1
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The general solution of the differential equation $$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$ is
A
$$\,\,\tan \,y - \cot \,x = C\,\,$$
B
$$\tan \,x - \cot \,y = C\,$$
C
$$\,\,\tan \,y + \cot \,x = C\,\,$$
D
$$\tan \,x + \cot \,y = C\,$$
2
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the differential equation $$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$ with initial condition $$x(0)=1.$$ The response $$x(t)$$ for $$t > 0$$ is
A
$$2 - {e^{ - 0.2t}}$$
B
$$2 - {e^{ 0.2t}}$$
C
$$50 - 49\,{e^{ - 0.2t}}$$
D
$$50 - 49\,{e^{ 0.2t}}$$
3
GATE ECE 2015 Set 2
Numerical
+2
-0
Let $$f\left( z \right) = {{az + b} \over {cz + d}}.$$ If $$f\left( {{z_1}} \right) = f\left( {{z_2}} \right)$$ for all $${z_1} \ne {z_2}.\,\,a = 2,\,\,b = 4$$ and $$C=5,$$ then $$d$$ should be equal to
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4
GATE ECE 2015 Set 2
Numerical
+2
-0
If $$C$$ denotes the counter clockwise unit circle. The value of the contour integral $${1 \over {2\pi i}}\oint\limits_c {{\mathop{\rm Re}\nolimits} \left\{ z \right\}dz} $$ is __________.
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