1
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
$$6$$
2
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
$$2\pi$$
3
GATE EE 2014 Set 3
+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 2011
+1
-0.3
The two vectors $$\left[ {\matrix{ {1,} & {1,} & {1} \cr } } \right]$$ and $$\left[ {\matrix{ {1,} & {a,} & {{a^2}} \cr } } \right]$$ where $$a = {{ - 1} \over 2} + j{{\sqrt 3 } \over 2}$$ are
A
Orthonormal
B
Orthogonal
C
Parallel
D
Collinear
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