GATE ME

Vector Calculus

Engineering Mathematics

(Past Years Questions)

Marks 1

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Let $$\phi $$ be an arbitrary smooth real valued scalar function and $$\overrightarrow V $$ be an arbitrary smooth vecto...
GATE ME 2015 Set 3
Curl of vector $$\,V\left( {x,y,x} \right) = 2{x^2}i + 3{z^2}j + {y^3}k\,\,$$ at $$x=y=z=1$$ is
GATE ME 2015 Set 2
Divergence of the vector field $${x^2}z\widehat i + xy\widehat j - y{z^2}\widehat k\,\,$$ at $$(1, -1, 1)$$ is
GATE ME 2014 Set 3
Curl of vector $$\,\,\overrightarrow F = {x^2}{z^2}\widehat i - 2x{y^2}z\widehat j + 2{y^2}{z^3}\widehat k\,\,$$ is
GATE ME 2014 Set 2
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \ove...
GATE ME 2012
The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {y - x} \right)\widehat j + \left( {x + y...
GATE ME 2008
Stokes theorem connects
GATE ME 2005
The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is
GATE ME 1996
If $$\overrightarrow V $$ is a differentiable vector function and $$f$$ is sufficienty differentiable scalar function th...
GATE ME 1995

Marks 2

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The surface integral $$\int {\int\limits_s {F.ndS} } $$ over the surface $$S$$ of the sphere $${x^2} + {y^2} + {z^2} =...
GATE ME 2017 Set 2
For the vector $$\overrightarrow V = 2yz\widehat i + 3xz\widehat j + 4xy\widehat k,$$ the value of $$\,\nabla .\left( {...
GATE ME 2017 Set 1
The value of the line integral $$\,\,\oint\limits_C {\overrightarrow F .\overrightarrow r ds,\,\,\,} $$ where $$C$$ is a...
GATE ME 2016 Set 3
A scalar potential $$\,\,\varphi \,\,$$ has the following gradient: $$\,\,\nabla \varphi = yz\widehat i + xz\widehat j ...
GATE ME 2016 Set 2
The value of $$\int\limits_C {\left[ {\left( {3x - 8{y^2}} \right)dx + \left( {4y - 6xy} \right)dy} \right],\,\,} $$ (wh...
GATE ME 2015 Set 3
The surface integral $$\,\,\int {\int\limits_s {{1 \over \pi }} } \left( {9xi - 3yj} \right).n\,dS\,\,$$ over the spher...
GATE ME 2015 Set 2
The velocity field on an incompressible flow is given by $$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_...
GATE ME 2015 Set 1
The integral $$\,\,\oint\limits_C {\left( {ydx - xdy} \right)\,\,} $$ is evaluated along the circle $${x^2} + {y^2} = {1...
GATE ME 2014 Set 1
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $$F = xi + yj...
GATE ME 2013
The divergence of the vector field $$\,3xz\widehat i + 2xy\widehat j - y{z^2}\widehat k$$ at a point $$(1,1,1)$$ is equa...
GATE ME 2009
The directional derivative of the scalar function $$f(x, y, z)$$$$ = {x^2} + 2{y^2} + z\,\,$$ at the point $$P = \left( ...
GATE ME 2008
The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $...
GATE ME 2007

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