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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 | |