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# Discrete Maths Test 2

This Test will cover complete Discrete Mathematics with very important questions, starting off from basics to advanced level.
Q. Let a matrix A = then the sum of elements of middle row of `A-1` will be __________.
 A. 0.5 B. -0.5 C. 0.4 D. -0.9
Q. Let a matrix A = , then A will be, __________.
 A. Involutory matrix. B. Idempotent matrix. C. Nilpotent matrix of class 3. D. Nilpotent matrix of class 4.
Q. Let A = and A-1 = then the product of `A` and `A-1` will be __________.
 A. 8 B. 9 C. -8 D. -9
Q. If a matrix A = is not invertible then the value of `"p"` will be __________.
 A. -12 B. 12 C. 4 D. -4

Q. The inverse of the matrix is __________.
 A. B. C. D.
Q. The matrix is a __________.
 A. Hermitian matrix. B. Skew-Hermitian matrix. C. Skew-symmetric matrix. D. Both b and c.
Q. Match the column I with column II and choose the correct option.
Column IColumn II
A. Orthogonal matrix1) determinant=0
B. Singular matrix2) determinant = always 1.
C. Real symmetric matrix3) Eigen values are always real.
D. Non-singular matrix4) Eigen values are not defined.
5) determinant is not defined.
 A. A→2, B→1, C→5, D→3 B. A→1, B→2, C→3, D→5 C. A→2, B→1, C→3, D→5 D. A→2, B→3, C→4, D→1
Q. The rank of matrix A = is __________.
 A. 1 B. 2 C. 3 D. None of the above
Q. The rank of the matrix is __________. Here `x` and `y` are integers and `x` lies between `1` and `10` and `y` lies between `-10` and `10`. Choose the most correct option.
 A. Rank depends upon the value of x and y. B. Rank will be Always 3. C. Rank will change on changing value of x and y. D. Rank will be Always 2.

Q. The following system of homogenous equation has non-trivial solution then value of `"p"` is __________.
``````
3x + 2y + pz = 0
4x - 2y + 6z = 0
5x + y = 0
``````
 A. 7 B. -7 C. 3 D. -3
Q. If the determinant of a matrix is equal to `12` and one of the eigen value is also equal to `12`. Then one eigen value of `adj(A)` will be equal to __________.
 A. 1 B. -1 C. 0 D. 2
Q. The sum of the eigen values of a given matrix A = is __________.
 A. 12 B. 10 C. 13 D. 15
Q. Which of the following statements is/are not correct?
 (i) Sum of eigen values of matrix A is equal to trace of matrix. (ii) Product of eigen values of matrix A is equal to determinant of matrix A (iii) For singular matrix, atleast one eigen value is equal to 0. (iv) Similar matrices have different eigen values.
 A. (iii) and (iv) only. B. Only (iv). C. (ii) and (iii) only. D. only (iii).
Q. For a given matrix A = One of the eigen value is `-5`. The other two eigen values are __________.
 A. 4, -1 B. 3, 2 C. 3, 3 D. 2, 5
Q. The eigen values of a matrix A = will be __________.
 A. Purely zeros. B. Purely imaginary. C. Purely real. D. None of the above.