An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by $$45^{\circ}$$, then $$\left(\tan 45^{\circ}=1\right)$$

A horizontal wire of mass '$$m$$', length '$$l$$' and resistance '$$R$$' is sliding on the vertical rails on which uniform magnetic field '$$B$$' is directed perpendicular. The terminal speed of the wire as it falls under the force of gravity is ( $$\mathrm{g}=$$ acceleration due to gravity)

Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is

A string is stretched between two rigid supports separated by $$75 \mathrm{~cm}$$. There are no resonant frequencies between $$420 \mathrm{~Hz}$$ and $$315 \mathrm{~Hz}$$. The lowest resonant frequency for the string is