1
GATE ECE 2015 Set 3
Numerical
+2
-0
Consider the differential equation $${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x\left( t \right) = 0$$
Given $$x(0) = 20$$ & $$\,x\left( 1 \right) = {{10} \over e},$$ where $$e=2.718,$$

The value of $$x(2)$$ is

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2
GATE ECE 2015 Set 3
Numerical
+1
-0
The Newton-Raphson method is used to solve the equation $$f\left( x \right) = {x^3} - 5{x^2} + 6x - 8 = 0.$$ Taking the initial guess as $$x=5$$, the solution obtained at the end of the first iteration is ________.
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3
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If $$C$$ is a circle of radius $$r$$ with centre $${z_0}$$ in the complex $$z$$-plane and if $$'n'$$ is a non-zero integer, then $$\oint\limits_c {{{dz} \over {{{\left( {z - {z_0}} \right)}^{n + 1}}}}} $$ equals
A
$$2\pi nj$$
B
$$0$$
C
$${{nj} \over {2\pi }}$$
D
$$2\pi n$$
4
GATE ECE 2015 Set 3
Numerical
+1
-0
Consider the function $$g\left( t \right) = {e^{ - t}}\,\sin \left( {2\pi t} \right)u\left( t \right)$$ ,where $$u(t)$$ is the unit step function. The area under $$g(t)$$ is _______________.
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