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

Which one of the following matrices has an inverse?

A

$$\begin{bmatrix} 1 & 4 & 8 \\ 0 & 4 & 2 \\ 0.5 & 2 & 4 \end{bmatrix}$$

B

$$\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 2 & 9 \end{bmatrix}$$

C

$$\begin{bmatrix} 1 & 4 & 8 \\ 0 & 4 & 2 \\ 1 & 2 & 4 \end{bmatrix}$$

D

$$\begin{bmatrix} 1 & 4 & 8 \\ 0 & 4 & 2 \\ 3 & 12 & 24 \end{bmatrix}$$

2
GATE EE 2024
MCQ (More than One Correct Answer)
+1
-0.33

Let $X$ be a discrete random variable that is uniformly distributed over the set {$-10, -9, \cdots, 0, \cdots, 9, 10$}. Which of the following random variables is/are uniformly distributed?

A

$X^2$

B

$X^3$

C

$(X - 5)^2$

D

$(X + 10)^2$

3
GATE EE 2024
MCQ (More than One Correct Answer)
+1
-0.33

Which of the following complex functions is/are analytic on the complex plane?

A

$f(z) = j\text{Re}(z)$

B

$f(z) = \text{Im}(z)$

C

$f(z) = e^{|z|}$

D

$f(z) = z^2 - z$

4
GATE EE 2024
Numerical
+1
-0.33

Consider the complex function $f(z) = \cos z + e^{z^2}$. The coefficient of $z^5$ in the Taylor series expansion of $f(z)$ about the origin is ______ (rounded off to 1 decimal place).

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