Consider a closed surface $$'S'$$ surrounding a volume $$V.$$ If $$\overrightarrow r $$ is the position vector of a point inside $$S$$ with $$\overrightarrow n $$ the unit normal on $$'S',$$ the value of the integral is

A fair dice is tossed two times. The probability that the $$2$$^nd toss results in a value that is higher than the first toss is

The solution of differential equation $${{dy} \over {dx}} = ky,y\left( 0 \right) = C$$ is

A numerical solution of the equation $$f\left( x \right) = x + \sqrt x - 3 = 0$$ can be obtained using Newton $$-$$ Raphson method. If the starting values is $$x=2$$ for the iteration then the value of $$x$$ that is to be used in the next step is