1
GATE ECE 2003
MCQ (Single Correct Answer)
+1
-0.3
The Laplace transform of i(t) tends to
$$I\left( s \right)\,\, = \,{2 \over {s\left( {1 + s} \right)}}$$

As $$t \to \infty $$ , the value of i(t) tends to

A
0
B
1
C
2
D
2
GATE ECE 2003
MCQ (Single Correct Answer)
+1
-0.3
Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be
A
$$4\,{e^{j4\pi f}}$$
B
$$2\,{e^{ - j8\pi f}}$$ v
C
$$4\,{e^{ - j4\pi f}}$$
D
$$2\,{e^{j8\pi f}}$$
3
GATE ECE 2003
MCQ (Single Correct Answer)
+1
-0.3
A sequence $$x\left( n \right)$$ with the $$z$$-transform $$X\left( z \right)$$ $$ = {z^4} + {z^2} - 2z + 2 - 3{z^{ - 4}}$$ is applied as an input to a linear, time-invariant system with the impulse response $$h\left( n \right) = 2\delta \left( {n - 3} \right)$$
where $$\matrix{ {\delta \left( n \right) = 1,} & {n = 0} \cr {0,} & {otherwise} \cr } $$

The output at $$n = 4$$ is
A
-6
B
zero
C
2
D
-4
4
GATE ECE 2003
MCQ (Single Correct Answer)
+2
-0.6
Let P be linearity, Q be time-invariance, R be causality and S be stability.

A discrete time system has the input-output relationship,


$$y\left( n \right) = \left\{ {\matrix{ {x\left( n \right),} & {n \ge 1} \cr {0,} & {n = 0} \cr {x\left( {n + 1} \right),} & {n \le - 1} \cr } } \right.$$

Where $$x\left( n \right)\,$$ is the input and $$y\left( n \right)\,$$ is the output. The above system has the properties

A
P, S but not Q, R
B
P, Q, S but not R
C
P, Q, R, S
D
Q, R, S but not P
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