1
GATE CSE 2024 Set 2
Numerical
+1
-0.33

Let $P$ be the partial order defined on the set {1,2,3,4} as follows:

$P = \{(x, x) \mid x \in \{1,2,3,4\}\} \cup \{(1,2), (3,2), (3,4)\}$

The number of total orders on {1,2,3,4} that contain $P$ is _________.

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2
GATE CSE 2024 Set 2
MCQ (Single Correct Answer)
+2
-0.66

Let $ x $ and $ y $ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $ z = xy $ and let the mean values of $ x, y, z $ be $ \bar{x} , \bar{y} , \bar{z} $, respectively. Which one of the following statements is TRUE?

A

$ \bar{z} = \bar{x} \bar{y} $

B

$ \bar{z} \leq \bar{x} \bar{y} $

C

$ \bar{z} \geq \bar{x} \bar{y} $

D

$ \bar{z} \leq \bar{x} $

3
GATE CSE 2024 Set 2
MCQ (More than One Correct Answer)
+2
-0.66

Let A be an n × n matrix over the set of all real numbers ℝ. Let B be a matrix obtained from A by swapping two rows. Which of the following statements is/are TRUE?

A

The determinant of B is the negative of the determinant of A

B

If A is invertible, then B is also invertible

C

If A is symmetric, then B is also symmetric

D

If the trace of A is zero, then the trace of B is also zero

4
GATE CSE 2024 Set 2
Numerical
+2
-0.66

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is ________

GATE CSE 2024 Set 2 Discrete Mathematics - Graph Theory Question 1 English

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