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## Marks 1

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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,} &amp; {1,} &amp; {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

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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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