Given a vector field $$\overrightarrow F = {y^2}x\widehat a{}_x - yz\widehat a{}_y - {x^2}\widehat a{}_z,$$ the line integral $$\int {F.dl} $$ evaluated along a segment on the $$x-$$axis from $$x=1$$ to $$x=2$$ is

A continuous random variable $$X$$ has a probability density function $$f\left( x \right) = {e^{ - x}},0 < x < \infty .$$ Then $$P\left\{ {X > 1} \right\}$$ is

When the Newton-Raphson method is applied to solve the equation $$\,\,f\left( x \right) = {x^3} + 2x - 1 = 0,\,\,$$ the solution at the end of the first iteration with the initial value as $${x_0} = 1.2$$ is

Thyristor $$T$$ in the figure below is initially off and is triggered with a single pulse of width $$10\mu s.$$ It is given that $$L = \left( {{{100} \over \pi }} \right)\mu H$$ and $$C = \left( {{{100} \over \pi }} \right)\mu F.$$ Assuming latching and holding currents of the thyristor are both zero and the initial charge on $$C$$ is zero, $$T$$ conducts for