1
GATE CE 2007
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
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Fluid Mechanics and Hydraulic Machines
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