1
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}} + 36y = 0\,\,$$ with $$\,y\left( 0 \right) = 3\,\,$$ and $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 0}} = - 36\,\,$$
A
$$\left( {3 - 18x} \right){e^{ - 6x}}$$
B
$$\left( {3 + 25x} \right){e^{ - 6x}}$$
C
$$\left( {3 + 20x} \right){e^{ - 6x}}$$
D
$$\left( {3 - 12x} \right){e^{ - 6x}}$$
2
GATE ECE 2016 Set 3
Numerical
+2
-0
Consider the first order initial value problem $$\,y' = y + 2x - {x^2},\,\,y\left( 0 \right) = 1,\,\left( {0 \le x < \infty } \right)$$ With exact solution $$y\left( x \right)\,\, = \,\,{x^2} + {e^x}.\,\,$$ For $$x=0.1,$$ the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size $$h=0.1$$ is __________.
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3
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $${1 \over {2\pi j}}\oint\limits_C {{{{e^z}} \over {z - 2}}dz} $$ along a closed contour $$c$$ in anti-clockwise direction for
(i) the point $${z_0} = 2$$ inside the contour $$c,$$ and
(ii) the point $${z_0} = 2$$ outside the contour $$c,$$ respectively, are
A
(i) $$2.72,$$ (ii) $$0$$
B
(i) $$7.39,$$ (ii) $$0$$
C
(i) $$0,$$ (ii) $$2.72$$
D
(i) $$0,$$ (ii) $$7.39$$
4
GATE ECE 2016 Set 3
Numerical
+1
-0
For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.
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