A differential equation $${{dx} \over {dt}} = {e^{ - 2t}}\,\,u\left( t \right)\,\,$$ has to be solved using trapezoidal rule of integration with a step size $$h=0.01$$ sec. Function $$u(t)$$ indicates a unit step function. If $$x(0)=0$$ then the value of $$x$$ at $$t=0.01$$ sec will be given by

Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ will be

A single phase full bridge converter supplies a load drawing constant and ripple free load current. If the triggering angle is $${30^ \circ },$$ the input power factor will be

A three phase fully controlled bridge converter is feeding a load drawing a constant and ripple free load current of $$10$$ $$A$$ at a firing angle of $${30^ \circ }.$$ The approximate Total Harmonic Distortion $$(\% \,\,THD)$$ and $$r.m.s$$ value of fundamental component of the input current will respectively be