1
GATE ME 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Solutions of Laplace's equation having continuous second-order partial derivatives are called
A
biharmonic functions
B
harmonic functions
C
conjugate harmonic functions
D
error functions
2
GATE ME 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
$$f\left( z \right) = u\left( {x,y} \right) + i\,\,\,\,v\left( {x,y} \right)$$ is an analytic function of complex variable $$z=x+iy$$ , where $$i = \sqrt { - 1} $$ If $$u(x,y)=2xy,$$ then $$v(x,y)$$ may be expressed as
A
$$ - {x^2} + {y^2} + $$ constant
B
$$ {x^2} - {y^2} + $$ constant
C
$$ {x^2} + {y^2} + $$ constant
D
$$ - \left( {{x^2} + {y^2}} \right) + $$ constant
3
GATE ME 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Given two complex numbers $${z_1} = 5 + \left( {5\sqrt 3 } \right)i$$ and $${z_2} = {2 \over {\sqrt 3 }} + 2i,$$ the argument of $${{{z_1}} \over {{z_2}}}$$ in degrees $$i$$
A
$$0$$
B
$$30$$
C
$$60$$
D
$$90$$
4
GATE ME 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
An analytic function of a complex variable $$z=x+iy,$$ where $$i = \sqrt { - 1} $$ is expressed as
$$f\left( z \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right).\,$$ If $$u(x,y)=2xy,$$
then $$v(x,y)$$ must be
A
$${x^2} + {y^2} + $$ constant
B
$${x^2} - {y^2} + $$ constant
C
$$-{x^2} + {y^2} + $$ constant
D
$$-{x^2} - {y^2} + $$ constant
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Turbo Machinery
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