1
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
A differential equation $${{dx} \over {dt}} = {e^{ - 2t}}\,\,u\left( t \right)\,\,$$ has to be solved using trapezoidal rule of integration with a step size $$h=0.01$$ sec. Function $$u(t)$$ indicates a unit step function. If $$x(0)=0$$ then the value of $$x$$ at $$t=0.01$$ sec will be given by
A
$$0.00099$$
B
$$0.00495$$
C
$$0.0099$$
D
$$0.0198$$
2
GATE EE 2008
MCQ (Single Correct Answer)
+1
-0.3
Equation $${e^x} - 1 = 0\,\,$$ is required to be solved using Newton's method with an initial guess $$\,\,{x_0} = - 1.\,\,$$ Then after one step of Newton's method estimate $${x_1}$$ of the solution will be given by
A
$$0.71828$$
B
$$0.36784$$
C
$$0.20587$$
D
$$0.0000$$
3
GATE EE 2008
MCQ (Single Correct Answer)
+1
-0.3
Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ will be
A
an - 1
B
an
C
nan
D
nan - 1
4
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
A three phase fully controlled bridge converter is feeding a load drawing a constant and ripple free load current of $$10$$ $$A$$ at a firing angle of $${30^ \circ }.$$ The approximate Total Harmonic Distortion $$(\% \,\,THD)$$ and $$r.m.s$$ value of fundamental component of the input current will respectively be
A
$$31\,\% $$ and $$6.8$$ $$A$$
B
$$31\,\% $$ $$7.8$$ $$A$$
C
$$66\,\% $$ $$6.8$$ $$A$$
D
$$66\,\% $$ $$7.8$$ $$A$$
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