The value of $$\mathop {\lim }\limits_{x \to 0} \left( {{{{x^3} - \sin \left( x \right)} \over x}} \right)$$ is

A parametric curve defined by $$x = \cos \left( {{{\pi u} \over 2}} \right),y = \sin \left( {{{\pi u} \over 2}} \right)\,\,$$ in the range $$0 \le u \le 1$$ is rotated about the $$x-$$axis by $$360$$ degrees. Area of the surface generated is

For the vector $$\overrightarrow V = 2yz\widehat i + 3xz\widehat j + 4xy\widehat k,$$ the value of $$\,\nabla .\left( {\nabla \times \overrightarrow \nabla } \right)\,\,$$ is ______________.

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________.