1
GATE EE 2024
MCQ (Single Correct Answer)
+2
-1.33

The input $x(t)$ and the output $y(t)$ of a system are related as

$$ y(t) = e^{-t} \int\limits_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad - \infty < t < \infty. $$

The system is

A

nonlinear.

B

linear and time-invariant.

C

linear but not time-invariant.

D

noncausal.

2
GATE EE 2024
MCQ (Single Correct Answer)
+2
-1.33

Consider the discrete-time systems $T_1$ and $T_2$ defined as follows:

{ $T_1 x[ n ] = x[ 0 ] + x[ 1 ] + \cdots + x[ n ] $}

{ $T_2 x[ n ] = x[ 0 ] + \frac{1}{2} x[ 1 ] + \cdots + \frac{1}{2^n} x[ n ] $}

Which one of the following statements is true?

A

$T_1$ and $T_2$ are BIBO stable.

B

$T_1$ and $T_2$ are not BIBO stable.

C

$T_1$ is BIBO stable but $T_2$ is not BIBO stable.

D

$T_1$ is not BIBO stable but $T_2$ is BIBO stable.

3
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

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
$$8{e^{ - 4t}}u(t)$$
4
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Consider the system as shown below:

GATE EE 2022 Signals and Systems - Linear Time Invariant Systems Question 6 English

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.
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