1
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 __________.
2
GATE ECE 2016 Set 3
+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) $$7.39$$
3
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 $$z=0$$ ________.
4
GATE ECE 2016 Set 3
+1
-0.3
In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be
A
4E and 0
B
4E and 1
C
4F and 0
D
4F and 1
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