1
GATE EE 2024
MCQ (More than One Correct Answer)
+2
-1.33

Consider the function $f(t) = (\text{max}(0,t))^2$ for $- \infty < t < \infty$, where $\text{max}(a,b)$ denotes the maximum of $a$ and $b$. Which of the following statements is/are true?

A

$f(t)$ is not differentiable.

B

$f(t)$ is differentiable and its derivative is continuous.

C

$f(t)$ is differentiable but its derivative is not continuous.

D

$f(t)$ and its derivative are differentiable.

2
GATE EE 2024
MCQ (More than One Correct Answer)
+2
-1.33

Which of the following differential equations is/are nonlinear?

A

$t \, x(t) + \frac{dx(t)}{dt} = t^2 e^t$, $x(0) = 0$

B

$\frac{1}{2} e^t + x(t) \frac{dx(t)}{dt} = 0$, $x(0) = 0$

C

$x(t) \cos t - \frac{dx(t)}{dt} \sin t = 1$, $x(0) = 0$

D

$x(t) + e^{\left(\frac{dx(t)}{dt}\right)} = 1$, $x(0) = 0$

3
GATE EE 2024
MCQ (Single Correct Answer)
+1
-0.33

If the following switching devices have similar power ratings, which one of them is the fastest?

A

SCR

B

GTO

C

IGBT

D

Power MOSFET

4
GATE EE 2024
MCQ (Single Correct Answer)
+1
-0.33

A single-phase triac based AC voltage controller feeds a series RL load. The input AC supply is 230 V, 50 Hz. The values of R and L are 10 Ω and 18.37 mH, respectively. The minimum triggering angle of the triac to obtain controllable output voltage is

A

15°

B

30°

C

45°

D

60°

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