Page 64 - Engineering Mathematics Workbook_Final

Vector Calculus

1 (d) a + b + c = 0 [JAM 2012]
2
2
2
(c) (d) 1
2
3
60. If C is a smooth curve in R from (0, 0,
[JAM 2010] )
0) to (2,1, 1 − , then the value of
)
$
$
$
+
)
)
+
+
2
+
57. Let F = ayi + z j xk and C is the  (2xy z dx + ( z x dy + (x y dz is
C
positive oriented closed curve given by
__________
x + 2 y 2 1 = , z = . If  F  dr  −
0
=
C (a) 1 (b) 0
then the value of a is _________ (c) 1 (d) 2
−
(a) 1 (b) 0 [JAM 2012]
1 61. The value of n for which the divergence
(c) (d) 1
2 r
of the function F = n , where
[JAM 2011] r
+
+
r xi y j zk , r  0 vanishes is
=
58. Consider the vector field
$
$
$
F = (ax + + ) a i + − (x + ) y k , _________
j
y
−
where a is constant. (a) 1 (b) 1
If F  curlF = 0 then the value of a is
___________ (c) 3 (d) 3 −
[JAM 2013]
(a) 1− (b) 0
2
3 62. Let  be the triangle R with vertices
(c) 1 (d) (0, 0) (1, 0) and (0, 1) and let
2
)
4
F ( , x y = − xyi + y + 1 j . The line
[JAM 2011]

integral  F dr taking anticlock
$
$
$
+
59. For C > 0, if ai + b j ck is the unit 
( ) wise orientation of  
normal vector at 1,1, 2 to the cone
1 −
z = x + 2 y , then ___________ (a) 6 (b) 0
2
1
2
2
2
(a) a + b − c = 0 (c) 6 (d) 6
[IISC 2006]
2
2
(b) a− 2 + b + c = 0
2
2
2
(c) a − b + c = 0

62