1
GATE EE 2022
+1
-0.33

Let a causal LTI system be governed by the following differential equation $$y(t) + {1 \over 4}{{dy} \over {dt}} = 2x(t)$$, where x(t) and y(t) are the input and output respectively. Its impulse response is

A
$$2{e^{ - {1 \over 4}t}}u(t)$$
B
$$2{e^{ - 4t}}u(t)$$
C
$$8{e^{ - {1 \over 4}t}}u(t)$$
D
$$8{e^{ - 4t}}u(t)$$
2
GATE EE 2022
+1
-0.33

Consider the system as shown below:

where y(t) = x(et). The system is

A
linear and causal.
B
linear and non-causal.
C
non-linear and causal.
D
non-linear and non-causal.
3
GATE EE 2016 Set 1
+1
-0.3
Consider a continuous-time system with input x(t) and output y(t) given by $$y\left(t\right)=x\left(t\right)\cos\left(t\right)$$. This system is
A
linear and time-invariant
B
Non-linear and time-invariant
C
linear and time-varying
D
Non-linear and time-varying
4
GATE EE 2015 Set 1
+1
-0.3
The impulse response g(t) of a system G, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of G as shown in Figure (b)?
A
$$\frac23$$
B
$$\frac34$$
C
$$\frac45$$
D
1
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