A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $$3$$ tosses. Let the random variable $$Y$$ denotes the number of heads. The value of var $$\left\{ Y \right\},$$ where var $$\left\{ . \right\}$$ denotes the variance, equal

The value of the contour integral in the complex - plane $$\oint {{{{z^3} - 2z + 3} \over {z - 2}}} dz$$ along the contour $$\left| z \right| = 3,$$ taken counter-clockwise is

In the circuit shown, the diodes are ideal, the inductance is small, and $${{\rm I}_0} \ne 0.$$ Which one of the following statements is true?

A phase-controlled, single-phase, full-bridge converter is fed from a $$230$$ $$V,$$ $$50$$ $$Hz,$$ $$AC$$ source. The fundamental frequency in $$Hz$$ of the voltage ripple on the $$DC$$ side is