Page 58 - Engineering Mathematics Workbook_Final

Vector Calculus

4 − 2 − 5
(a) (b) (a) (b) 3
3 3 2

2 4 (c) 4 (d) 5
(c) (d)
3 3 [JAM MA 2018]
ur u r
[JAM MA 2014]
23. The value of the integral   F  dS ,
20. The value of the integral ur S
$
$
$
 (x + ) y dx x dy , where C is the where F = 3x i + 2y j + zk and S is
+
2
C the closed surface given by the planes
triangle with vertices (0, 0), (2, 0) and x = 0, x =
0
0
2
(2, 4) in the anticlockwise direction is 1, y = , y = , z = and
z =
(a) 5/3 (b) 10/3 3 is
(c) 20/3 (d) 40/3 (a) 6 (b) 18
[JAM GP 2010] (c) 24 (d) 36

$
$
ur x i − y j [JAM GP 2009]
21. For a > 0, b > 0, let F =
b x + a y 2 ur $ $ 2 $
2
2 2
−
+
be a planar vector field. 24. The flux of F = y i x j z k along
the outward normal, across the surface of
Let the solid
C = (  , x ) y  R x + y = a + b 2 
2
2
2
2
)
−
x
2
z
x
be the circle oriented anti-clockwise.  ( , , y z  R 3 0   1, 0  y  1, 0   2 x − y 2 
ur
r
C  F dr =  is equal to
Then
2 2 5
(a) (b) 2 (a) (b)
ab 3 3
(c) 2 ab (d) 0 (c) 8 (d) 4
3 3
22. If
ur
$
$
) (3x −
F ( , x y = 8y ) i + (4y − 6xy ) j [JAM MA 2017]
r
for ( ,x y ) R 2 , then  ur dr , 25. Let S be the closed surface forming the
F 
C boundary of the region V bounded by
where C is the boundary of the triangular 2 2
y =
6
0
0
region bounded by the lines x = , x + ur 3, z = , z = . A vector
y = 0 and x + y = 1 oriented in the
field F is defined over V with
anti-clockwise direction, is ur
+
 F = 2y z + 1. Then the value of

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