1
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a complex variable $$z.$$ Which ONE of the following statements is TRUE?
A
If $$f(z)$$ is differentiable at $${z_0},$$ then $$g(z)$$ & $$h(z)$$ are also differentiable at $${z_0}.$$
B
If $$g(z)$$ & $$h(z)$$ are differentiable at $${z_0},$$ then $$f(z)$$ is also differentiable at $${z_0}.$$
C
If $$f(z)$$ is continuous at $${z_0},$$ then it is differentiable at $${z_0}.$$
D
If $$f(z)$$ is differentiable at $${z_0},$$ then so are its real and imaginary parts.
2
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The Laplace transform of $$f\left( t \right) = 2\sqrt {t/\pi }$$$$\,\,\,\,\,$$ is$$\,\,\,\,\,$$ $${s^{ - 3/2}}.$$ The Laplace transform of $$g\left( t \right) = \sqrt {1/\pi t}$$ is
A
$$3{s^{ - 5/2}}/2$$
B
$${s^{ - 1/2}}$$
C
$${s^{1/2}}$$
D
$${s^{3/2}}$$
3
GATE EE 2015 Set 2
Numerical
+2
-0
In the given rectifier, the delay angle of the thyristor $${T_1}$$ measured from the positive going zero crossing of $${V_s}$$ is $${30^ \circ }$$. If the input voltage $${V_s}$$ is $$100$$ $$sin$$ $$\left( {100\,\pi t} \right)$$ $$V,$$ the average voltage across $$R$$ (in Volt) under steady-state is ________.
4
GATE EE 2015 Set 2
Numerical
+2
-0
For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is $${T_s}.$$ If the voltage $${V_L}$$ is as shown, the duty cycle of the switch $$S$$ is __________.
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