Page 71 - Engineering Mathematics Workbook_Final

Vector Calculus

110. The value of  ˆ . F n ds where S is the (c) 4 (d) 8
S 3 3
surface of the sphere x + y + z = 4where
2
2
2
2
ˆ
114. The value of  ( 4xi − 2y j + 2 z k ).n ds
=
+
ˆ n is the unit normal and F xi + yj zk is s
where S is bounted by x + y = 4,z = and
2
2
0
_____
z = 3is
(a) 32 (b) 16
(a) 16 (b) 48
(c) 8 (d) 64
(c) 32 (d) 84
111. The flux of the vector filed
115. The value of
+
F xi + yj zk flowing out through the
=
s  ( ( x − yz ) i − 2x yj + zk ) ˆ .nds where S is
2
3
x 2 y 2 z 2
surface of the ellipsoid + + = 1
a 2 b 2 c 2 the surface of the cube bounded by
= =
a  b   0is x y z = 2 and co-ordinate planes is ___
c
(a) abc (b) 3 abc


(c) 2 abc (d) 4 abc
)
112. Let w = (  , ,x y z  R 3 :1 x + y + z   4 32 56
2
2
2
(a) (b)
and F w → defined by 3 3
R
3
:
x
( , , y z ) (c) 16 (d) 64
F = 3 for ( , , y z  3 3
x
) w . If 
( x + 2 y + 2 z 2 ) 2 y
116. Let I =  e dx + (e / y n x + ) x dy where C is
,
denotes the boundary of oriented by the c x
the positive oriented boundary of the region
out ward normal ˆ nto , then  ˆ . F n ds is
 1
enclosed by Y = + 2 , 2
1 x y = and x =
(a) 0 (b) 4 2
(c) 8 (d) 12 then the value of I = _____
113. Let S be the sphere x + y + z = 1. The 1 5
2
2
2
(a) 8 (b) 24
value of surface integral
7 3
  ( sin ,cosx y 2 x ,2z z sin y ) ( . , ,x y z is (c) (d)
)
−
s 24 8
____ C = (  , x ) y  R 2 ,max 1
117. Let  , x y = the
 2
(a) (b) value of line integral
3 3

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