GATE MA 2023 Paper 1 — page 20

Questions 58–60 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 20 of 22

Let

, where

is the permutation group on 8 elements. Suppose

is the product of

and

, where

is a 4-cycle and

is a 3-cycle in

. If

and

are disjoint cycles, then the number of elements in

which are conjugate to

is __________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be a

real matrix with

, where

and

is the

identity matrix. If

, then the trace of

is __________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be a

real matrix such that

is the degree of the minimal polynomial of

, then

equals __________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

2023 · Paper 1