1
GATE CE 2007
+2
-0.6
The velocity vector is given as $${\mkern 1mu} \vec V = 5xy\widehat i + 2{y^2}\widehat j + 3y{z^2}\widehat k.{\mkern 1mu} {\mkern 1mu}$$ The divergence of this velocity vector at $$(1,1,1)$$ is
A
$$9$$
B
$$10$$
C
$$14$$
D
$$15$$
2
GATE CE 2006
+2
-0.6
The directional derivative of $$\,\,f\left( {x,y,z} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at the point $$P(2,1,3)$$ in the direction of the vector $${\mkern 1mu} \vec a = \widehat i - 2\widehat k{\mkern 1mu}$$ is _________.
A
$$-2.785$$
B
$$-2.145$$
C
$$-1.789$$
D
$$1.000$$
3
GATE CE 2005
+2
-0.6
Value of the integral $$\,\,\oint {xydy - {y^2}dx,\,\,}$$ where, $$c$$ is the square cut from the first quadrant by the line $$x=1$$ and $$y=1$$ will be (Use Green's theorem to change the line integral into double integral)
A
$$1/2$$
B
$$1$$
C
$$3/2$$
D
$$5/3$$
4
GATE CE 2005
+2
-0.6
The line integral $$\int {\,\,V.dr\,\,}$$ of the vector function $$V\left( r \right) = 2xyz\widehat i + {x^2}z\widehat j + {x^2}y\widehat k\,\,$$ from the origin to the point $$P(1,1,1)$$
A
is $$1$$
B
is zero
C
is $$-1$$
D
cannot be determined without specifying the path
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Environmental Engineering
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Medical
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