1
GATE EE 2022
+1
-0.33

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

A
$$20\widehat i + 7\widehat j$$
B
$$20\widehat i + 7\widehat j + 12\widehat k$$
C
$$20\widehat i + 12\widehat k$$
D
$$20\widehat i$$
2
GATE EE 2022
+1
-0.33

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

A
3
B
8
C
10
D
5
3
GATE EE 2016 Set 2
+1
-0.3
The value of line integral $$\,\,\int {\left( {2x{y^2}dx + 2{x^2}ydy + dz} \right)\,\,}$$ along a path joining the origin $$(0, 0, 0)$$ and the point $$(1, 1, 1)$$ is
A
$$0$$
B
$$2$$
C
$$4$$
D
$$6$$
4
GATE EE 2014 Set 1
+1
-0.3
The line integral of function $$F=yzi,$$ in the counterclockwise direction, along the circle $${x^2} + {y^2} = 1$$ at $$z=1$$ is
A
$$- 2\pi$$
B
$$- \pi$$
C
$$\pi$$
D
$$2\pi$$
EXAM MAP
Medical
NEET