Page 76 - Engineering Mathematics Workbook_Final

Vector Calculus

148. Divergence of the vector field 21 151. The figures show diagrammatic

)
v ( , ,x y z = − ( cosx xy + y ) ( cosi + y xy ) j representations of vector fields, X , Y
 2 and Z respectively. Which one of the
+  ( sin z 2 ) x+ 2 + y  k
  following choices is true?

2
(a) 2 cosz z

2
z
(b) sin xy + 2 cos z
x
(c) sin xy − cosz

(d) none of these [GATE-2007 (PI)]
(a)  X = 0, Y  0, Z  0
149. For a vector E, which one of the
following statement is NOT TRUE? X  0, Y = 0, Z 
(b)  0
(a) If  E = 0,E is called solenoidal
(c)  X  0, Y  0, Z  0
(b) If  E = 0,E is called
conservative (d)  X = 0, Y = 0, Z = 0

(c) If  E = 0,E is called irrotational [GATE-2017-EE SESSION-II]

(d) If  E = 0,E is called irrotational 152. Consider the two-dimensional velocity
field given by
$
[GATE-2013 (IN)] V = (5 a x b y i+ 1 + 1 ) + (4 a x b y j+ 2 + 2 ) $

where a b a and b are constants.
150. A vector P is given by 1 1 2 2
2
P = x ya x − x y 2 y a − x yza z . Which one of the following conditions
3
2
needs to be satisfied for the flow to be
Which one of the following statement is incompressible?
TRUE?
(a) a + 1 b = 1 0 (b) a + 1 b = 2 0
(a) P is solenoidal, but not irrotational
(c) a + 2 b = 2 0 (d) a + 2 b = 2 0
(b) P is irrotational, but not solenoidal
[GATE-2017-ME SESSION-1]
(c) P is neither solenoidal nor
irrotational

(d) P is both solenoidal and irrotational

[2015-EC-SET 1]

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