1
GATE EE 2016 Set 2
Numerical
+2
-0
Let $$y(x)$$ be the solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y = 0\,\,$$ with initial conditions $$y(0)=0$$ and $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 0}} = 1.\,\,$$ Then the value of $$y(1)$$ is __________.
2
GATE EE 2016 Set 2
+1
-0.3
Consider the function $$f\left( z \right) = z + {z^ * }$$ where $$z$$ is a complex variable and $${z^ * }$$ denotes its complex conjugate. Which one of the following is TRUE?
A
$$f(z)$$ is both continuous and analytic
B
$$f(z)$$ is continuous but not analytic
C
$$f(z)$$ is not continuous but is analytic
D
$$f(z)$$ is neither continuous nor analytic
3
GATE EE 2016 Set 2
+1
-0.3
The solution of the differential equation, for
$$t > 0,\,\,y''\left( t \right) + 2y'\left( t \right) + y\left( t \right) = 0$$ with initial conditions $$y\left( 0 \right) = 0$$ and $$y'\left( 0 \right) = 1,$$ is $$\left[ {u\left( t \right)} \right.$$ denotes the unit step function$$\left. \, \right]$$,
A
$$t{e^{ - t}}\,u\left( t \right)$$
B
$$\left( {{e^{ - t}} - t{e^{ - t}}} \right)u\left( t \right)$$
C
$$\left( { - {e^{ - t}} + t{e^{ - t}}} \right)u\left( t \right)$$
D
$${e^{ - t}}u\left( t \right)$$
4
GATE EE 2016 Set 2
Numerical
+2
-0
A full-bridge converter supplying an RLE load is shown in figure. The firing angle of the bridge converter is 120º. The supply voltage $${v_m}\left( t \right) = 200\pi \sin \left( {100\pi t} \right)\,V,$$$$$R = 20 Ω, E = 800 V$$$The inductor L is large enough to make the output current IL a smooth dc current. Switches are lossless. The real power fed back to the source, in kW, is __________.
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