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)
+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
3
GATE ECE 2003
MCQ (Single Correct Answer)
+2
-0.6
Let x(t) = $$\,2\cos (800\pi t) + \cos (1400\pi t)$$. x(t) is sampled with the rectangular pulse train shown in figure. The only spectral components (in KHz) present in the sampled signal in the frequency range 2.5 kHz to 3.5 kHz are GATE ECE 2003 Signals and Systems - Sampling Question 12 English
A
2.7, 3.4
B
3.3, 3.6
C
2.6, 2.7, 3.3, 3.4
D
2.7, 3.3
4
GATE ECE 2003
MCQ (Single Correct Answer)
+2
-0.6
The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0 $$k\Omega $$ and C = 1.0 $$\mu F$$.

Let H(t) denote the frequency response of the RC-LPF. Let $${f_1}$$ be the highest frequency such that $$0 \le \left| f \right| \le {f_1},{{\left| {H({f_1})} \right|} \over {H(0)}} \ge 0.95$$. Then $${f_1}$$ (in Hz) is

A
327.8
B
163.9
C
52.2
D
104.4
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