The value of the quantity, where $$P = \int\limits_0^1 {x{e^x}\,dx\,\,\,} $$ is

At $$t=0,$$ the function $$f\left( t \right) = {{\sin t} \over t}\,\,$$ has

Divergence of the $$3$$ $$-$$ dimensional radial vector field $$\overrightarrow r $$ is

A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probability that the $$2$$^nd removed ball is red is