1
GATE EE 2025
MCQ (Single Correct Answer)
+2
-0.67

Let continuous-time signals $x_1(t)$ and $x_2(t)$ be

$x_1(t)=\left\{\begin{array}{cc}1, & t \in[0,1] \\ 2-t, & t \in[1,2] \\ 0, & \text { otherwise }\end{array}\right.$

and $x_2(t)=\left\{\begin{array}{cc}t, & t \in[0,1] \\ 2-t, & t \in[1,2] \\ 0, & \text { otherwise }\end{array}\right.$.

Consider the convolution

$y(t)=x_1(t) * x_2(t)$. Then $\int\limits_{-\infty}^{\infty} y(t) d t$ is :

A
1.5
B
2.5
C
3.5
D
4
2
GATE EE 2025
MCQ (Single Correct Answer)
+2
-0.67
The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system $S$. The output is observed to be the continuous-time unit step signal $u(t)$. Which one of the following statements is true?
A
Every bounded input signal applied to $S$ results in a bounded output signal.
B
It is possible to find a bounded input signal which when applied to $S$ results in an unbounded output signal.
C
On applying any input signal to $S$, the output signal is always bounded.
D
On applying any input signal to $S$ the output signal is always unbounded.
3
GATE EE 2025
Numerical
+2
-0
An ideal low pass filter has frequency response given by $$ H(j \omega)= \begin{cases}1, & |\omega| \leq 200 \pi \\ 0, & \text { otherwise }\end{cases} $$ Let $h(t)$ be its time domain representation. Then $h(0)=$ ____________ (round off to the nearest integer)
Your input ____
4
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

Kavya__________go to work yesterday as she________ feeling well. Select the most approrpriate option to complete the above sentence.

A
didn't; isn't
B
wouldn't; wasn't
C
wasn't; wasn't
D
couldn't; wasn't
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