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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)| = X`^{6}

. Then the value of `X`

will be __________.Q. The maximum no. of different possible non-zero entries in a skew-symmetric matrix of order

`11`

is __________. Q. The value of the determinant is __________.

Q. The sum of minimum and maximum value of a determinant of second order whose elements are either

`0`

or `1`

is equal to __________.Q. If A = then the value of the determinant of

`[ A`^{2}+2A-3I ]

will be equal to __________.
Q. For a matrix A = one of the eigen value is

`+3`

then which of the following is an eigen vector?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

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 __________.Q. Let a matrix A = and it is given that

`|A| = 0`

then value of `abc`

can be __________.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. |

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 __________.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 __________.Q. Let a matrix A = has one eigen value, which is

`4`

. The sum of other two eigen values is __________.Q. One of the eigen vector of the matrix A = is __________.

Q. The eigen vectors of matrix A = are __________.

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