In the following circuit, the battery has an emf of \(2\mathrm{V}\) and an internal resistance of \(\frac{2}{3}\  \Omega\). The power consumption in the entire circuit is _______ \(W\).

If we need a magnification of \(375\) from a compound microscope of tube length \(150\; \mathrm{mm}\) and an objective of focal length \(5\; \mathrm{mm}\), the focal length of the eye-piece, should be close to.....\(mm\)

The output of the given combination gates represents

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are \(1\, hour\) and \(8\, hours\) respectively. The radius of the orbit of nearer satellite is \(2 \times 10^{3}\, {km}\). The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is \(\frac{\pi}{{x}}\, {rad} \,{h}^{-1}\) where \({x}\) is ..... .

The radius of third stationary orbit of electron for Bohr's atom is \(R\). The radius of fourth stationary orbit will be what?

A metal plate of area \(1\times10^{-4}\, m^2\) is illuminated by a radiation of intensity \(16\, m\,W/m^2\). The work function of the metal is \(5\,eV\). The energy of the incident photons is \(10\, eV\) and only \(10\%\) of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : \([1\, eV = 1.6\times10^{-19}\, J]\)

A coil of cross-sectional area  \(A\) having \(n\)  turns is placed in a uniform magnetic field \(B.\)  When it is rotated with an angular velocity \(\omega ,\)  the maximum \(e.m.f.\)  induced in the coil will be

A block '\(A\)' takes \(2\,s\) to slide down a frictionless incline of \(30^{\circ}\) and length ' \(l\) ', kept inside a lift going up with uniform velocity ' \(v\) '. If the incline is changed to \(45^{\circ}\), the time taken by the block, to slide down the incline, will be approximately \(........\,s\)

A charge of \(4\,\mu C\) is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be.

Two identical metallic spheres \(A\) and \(B\) when placed at certain distance in air repel each other with a force of \(F\). Another identical uncharged sphere \(C\) is first placed in contact with \(A\) and then in contact with \(B\) and finally placed at midpoint between spheres \(A\) and \(B\). The force experienced by sphere \(C\) will be.

The displacement of a particle executing SHM is given by \(x=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{m}\). The time period of motion is \(3.14 \mathrm{~s}\). The velocity of the particle at \(\mathrm{t}=0\) is_________ \(\mathrm{m} / \mathrm{s}\).