The energy of an electron in an orbit of the Bohr's atom is \(-0.04 E _0 eV\) where \(E _0\) is the ground state energy. If \(L\) is the angular momentum of the electron in this orbit and h is the Planck's constant, then \(\frac{2 \pi L}{ h }\) is _________ :

In a double slit experiment shown in figure, when light of wavelength \(400 \mathrm{~nm}\) is used, dark fringe is observed at \(P\). If \(D=0.2 \mathrm{~m}\). the minimum distance between the slits \(S_1\) and \(S_2\) is ____________ \(mm\).

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 relation between root mean square speed \(\left( v _{ rms }\right)\) and most probable speed \(\left( v _{ p }\right)\) for the molar mass \(M\) of oxygen gas molecule at the temperature of \(300\, K\) will be

Two identical symmetric double convex lenses of focal length \(f\) are cut into two equal parts \(L_1, L_2\) by \(A B\) plane and \(L_3, L_4\) by \(X Y\) plane as shown in figure respectively. The ratio of focal lengths of lenses \(L_1\) and \(L_3\) is ________.

A circular coil of radius \(10\, cm\) is placed in a uniform magnetic field of \(3.0 \times 10^{-5}\, T\) with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in \(0.2\,s.\) The maximum value of \(EMF\) induced (in \(\mu V\) ) in the coil will be close to the integer\(....\mu V\)

The vehicles carrying inflammable fluids usually have _______ metallic chains touching the ground.

The formula \(X = 5YZ^2\),  \(X\) and \(Z\) have dimensions of capacitance and magnetic field respectively. What are the dimensions of \(Y\) in \(SI\) units?

The angular speed of truck wheel is increased from \(900\, rpm\) to \(2460\, rpm\) in \(26\) seconds. The number of revolutions by the truck engine during this time is (Assuming the acceleration to be uniform).

Four particles, each of mass \(M\) and equidistant from each other, move along a circle of radius \(R\) under the action of their mutual gravitational attraction. The speed of each particle is

The logic gate equivalent to the given circuit diagram is:

The equivalent resistance between \(A\) and \(B\) of the network shown in figure