1
GATE EE 2026
Numerical
+1
-0

Given that $\vec{F}(x, y, z)=\sin (y) \hat{x}+\cos (x) \hat{y}+5 \hat{z}$, the integral $\iint_S \vec{F}(x, y, z) \cdot \overrightarrow{d s}$ over the unit sphere $S$ centered at the origin evaluates to $\_\_\_\_$ . (Round off to one decimal place)

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2
GATE EE 2016 Set 2
MCQ (Single Correct Answer)
+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
$$6$$
3
GATE EE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Let $$\,\,\nabla .\left( {fV} \right) = {x^2}y + {y^2}z + {z^2}x,\,\,$$ where $$f$$ and $$V$$ are scalar and vector fields respectively. If $$V=yi+zj+xk,$$ then $$\,V.\left( {\nabla f} \right)$$ is
A
$${x^2}y + {y^2}z + {z^2}x$$
B
$$2xy+2yz+2zx$$
C
$$x+y+z$$
D
$$0$$
4
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+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
$$2\pi $$

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