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# Discrete Maths Test 4

This Test will cover complete Discrete Maths with very important questions, starting off from basics to advanced level.
Q. Choose the correct match codes.
 1. Periodic matrix A. A2=A 2. Involuntary matrix B. A2=I 3. Idempotent matrix C. Ak=0 4. Nilpotent matrix D. Ak+1=A
 A. 1-C, 2-B, 3-D, 4-A B. 1-C, 2-B, 3-A, 4-D C. 1-A, 2-B, 3-C, 4-D D. 1-D, 2-A, 3-C, 4-A
Q. If A and B are Hermitian matrix, then which of the following is true?
 i. A+B is Hermitian. ii. AB+BA is also Hermitian. iii. AB-BA is skew Hermitian.
 A. (i), (ii) only B. (i), (ii) and (iii) C. (ii) and (iii) only D. (i) and (iii) only
Q. Consider the matrix A = If An = zero matrix of order 3x3. Then the sum of the roots of `Xn - 6Xn - 1 + 11Xn - 2 - 6Xn - 3 = 0` is __________, such that `n` is minimum.
 A. 3 B. 7 C. 6 D. 8
Q. The rank of the matrix is __________.
 A. 0 B. n C. n-1 D. 1

Q. Consider the matrix A =
 A. Det(A)=36 , trace(A)=13 B. Det(A)=54 , trace(A)=12 C. Det(A)=60 , trace(A)=13 D. Det(A)=36 , trace(A)=12
Q. Choose the correct option for the given matrix A =
 A. The sum and product of all eigen values of the above matrix are 6 and 8. B. The sum and product of all eigen values of the above matrix are 8 and 6. C. The sum and product of all eigen values of the above matrix are 5 and 8. D. The sum and product of all eigen values of the above matrix are 8 and 5.
Q. The characteristic roots of the matrix A = will be __________.
 A. 1, 3, -7, 6 B. 1, -9, 4, 2 C. 6, 3, 2, -11 D. None of the above.
Q. If `"p"` be an eigen value of a non-singular matrix `B`, then which of the following is an eigen value of `(adj B)`?
 A. 1/p B. p*det(B) C. p/det⁡(B) D. det(B)/p
Q. If `"p"` is the eigen value of a `n x n` matrix `B`, then the eigen value of `Bxyz` is __________.
 A. pn B. 1/pn C. 1/pxyz D. pxyz

Q. The number of algebraic terms in the expansion of a determinant of order `6` will be __________.
 A. 20 B. 120 C. 720 D. 300
Q. If the determinant of the matrix B = is 8, then the determinant of transposed matrix i.e `|Bt|` will be equal to __________.
 A. 6 B. 9 C. 18 D. None of these
Q. The rank of a given matrix A = will be __________.
 A. 1 B. 0 C. 2 D. 3
Q. What it correct for the below system of linear equation:
```X - 2Y + 3Z = -2
-X + Y - 2Z = 3
2X - Y + 3Z = -7```
 A. No solution B. Unique solution C. Infinite solutions D. Finite solutions
Q. The modulus of eigen values of a unitary matrix is __________.
 A. 0 B. 1 C. 3 D. None of these
Q. The matrix `P` is the inverse of a matrix `Q`. If `I` denotes the identity matrix, which one of the following option is correct?
 A. PQ = I but QP ≠ I B. QP = I but PQ ≠ I C. PQ = I and QP = I D. PQ - QP = I