Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less than $$1/2$$ is

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is

A half-controlled single-phase bridge rectifier is supplying an $$R$$-$$L$$ load. It is operated at a firing angle $$α$$ and the load current is continuous. The fraction of cycle that the freewheeling diode conducts is