Page 82 - Engineering Mathematics Workbook_Final

Vector Calculus

188. The flux of the vector filled (a) 2 (b) 4
F = xi + y j + zk flowing out through
(c) 8 (d) 12
the surface of the ellipsoid
x 2 + y 2 + z 2 =   0 [CSIR]
a 2 b 2 c 2 1. a b c  is



(a) abc (b) 3 abc 192. The surface integral   F  n ds
S
(c) 2 abc (d) 4 abc over the surface S of the sphere
2
2
2
189. The value of x + y + z = 9 , where
)
)
) (x z j +
S  ( ( x − yz i − 2x y j + zk  n ds F = (x + y i + + ) ( y + ) z k
$
3
2
where S is the surface of the cube and n is the unit outward surface normal,
2
z
y
bounded by x = = = and co- yields _____.
ordinate planes is ________ [GATE-17-ME]
32 56 193. Let a > 0 and let
(a) (b)
3
3 3 S = (  x , , y ) z  R x + y + z = a 2 
2
2
2
)
4
16 64 . Evaluate  S  ( x + 4 y + 4 z ds .
(c) (d)
3 3


2 a 6 12 a 4
2
2
2
190. Let S be the sphere x + y + z = 1. (a) (b)
5 5
The value of surface integral


12 a 8 12 a 6
  ( sin ,cos x ,2z z sin y  ) ( , , y z ds is (c) (d)
)
2
−
y
x
x
S 5 5
_______ 1 $
 2 194. Consider the function F = r 2 r , where
(a) (b)
3 3 r is distance from the origin and r is the
$
4 8 unit vector in the radial direction. The
(c) (d) divergence of this function over a sphere
3 3 of radius1, which includes the origin is
_____.
191. Let S be the unit sphere
2
x + y + z = 1. Then the value of (a) 0 (b) 2
2
2
surface integral (c) 4 (d) R
)
 S    (  2x + 3x − y + 5z  2  ds is
2
2

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