Explore topic-wise MCQs in Discrete Mathematics.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

Suppose (2, 5, 8, 4) and (3, 6) are the two permutation groups that form cycles. What type of permutation is this?

A. odd
B. even
C. acyclic
D. prime
Answer» C. acyclic
2.

Let M be an 4×4 matrix with real entries such that Mk=0, for some k≥1. Find the determinant value of (I+M), where, I be the 4 x 4 identity matrix.

A. 72
B. 1
C. 4
D. 36
Answer» C. 4
3.

If 54th row of a 67th row matrix is linearly independent with each other then find the rank of the matrix.

A. 61
B. 54
C. 187
D. 32
Answer» C. 187
4.

If Y98 (a raised to the power of 5) = 0 and Y is a 97-square matrix. Determine the value of Y97.

A. I+Y
B. -Y+3
C. 0
D. Y2
Answer» D. Y2
5.

Suppose, M is a lower triangular matrix with all diagonal entries zero. The resultant matrix of M+I will be ___________

A. idempotent
B. singular
C. nilpotent
D. inverse
Answer» C. nilpotent
6.

Let X be a n-square matrix such that Y = X + 8I. Which of the following property will exist?

A. idempotent
B. Y transpose is nilpotent
C. X nilpotent
D. Y inverse
Answer» C. X nilpotent
7.

Let (z, *) is a group with x*y=x+y-2 then inverse of x is ___________

A. -(x+4)
B. (x2+6)
C. (x+y)/5
D. (3y+4x2)
Answer» B. (x2+6)
8.

The dihedral group having order 6 can have degree _____________

A. 3
B. 26
C. 326
D. 208
Answer» B. 26
9.

Suppose Km={P∈Sm|, |P| is odd prime}. Determine the set for which m≥3 Km a subgroup of Sm.

A. {3, 5, 7, 11, 13, …}
B. {-14, -8, -3, 0, 3, 8, 14}
C. {2, 4, 6, 8, 10, 12}
D. {12, 25, 56, 78, 134,…}
Answer» B. {-14, -8, -3, 0, 3, 8, 14}
10.

Consider an integer 23 such that 23 >= 3p for a 2p-cycle in a permutation group, then p is ___________

A. odd prime
B. even prime
C. rational number
D. negative prime
Answer» B. even prime