A series LCR circuit with $$R = {{250} \over {11}}\,\Omega $$ and $${X_L} = {{70} \over {11}}\,\Omega $$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ $$\mu$$F. (Take : $$\pi = {{22} \over 7}$$)

The refractive index of an equilateral prism is $$\sqrt 2 $$. The angle of emergence under minimum deviation position of prism, in degree, is ___________.

A hydrogen atom in its first excited state absorbs a photon of energy x $$\times$$ 10^$$-$$2 eV and excited to a higher energy state where the potential energy of electron is $$-$$1.08 eV. The value of x is ______________.

The circuit diagram used to study the characteristic curve of a zener diode is connected to variable power supply (0 $$-$$ 15 V) as shown in figure. A zener diode with maximum potential V_z = 10 V and maximum power dissipation of 0.4 W is connected across a potential divider arrangement. The value of resistance R_P connected in series with the zener diode to protect it from the damage is ________________ $$\Omega$$.