1
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
For an analytic function $$f\left( {x + i\,y} \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right),\,u$$ is given by $$u = 3{x^2} - 3{y^2}.$$ The expression for $$v,$$ considering $$k$$ is to be constant is
A
$$3{y^2} - 3{x^2} + k$$
B
$$6x - 6y + k$$
C
$$6y - 6x + k$$
D
$$6xy + k$$
2
GATE CE 2010
MCQ (Single Correct Answer)
+1
-0.3
The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is
A
$$5$$
B
$$\sqrt 5 $$
C
$${1 \over {\sqrt 5 }}$$
D
$${1 \over 5}$$
3
GATE CE 2009
MCQ (Single Correct Answer)
+1
-0.3
The analytical function has singularities at, where $$f(z) = {{z - 1} \over {{z^2} + 1}}$$
A
1 and -1
B
1 and i
C
1 and -i
D
i and -i
4
GATE CE 2007
MCQ (Single Correct Answer)
+1
-0.3
Potential function $$\phi $$ is given as $$\phi \, = \,{x^2}\, - \,{y^2}$$. What will be the stream function $$\psi $$ with the condition $$\psi \, = \,0$$ at x = 0, y = 0?
A
$$2xy$$
B
$${x^2}\, + \,\,{y^2}$$
C
$${x^2}\, - \,\,{y^2}$$
D
$$2{x^2}{y^2}$$
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Fluid Mechanics and Hydraulic Machines
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Medical
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