< Discrete Mathematics Online Interview Questions | Test 3 | Studytonight
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# Discrete Mathematics Test 3

This Test will cover complete Discrete Maths with very important questions, starting off from basics to advanced level.
Q. Let `X` be a positive integer and matrix A = If `|adj (A)| = X6`. Then the value of `X` will be __________.
 A. 10 B. 100 C. 1000 D. 106
Q. The maximum no. of different possible non-zero entries in a skew-symmetric matrix of order `11` is __________.
 A. 11 B. 22 C. 110 D. 121
Q. The value of the determinant is __________.
 A. 8 B. 9 C. -8 D. -9
Q. The sum of minimum and maximum value of a determinant of second order whose elements are either `0` or `1` is equal to __________.
 A. 0 B. 1 C. -1 D. 2

Q. If A = then the value of the determinant of `[ A2+2A-3I ]` will be equal to __________.
 A. 112 B. -112 C. 400 D. -400
Q. For a matrix A = one of the eigen value is `+3` then which of the following is an eigen vector?
 A. B. C. D.
Q. For what values of `α` and `β`, the following simultaneous equations have an infinite no. of solutions?
```X + Y + Z = 5
X + 3Y + 3Z = 9
X + 2Y + αZ = β
```
 A. 2, 7 B. 3, 8 C. 8, 3 D. 7, 2
Q. For the homogenous system of linear equation, `AX = 0`, if the rank of matrix `A` is equal to no. of unknowns variable then it has __________.
 A. Many solutions B. No solutions C. Unique solutions D. Two solutions
Q. Let a matrix A = and it is given that `|A| = 0` then value of `abc` can be __________.
 A. 8 B. 9 C. 10 D. 11

Q. Which of the following option is correct?
 S1: Sum of the eigen values of a matrix = trace of a matrix. S2: For singular matrices, atleast one of the eigen value = 0. S3: The determinant of involutory matrix is either +1 or -1.
 A. S1 is true but S2 is false. B. S3 and S1 are true only. C. All statements are false. D. All statements are true.
Q. The trace of a matrix is `9` and the determinant of that matrix is `24`. Then the eigen values for that matrix will be __________.
 A. 2, 3 and 6 B. 3, 4 and 2 C. 8, 1 and 3 D. None of these
Q. A is a 4 x 5 real matrix and AX = B is an inconsistent system of equation. The highest possible rank of `A` will be __________.
 A. 4 B. 5 C. 3 D. 1
Q. Let a matrix A = has one eigen value, which is `4`. The sum of other two eigen values is __________.
 A. K + 2 B. K - 2 C. K - 4 D. K + 4
Q. One of the eigen vector of the matrix A = is __________.
 A. B. C. D.
Q. The eigen vectors of matrix A = are __________.
 A. B. C. D. None of the above