1
GATE EE 2016 Set 2
Numerical
+2
-0
The line integral of the vector field $$\,\,F = 5xz\widehat i + \left( {3{x^2} + 2y} \right)\widehat j + {x^2}z\widehat k\,\,$$ along a path from $$(0, 0, 0)$$ to $$(1,1,1)$$ parameterized by $$\left( {t,{t^2},t} \right)$$ is _________.
2
GATE EE 2015 Set 2
+2
-0.6
Match the following.

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

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

A
$$P = 2,Q = 1,R = 4,S = 3$$
B
$$P = 4,Q = 1,R = 3,S = 2$$
C
$$P = 4,Q = 3,R = 1,S = 2$$
D
$$P = 3,Q = 4,R = 2,S = 1$$
3
GATE EE 2013
+2
-0.6
The curl of the gradient of the scalar field defined by $$\,V = 2{x^2}y + 3{y^2}z + 4{z^2}x$$ is
A
$$4xy{a_x} + 6yz{a_y} + 8zx{a_z}$$
B
$$4{a_x} + 6{a_y} + 8{a_z}$$
C
$$\left( {4xy + 4{z^2}} \right){a_x} + \left( {2{x^2} + 6yz} \right){a_y} + \left( {3{y^2} + 8zx} \right){a_z}$$
D
$$0$$
4
GATE EE 2013
+2
-0.6
Given a vector field $$\overrightarrow F = {y^2}x\widehat a{}_x - yz\widehat a{}_y - {x^2}\widehat a{}_z,$$ the line integral $$\int {F.dl}$$ evaluated along a segment on the $$x-$$axis from $$x=1$$ to $$x=2$$ is
A
$$2.33$$
B
$$0$$
C
$$-2.33$$
D
$$7$$
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