1
GATE ECE 2025
MCQ (More than One Correct Answer)
+2
-0

Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle $C$ in the complex plane is/are TRUE?

A
$\oint_C e^z d z=0$
B
$\oint_C z^n d z=0$, where $n$ is an even integer
C
$\oint_C \cos z d z \neq 0$
D
$\oint_C \sec z d z \neq 0$
2
GATE ECE 2025
Numerical
+2
-0
Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable $X$ denote the sum of the outcomes obtained. The expectation of $X$ is ___________ (rounded off to two decimal places).
Your input ____
3
GATE ECE 2025
Numerical
+2
-0

Consider the vectors

$$ a=\left[\begin{array}{l} 1 \\ 1 \end{array}\right], b=\left[\begin{array}{c} 0 \\ 3 \sqrt{2} \end{array}\right] $$

For real-valued scalar variable $x$, the value of

$$ \min _x\|a x-b\|_2 $$

is___________(rounded off to two decimal places).

$\|\cdot\|_2$ denotes the Euclidean norm, i.e., for $y=\left[\begin{array}{l}y_1 \\ y_2\end{array}\right],\|y\|_2=\sqrt{y_1^2+y_2^2}$.

Your input ____
4
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3 \Omega$ resistor are as indicated.

The voltage (in Volts) at node $X$ is __________ .

GATE ECE 2025 Network Theory - Network Theorems Question 1 English
A
$\frac{20}{3}$
B
$\frac{32}{3}$
C
$\frac{22}{3}$
D
$\frac{2}{3}$
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