Let the probability density function of a random variable x be given as

f(x) = ae^$$-$$2|x|

The value of a is _________.

A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Which power device is best suited for this purpose?

A single-phase full-bridge diode rectifier feeds a resistive load of 50 $$\Omega$$ from a 200 V, 50 Hz single phase AC supply. If the diodes are ideal, then the active power, in watts, drawn by the load is _________. (round off to nearest integer).

The voltage at the input of an AC-DC rectifier is given by $$v(t) = 230\sqrt 2 \sin \omega t$$ where $$\omega = 2\pi \times 50$$ rad/s. The input current drawn by the rectifier is given by

$$i(t) = 10\sin \left( {\omega t - {\pi \over 3}} \right) + 4\sin \left( {3\omega t - {\pi \over 6}} \right) + 3\sin \left( {5\omega t - {\pi \over 3}} \right)$$

The input power factor, (rounded off to two decimal places), is _________ lag.