1
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
The input x(t) and output y(t) of a system are related as $$\int_{-\infty}^tx\left(\tau\right)\cos\left(3\tau\right)d\tau$$.The system is
A
time-invariant and stable
B
stable and not time-invariant
C
time-invariant and not stable
D
not time-invariant and not stable
2
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
L et y[n] denote the convolution of h[n] and g[n], where $$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$ and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals
A
0
B
1/2
C
1
D
3/2
3
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
The Fourier transform of a signal h(t) is $$H\left(j\omega\right)=\left(2\cos\omega\right)\left(\sin2\omega\right)/\omega$$. The value of h(0) is
A
1/4
B
1/2
C
1
D
2
4
GATE EE 2012
MCQ (Single Correct Answer)
+1
-0.3
The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is
A
$$-\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
B
$$-\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
C
$$\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
D
$$\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
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