Let $$f(x,y,z) = 4{x^2} + 7xy + 3x{z^2}$$. The direction in which the function f(x, y, z) increases most rapidly at point P = (1, 0, 2) is

Let $$\overrightarrow E (x,y,z) = 2{x^2}\widehat i + 5y\widehat j + 3z\widehat k$$. The value of $$\mathop{\int\!\!\!\int\!\!\!\int}\limits_{\kern-5.5pt V} {(\overrightarrow \nabla \,.\,\overrightarrow E )dV} $$, where V is the volume enclosed by the unit cube defined by 0 $$\le$$ x $$\le$$ 1, 0 $$\le$$ y $$\le$$ 1, and 0 $$\le$$ z $$\le$$ 1, is

List-$${\rm I}$$
$$P.$$ Stoke's Theorem
$$Q.$$ Gauss's Theorem
$$R.$$ Divergence Theorem
$$S.$$ Cauchy's Integral Theorem

List-$${\rm I}{\rm I}$$
$$1.$$
$$2.$$
$$3.$$
$$4.$$