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GATE EE

Vector Calculus

Engineering Mathematics

Previous Years Questions

Marks 1

More
Let $$\overrightarrow E (x,y,z) = 2{x^2}\widehat i + 5y\widehat j + 3z\widehat k$$. The value of $$\mathop{\int\!\!\!\in...
GATE EE 2022
Let $$f(x,y,z) = 4{x^2} + 7xy + 3x{z^2}$$. The direction in which the function f(x, y, z) increases most rapidly at poin...
GATE EE 2022
The value of line integral $$\,\,\int {\left( {2x{y^2}dx + 2{x^2}ydy + dz} \right)\,\,} $$ along a path joining the orig...
GATE EE 2016 Set 2
Let $$\,\,\nabla .\left( {fV} \right) = {x^2}y + {y^2}z + {z^2}x,\,\,$$ where $$f$$ and $$V$$ are scalar and vector fiel...
GATE EE 2014 Set 3
The line integral of function $$F=yzi,$$ in the counterclockwise direction, along the circle $${x^2} + {y^2} = 1$$ at $...
GATE EE 2014 Set 1
The two vectors $$\left[ {\matrix{ {1,} & {1,} & {1} \cr } } \right]$$ and $$\left[ {\matrix{ {1,} &am...
GATE EE 2011
Divergence of the $$3$$ $$-$$ dimensional radial vector field $$\overrightarrow r $$ is
GATE EE 2010
Divergence of the vector field $$v\left( {x,y,z} \right) = - \left( {x\,\cos xy + y} \right)\widehat i + \left( {y\,\co...
GATE EE 2007
Given a vector field $${\overrightarrow F ,}$$ the divergence theorem states that
GATE EE 2002
The directional derivative of $$f\left( {x,y} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at point $$P\left( {2,1,3} \right)...
GATE EE 1994

Marks 2

More
The line integral of the vector field $$\,\,F = 5xz\widehat i + \left( {3{x^2} + 2y} \right)\widehat j + {x^2}z\widehat ...
GATE EE 2016 Set 2
Match the following. List-$${\rm I}$$ $$P.$$ Stoke's Theorem $$Q.$$ Gauss's Theorem $$R.$$ Divergence Theorem $$S.$$ Ca...
GATE EE 2015 Set 2
Given a vector field $$\overrightarrow F = {y^2}x\widehat a{}_x - yz\widehat a{}_y - {x^2}\widehat a{}_z,$$ the line i...
GATE EE 2013
The curl of the gradient of the scalar field defined by $$\,V = 2{x^2}y + 3{y^2}z + 4{z^2}x$$ is
GATE EE 2013
The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} = ...
GATE EE 2012
$$F\left( {x,y} \right) = \left( {{x^2} + xy} \right)\,\widehat a{}_x + \left( {{y^2} + xy} \right)\,\widehat a{}_y.\,\,...
GATE EE 2009
for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1,...
GATE EE 2005

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