In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 k$$\Omega $$ are used. The figure of merit of the galvanometer is 60 $$\mu A/$$division. In the absence of shunt resistance, the galvanometer produces a deflection of $$\theta $$ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $$\theta /2,$$ is closest to :

The de-Broglie wavelength ($$\lambda $$_B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state ($$\lambda $$_G) by :

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths ^{$$\lambda $$}N, ^{$$\lambda $$}A respectively. The ratio $${{{}^\lambda N} \over {{}^\lambda A}}$$is closest to :

A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :