a+bt$ where $a=10{\text{rad s}}^{-1}$ and $b=5{\text{rad s}}^{-2}$. The velocity and acceleration of the point $A$ at $t=0$ is

If a thermometer reads freezing point of water as ${20}^{\circ }\text{C}$ and boiling point as ${150}^{\circ }\text{C},$ how much thermometer would read when the actual temperature is ${60}^{\circ }\text{C}$?

A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle of ${45}^{\circ }$ with the X-axis. The two motions are given by

$x=x_{0}sin\omega t$ and $s=s_{0}sin\omega t$

Find the amplitude of the resultant motion.

Two point P and Q diametrically opposite on a disc of radius $R$ have velocities $v$ and $2v$ as shown in figure. Find the angular speed of Q w.r.t P.

A moving body of mass m and velocity 3 km/h collides with a body at rest of mass 2m and sticks to it. Now the combined mass starts to move. What will be the combined velocity

In the spectrum of hydrogen atom, ratio of the longest wavelength in Lyman series to the longest wavelength in Balmer series is:

A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is</br>

If $V_D=12\text{V}$ and $V_E=8\text{V}$ then

A body cools down from ${80}^{\circ }\text{C}$ to ${60}^{\circ }\text{C}$ in 10 minutes when the temperature of surroundings is ${30}^{\circ }\text{C}$. The temperature of the body after next $10$ minutes will be

Two boys $A$ and $B$ of mass $60\text{kg}$ and $40\text{kg}$ are standing on a platform. Both start walking towards each other with the same velocity $5\text{m/s}$. Find the velocity of the platform if mass of the platform is $100\text{kg}$.

Two prisms A and B are in contact with each other.The dispersive powers of A and B are 0.04 and 0.03 respectively.The angular dispersion produced by A is $8^{\circ }$. The net angular dispersion produced by the combination, if the combination does not produce a net deviation is

A metal plate is exposed to light of wavelength $\lambda$. It is observed that electrons are ejected from the surface of the plate. When a retarding uniform electric field $E$ is imposed, no electron can move away from the plate farther than a certain distance $d$. Then the threshold wavelength ${\lambda }_0$ for the material of plate is (e is the electronic charge, h is Plank’s constant and $c$ is the speed of light)

Three blocks are connected by different inextensible string as shown in the figure. If the velocity of block $A$ is $10\text{m/s}$, the velocity of block $C$ is

The bob of a pendulum at rest is given a sharp hit to impact a horizontal velocity $\sqrt{3.5gl}$, where $l$ is the length of the pendulum. Find the height at which tension in the string is zero.

A body of mass $600\text{gm}$ is attached to a spring of spring constant $k=100\text{N/m}$ and it is performing damped oscillations. If damping constant is $0.2$ and driving force is $F=F_0\cos \left(\omega t\right)$ where $F_0=20\text{N}$, find the amplitude of oscillations at resonance.

For the arrangement shown in the figure, find the final magnification of the extended object $AB$ after two successive reflections. Take the first reflection from mirror $M_1$.

An ideal monoatomic gas at temperature ${27}^{\circ }\text{C}$ and pressure ${10}^6{\text{N/m}}^2$ occupies $10\text{L}$ volume. $10,000\text{cal}$ of heat is added to the system without changing the volume. Calculate the change in temperature of the gas. Given:$R=8.31\text{J/mol-K}$ and $J=4.18\text{J/cal}$

If $y=4^x+5e^x+3$, then $\frac{dy}{dx}$ is

A player catches a ball of mass $150\text{gm}$ moving at a speed of $20\text{m/s}$. If the process of catching has to be completed in $0.1\text{sec}$, what is magnitude of the impulsive force imparted by the ball to the hands of the player?

One $\text{mole}$ of a gas in a cylinder is compressed from $8{\text{m}}^3$ to $2{\text{m}}^3$ quasi-statically at a constant temperature of $300\text{K}$. Workdone during this process is

($\ln 2=0.693$)

Two particles are projected from towers of different heights with velocities as shown in the figure. Find angle ${}^{\prime }{\theta }^{\prime }$; if the particles collide



(Given particles collide after 1 second and particles are projected at the same instant)

A particle is projected at angle $\theta$ with horizontal, with velocity $v_0$ at $t=0$. Find the radius of curvature at $t=0$.

Two waves have equations $x_1=a\sin (kx-\omega t+{\varphi }_1)$ and $x_2=a\sin (kx-\omega t+{\varphi }_2)$. If in the resultant wave the frequency and amplitude remain equal to amplitude and frequency of each superimposing waves, the phase difference between them is

An ideal fluid is flowing through the given tubes which is placed on a horizontal surface. If the liquid has velocities $v_A$ and $v_B$, and pressures $P_A$ and $P_B$ at points $A$ and $B$ respectively, then the correct relation is:

(The figure shown below is as if the system is seen from the top)

Find the acceleration of the particle at $x=3\text{m}$.

The excess pressure inside one soap bubble is three times that inside a second soap bubble, then the ratio of their surface areas is:

The figure shown below represents two paths that are taken by an ideal gas to go from the state A to state C. In process $\text{AB},400\text{J}$ of heat is added to the system and in process $\text{BC},100\text{J}$ of heat is added to system. The heat absorbed by system in process $\text{AC}$ will be