The change in the internal energy of the mass of gas, when the volume changes from V to 2 V at constant pressure P is \(\left(\gamma=\frac{\mathrm{Cp}}{\mathrm{Cv}}\right)\)
If the length of the potentiometer wire is increased by keeping constant potential difference across the wire, then
The temperature of an air bubble while rising from bottom to surface of a lake remains constant but diameter is doubled. If pressure on the surface is \(h\) meter of mercury column and relative density of mercury is ' \(\rho\) ' then the depth of the lake is
The apparent wavelength of light from a star moving away from the earth is \(0.02 \%\) more than the actual wavelength. The velocity of star is \(\left[\mathrm{c}=\right.\) velocity of light \(\left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right]\)
A force acting on a body of mass 5 Kg is \((4 \hat{i}-2 \hat{j}+3 \hat{k}) \mathrm{N}\). If the body is initially at rest then the magnitude of its velocity at the end of 10 second in \(\mathrm{m} / \mathrm{s}\) will be
In a cyclic process, work done by the system is
A metal sphere cools at a rate of \(1.5^{\circ} \mathrm{C} / \mathrm{min}\) when its temperature is \(80^{\circ} \mathrm{C}\). When the temperature of the sphere is \(40^{\circ} \mathrm{C}\), its rate of cooling is \(0.3^{\circ} \mathrm{C} / \mathrm{min}\). The temperature of the surrounding \(\left(\theta_0\right)\) is
The resultant logic gate from the combination of following gates is
The length of closed and open pipe is same. The ratio of frequency of \(\mathrm{n}^{\text {th }}\) overtone for closed pipe to that of open pipe is (Neglect end correction)
In an n-p-n transistor amplifier, the collector current is 9 mA . If \(90 \%\) of the electrons emitted reach the collector, then
An a.c. e.m.f. of peak value \(=230 \mathrm{~V}\) and frequency 50 Hz is connected to a circuit with \(\mathrm{R}=11.5 \Omega, \mathrm{~L}=2.5 \mathrm{H}\) and a capacitor all in series. The value of capacitance is ' C ' for the current in the circuit to be maximum. The value of C and maximum current are respectively \(\left(\pi^2=10\right)\).
An element \(\overrightarrow{\Delta l}=\Delta \mathrm{xi}\) is placed at the origin and carries a current of 10 A . The magnitude of magnetic field on the Y axis at a distance of 0.5 m if \(\Delta x=1 \mathrm{~cm}\) is \(\left(\frac{\mu_0}{4 \pi}=10^{-7}\right.\) SI unit \()\left(\sin 90^{\circ}=1\right)\)
The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value then its new time period will become
Four polaroids are placed such that the optic axis of each is inclined at an angle of \(30^{\circ}\) the optic axis of the preceding one. If unpolarised light of intensity ' \(\mathrm{I}_0\) ' falls on the first polaroid, the intensity of light transmitted from the fourth polaroid is \(\left[\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]\)
Two bodies A and B move in same straight line starting from same position. Body moves with constant velocity ' u ' and body B moves with constant acceleration ' \(a\) '. When their velocities become equal, the distance between them is
Three vectors are expressed as \(\vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}\) and \(\vec{c}=-\hat{k}\). The unit vector along the direction of sum of these vectors is
The ratio of angular momentum of an electron in \(\mathrm{n}^{\text {th }}\) orbit of hydrogen atom to the velocity of electron in \(\mathrm{n}^{\text {th }}\) orbit is proportional to
The density of a cube is measured by measuring its mass and length of its sides. The \% error in the measurement of mass and length are \(5 \%\) and \(6 \%\) respectively. The percentage error in the measurement of density is
If a gas is compressed isothermally then the r.m.s. velocity of its molecules
A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle \(\theta_1\) in first 2 s and a further angle \(\theta_2\) in the next 2 s , the ratio \(\theta_1: \theta_2\) is
A mass attached to a spring performs S.H.M. whose displacement is \(\mathrm{x}=3 \times 10^{-3} \cos 2 \pi \mathrm{t}\) metre. The time taken to obtain maximum speed for the first time is
The reading of the ammeter in the following circuit is
