According to Bohr's theory, the moment of momentum of an electron revolving in \(4^{\text {th }}\) orbit of hydrogen atom is _______.

A \(5 \,V\) battery is connected across the points \(X\) and \(Y\). Assume \(D_{1}\) and \(D_{2}\) to be normal silicon diodes. Find the current (in \(A\)) supplied by the battery if the \(+ve\) terminal of the battery is connected to point \(X\)

A radio-active material is reduced to \(1 / 8\) of its original amount in \(3\) days. If \(8 \times 10^{-3}\,kg\) of the material is left after \(5\) days. The initial amount of the material is \(.......\,g\)

Match List - I with List - II.

List - I	List - II
(A) Electric field inside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(I) \(\sigma / \epsilon_0\)
(B) Electric field at distance \(r >0\) from a uniformly charged infinite plane sheet with surface charge density \(\sigma\).	(II) \(\sigma / 2 \epsilon_0\)
(C) Electric field outside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(III) \(0\)
(D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density \(\sigma\).	(IV) \(\frac{\sigma R^2}{\epsilon_0 r^2}\)

Choose the correct answer from the options given\(\text{ }\)below\(\text{ }\):

A galvanometer has a resistance of \(50 \Omega\) and allows a maximum current of \(5 \mathrm{~mA}\) to pass. What is the necessary series resistance to connect to convert it to a voltmeter that can measure \(100 \mathrm{~V}\)?

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5D ? ['D' stands for dioptre]

An automobile, travelling at \(40\, km/h\), can be stopped at a distance of \(40\, m\) by applying brakes. If the same automobile is travelling at \(80\, km/h\), the minimum stopping distance, in metres, is (assume no skidding)..........\(m\)

An object of mass \(5\, kg\) is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of \(10\, N\) throughout the motion. The ratio of time of ascent to the time of descent will be equal to \(\left[\right.\)Use \(g =10 \,ms ^{-2}]\)

A square loop of area \(25\,cm ^2\) has a resistance of \(10\,\Omega\). The loop is placed in uniform magnetic field of magnitude \(40.0 T\). The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in \(1.0 sec\), will be \(..........\times 10^{-3}\)

Asseretion \(A:\) If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is \(5\, {mm}\) and there are \(50\) total divisions on circular scale, then least count is \(0.001\, {cm}\). Reason \(R:\) Least Count \(=\frac{\text { Pitch }}{\text { Total divisions on circular scale }}\) In the light of the above statements, choose the most appropriate answer from the options given below: