1
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+2
-0

Consider a Boolean expression given by $F(X, Y, Z) = \Sigma(3,5,6,7)$.

Which of the following statements is/are CORRECT?

A

$F(X, Y, Z) = \\Pi(0,1,2,4)$

B

$F(X, Y, Z) = XY + YZ + XZ$

C

$F(X, Y, Z)$ is independent of input $Y$

D

$F(X, Y, Z)$ is independent of input $X$

2
GATE CSE 2024 Set 1
Numerical
+2
-0

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively.

GATE CSE 2024 Set 1 Digital Logic - Combinational Circuits Question 1 English

For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is ______________

Your input ____
3
GATE CSE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x) = \max \{x, x^3\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers. The set of all points where $f(x)$ is NOT differentiable is

A

{-1, 1, 2}

B

{-2, -1, 1}

C

{0, 1}

D

{-1, 0, 1}

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

The product of all eigenvalues of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$ is

A

-1

B

0

C

1

D

2

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