The percentage error in the measurement of mass and velocity are $3 \%$ and $4 \%$, respectively. The percentage error in the measurement of kinetic energy is

A car travelling at 80 kmph can be stopped at a distance of 60 m by applying brakes. If the same car travels at 160 kmph and the same braking force is applied, the stopping distance is

A 2 kg ball thrown vertically upward and another 3 kg ball projected with certain angle $\left(\theta \neq 90^{\circ}\right)$ both will have same time of flight, then this ratio of their maximum heights is

In a sport event, a disc is thrown such that it reaches its maximum range of 80 m , the distance travelled in first 3 s is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a horizontal force of 40 N applied to the other end of the rope. If the linear density of the rope is $0.5 \mathrm{kgm}^{-1}$ and initially the block is at rest, the time in which the block moves a distance of 9 m is

A block of mass 1.5 kg kept on a rough horizontal surface is given a horizontal velocity of $10 \mathrm{~ms}^{-1}$. If the block comes to rest after travelling a distance of 12.5 m , the coefficient of kinetic friction between the surface and the block is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A force of $\left(6 x^2-4 x+3\right) \mathrm{N}$ acts on a body of mass 0.75 kg and displaces it from $x=2 \mathrm{~m}$ to $x=5 \mathrm{~m}$. The work done by the force is

A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \mathrm{~ms}^{-1}$ and the coefficient of restitution is 0.75 , the total distance travelled by the ball before it comes to rest is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A solid cylinder rolls down an inclined plane without slipping. If the translation kinetic energy of the cylinder is 140 J . The total kinetic energy of the cylinder is

Two blocks of masses $m$ and $2 m$ are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest, the speed of the centre of mass of the system of two blocks after a time of 5.4 s is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The displacement of a particle executing simple harmonic motion is $y=A \sin (2 t+\phi) \mathrm{m}$, where $t$ is time in second and $\phi$ is phase angle. At time $t=0$, the displacement and velocity of the particle are 2 m and $4 \mathrm{~ms}^{-1}$. The phase angle, $\phi=$

The displacement of a damped oscillator is $x(t)=\exp (-0.2 t) \cos (3.2 t+\phi)$, where $t$ is time in second The time requirement for the amplitude of the oscillator to become $\frac{1}{e^{1.2}}$ times its initial amplitude is

Maximum height reached by a rocket fired with a speed equal to $50 \%$ of the escape speed from the surface of the earth is ( $R=$ Radius of the earth)

If the work done in stretching a wire by 1 min is 2 J . The work necessary for stretching another wire of satrs material but with double radius of cross-section and half the length by 1 mm is

If $S_1, S_2$ and $S_3$ are the tensions at liquid-air, solid-air and solid-liquid interfaces respectively and $\theta$ is the angle of contact at the solid-liquid interface, then

If ambient temperature is 300 K , the rate of cooling at 600 K is $H$. In the same surroundings, the rate of cooling at 900 K is

An ideal heat engine operates in Carnot cycle between $127^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. It absorbs $5 \times 10^4 \mathrm{Cal}$ of heat at height temperature. Amount of heat converted to work is

One mole of a gas having $\gamma=\frac{7}{5}$ is mixed with one mole of a gas having $\gamma=\frac{4}{3}$. The value of $\gamma$ for the mixture is ( $\gamma$ is the ratio of the specific heats of the gas)

A Carnot heat engine has an efficiency of $10 \%$. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is

The rms velocity of a gas molecules oí mass $m$ at a given temperature is proportional to

The speed of a wave on a string is $150 \mathrm{~ms}^{-1}$ when the tension is 120 N . The percentage increase in the tension in order to raise the wave speed by $20 \%$ is

The minimum deviation produced by a hollow prism filled with a certain liquid is found to be $30^{\circ}$. The light ray is also, found to be refracted at an angle of $30^{\circ}$. Then, the refractive index of the liquid is

In Young's double slit experiment, the intensity at a point where the path difference is $\frac{\lambda}{6}$ ( $\lambda$ being the wavelength of the light used) is $I$. If $I_0$ denotes the maximum intensity, $\frac{I}{I_0}$ is equal to

Two particles of equal mass $m$ and equal charge $q$ are separated by a distance of 16 cm . They do not experience any force. The value of $\frac{q}{m}$ is (if $G$ is the universal gravitational constant and $g$ is the acceleration due to gravity)

In the following diagram, the work done in moving a point charge from point $P$ to points $A, B$ and $C$ are $W_A, W_B$ and $W_C$ respectively. Then ( $A, B, C$ are points on semi-circle and point charge $q$ is at the centre of semi-circle)

Four condensers each of capacitance $8 \mu \mathrm{~F}$ are joined as shown in the figure. The equivalent capacitance between the points $A$ and $B$ will be

A steady current is flowing in a metallic conductor of non-uniform cross-section. The physical quantity which remains constant is

The resistance between points $A$ and $C$ in the given network is

A wire shaped in a regular hexagon of side 2 cm carries a current of 4 A . The magnetic field at the centre of hexagon is

A tightly wound coil of 200 turns and of radius 20 cm carrying current 5 A . Magnetic field at the centre of the coil is

The domain in ferromagnetic material is in the form of a cube of side $2 \mu \mathrm{~m}$. Number of atoms in that domain is $9 \times 10^{10}$ and each atom has a dipole movement of $9 \times 10^{-24} \mathrm{Am}^2$. The magnetisation of the domain is (approximately).

Magnetic field at a distance of $r$ from $Z$-axis is $B=B_0$ $r t \hat{\mathbf{k}}$ present in the region. $B_0$ is constant and $t$ is time. The magnitude of induced electric field at a distance of $r$ from $Z$-axis is

A series $L-C-R$ circuit is shown in the figure. Where the inductance of 10 H , capacitance $40 \mu \mathrm{~F}$ and resistance $60 \Omega$ are connected to a variable frequency 240 V source. The current at resonating frequency is

An electromagnetic wave travel in a medium with a speed of $2 \times 10^8 \mathrm{~ms}^{-1}$. The relative permeability of the medium is 1 . Then, the relative permittivity is

The longest wavelength of light that can initiate photo electric effect in the metal of work function 9 eV is

A hydrogen atom falls from $n$th higher energy orbit to first energy orbit $(n=1)$. The energy released is equal to 12.75 eV . The $n$th orbit is

The decrease in each day in the uranium mass of the material in a uranium reactor operating at a power of 12 MW is (Energy released in one ${ }_{92} \mathrm{U}^{235}$ fission is about 200 MeV )

When a signal is applied to the input of a transistor, it was found that output signal is phase-shifted by $180^{\circ}$. The transistor configuration is

The voltage $V_0$ in the network shown is

A message signal of 3 kHz is used to modulate a carric signal frequency 1 MHz , using amplitude modulation. The upper side band frequency and band width respectively are