GATE CSE Engineering Mathematics PYQs & Answers — Page 3

Questions 21–30 of 55. Imported answers require independent review unless marked reviewed.

Let

be a set and

denote the powerset of

. Define a binary operation

as follows:

Let

. Which of the following statements about

is/are correct?

Your answerSelect all correct options. You can choose more than one.

is a group.

Every element in

has an inverse, but

is NOT a group.

For every

, the inverse of

is the complement of

For every

, the inverse of

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Consider a random experiment where two fair coins are tossed. Let

be the event that denotes HEAD on both the throws,

be the event that denotes HEAD on the first throw, and

be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

and

are independent.

and

are independent.

and

are independent.

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Let

be a simple, finite, undirected graph with vertex set

. Let

denote the maximum degree of

and let

denote the set of all possible colors. Color the vertices of

using the following greedy strategy: for

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

This procedure results in a proper vertex coloring of

The number of colors used is at most

The number of colors used is equal to the chromatic number of

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Consider the following two statements with respect to the matrices

and

Statement 1:

Statement 2:

where

represents the trace of a matrix. Which one of the following holds?

Your answerChoose one option.

Statement 1 is correct and Statement 2 is wrong.

Statement 1 is wrong and Statement 2 is correct.

Both Statement 1 and Statement 2 are correct.

Both Statement 1 and Statement 2 are wrong.

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Which of the following statements is/are TRUE for a group

Your answerSelect all correct options. You can choose more than one.

If for all

, then

is commutative.

If for all

, then

is commutative. Here, 1 is the identity element of

If the order of

is 2, then

is commutative.

is commutative, then a subgroup of

need not be commutative.

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The number of arrangements of six identical balls in three identical bins is _____.

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The value of the following limit is ____________.

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Which one of the following is the closed form for the generating function of the sequence

defined below?

Your answerChoose one option.

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Consider solving the following system of simultaneous equations using LU decomposition.

where

and

are denoted as

Which one of the following is the correct combination of values for

, and

Your answerChoose one option.

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The following simple undirected graph is referred to as the Peterson graph.

Diagram for Computer Science and Information Technology question 50

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The chromatic number of the graph is 3.

The graph has a Hamiltonian path.

The following graph is isomorphic to the Peterson graph.

Diagram for Computer Science and Information Technology question 50 (figure 2)

The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)

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GATE CSE Engineering Mathematics PYQs

Question 51

Question 53

Question 55

Question 20

Question 27

Question 32

Question 34

Question 36

Question 45

Question 50