Two light beams of intensities \(4\,I\) and \(9\,I\) interfere on a screen. The phase difference between these beams on the screen at point \(A\) is \(zero\) and at point \(B\) is \(\pi\). The difference of resultant intensities, at the point \(A\) and \(B\), will be \(....I\).

If the radius of earth shrinks by \(2 \%\) while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.

A particle of mass \(m\) and charge \(q\) is in an electric and magnetic field given by \(\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k\) The charged particle is shifted from the origin to the point \(P(x = 1 ;\, y = 1)\) along a straight path. The magnitude of the total work done is

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \(S\) having surface charge density \(+\sigma\). The electron at \(t=0\) is at a distance of 1 m from \(S\) and has a speed of \(1 m s ^{-1}\). The maximum value of \(\sigma\), if the electron strikes \(S\) at \(t=1 s\) is \(\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{ C }{ m ^2}\). The value of \(\alpha\) is __________ .

A thin convex lens \(L\) (refractive index \(= 1.5\)) is placed on a plane mirror \(M\). When a pin is placed at \(A\), such that \(OA = 18\, cm\), its real inverted image is formed at \(A\) itself, as shown in figure. When a liquid of refractive index \({\mu _1}\) is put between the lens and the mirror, the pin has to be moved to \(A’\). such that \(OA’ = 27\,cm\), to get its inverted real image at \(A'\) itself. The value of \({\mu _1}\) will be

An object of mass 1000 g experiences a time dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N\). The power generated by the force at time \(t\) is :

On interchanging the resistances, the balance point of a meter bridge shifts to the left by \(10\ cm\). The resistance of their series combination is \(1\ k\Omega\). How much was the resistance on the left slot before interchanging the resistances?  ..................  \(\Omega\)

Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be.

Suppose that intensity of a laser is \(\left(\frac{315}{\pi}\right)\, W / m ^{2} .\) The \(rms\) electric field, in units of \(V / m\) associated with this source is close to the nearest integer is \(\left(\epsilon_{0}=8.86 \times 10^{-12} C ^{2} Nm ^{-2} ; c =3 \times 10^{8} ms ^{-1}\right)\)

A compound microscope consists of an objective lens of focal length \(1 \,cm\) and an eye piece of focal length \(5 \,cm\) with a separation of \(10 \,cm\) The distance between an object and the objective lens, at which the strain on the eye is minimum is \(\frac{ n }{40}\, cm .\) The value of \(n\) is\(....\)

In the given figure, two wheels \(P\) and \(Q\) are connected by a belt \(B\). The radius of \(P\) is three times as that of \(Q\). In case of same rotational kinetic energy, the ratio of rotational inertias \(\left(\frac{{I}_{1}}{{I}_{2}}\right)\) will be \({x}: 1\). The value of \({x}\) will be \(.....\, .\)

The temperature \(\theta\) at the junction of two insulating sheets, having thermal resistances \(R _{1}\) and \(R _{2}\) as well as top and bottom temperatures \(\theta_{1}\) and \(\theta_{2}\) (as shown in figure) is given by

The voltage across the \(10\, \Omega\) resistor in the given circuit is \(x\) volt. The value of \('x'\) to the nearest integer is..........