Determinants Test

Determinants

This is Determinants Test-05 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If A is a square matrix such that \({A^2} = A\;,\)then , det.(A) = ………
  • A
    1or - 1
  • B
    2 or -2
  • C
    0 or 1
    Correct
  • D
    none of these
2
If A’ is the transpose of a square matrix A , then
  • A
    \(\left| A \right| = \left| {A'} \right|\)
    Correct
  • B
    \(\left| A \right| + \left| {A'} \right| = 0\)
  • C
    none of these
  • D
    \(\left| A \right| \ne \left| {A'} \right|\)
3
Let A and B be \(3{\text{ }} \times {\text{ }}3\) matrices , then AB =O implies
  • A
    A=O & B = O
  • B
    A =O or B = O
  • C
    \(\left| A \right| = 0\,\,\,\& \,\,\,\left| B \right| = O\)
  • D
    either \(\left| A \right| = 0\,\,\,\,or\,\,\,\,\left| B \right| = O\)
    Correct
4
If A and B are any \({\text{2 }} \times {\text{ 2}}\) matrices , then det. (A+B) = 0 implies
  • A
    detA + det B =0
  • B
    det A = 0 and det B = 0
  • C
    det A = 0 or det B = 0
  • D
    none of these
    Correct
5
If A and B are square matrices of same order and A’ denotes the transpose of A , then
  • A
    ( AB )’ = A’B’
  • B
    ( AB )’ = B’A’
    Correct
  • C
    AB = O \( \Rightarrow \) A = 0 or B = 0
  • D
    AB = O \( \Rightarrow \)\(\left| A \right| = 0\) and \(\left| B \right| = 0\)
6
In a third order determinant , each element of the first column consists of sum of two terms , each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms . Then it can be decomposed into n determinants , where n has value
  • A
    9
  • B
    16
  • C
    1
  • D
    24
    Correct
7
If each element of a \(3{\text{ }} \times {\text{ }}3\) matrix A is multiplied by 3 , then the determinant of the newly formed matrix is
  • A
    \({(\det \det A)^3}\)
  • B
    3 det A
  • C
    9 det A
  • D
    27 det . A
    Correct
8
If A is a non singular matrix of order 3 , then \(\left| {adj(adj A)} \right|\)
  • A
    \({\left| A \right|^6}\)
  • B
    none of these
  • C
    \({\left| A \right|^4}\)
    Correct
  • D
    \({\left| A \right|^3}\)
9
If the matrix AB = O , then
  • A
    none of these.
  • B
    A = O and B = O
  • C
    It is not necessary that either A = O or B = O
    Correct
  • D
    A = O or B = O
10
\(\left| {\begin{array}{*{20}{c}} 0&{a - b}&{a - c} \\ {b - a}&0&{b - c} \\ {c - a}&{c - b}&0 \end{array}} \right|\) =
  • A
    1
  • B
    0
    Correct
  • C
    none of these
  • D
    abc
11
If A is a square matrix such that \({A^3}\) = I , then \({A^{ - 1}}\) is equal to
  • A
    none of these.
  • B
    I
  • C
    A
  • D
    \({A^2}\)
    Correct
12
The system of equations AX = B of n equations in n unknowns has a unique solution if
  • A
    Det. \(A{\text{ }} \ne {\text{ }}0\)
    Correct
  • B
    none of these
  • C
    Det. \(A{\text{ }} \ne {\text{ }}0\) , ( adj. A ) B = O
  • D
    Det. A = 0 , ( adj. A ) B = O
13
The point (3, 2 ) is reflected in the y – axis and then moved a distance of 5 units towards the negative side of y – axis .The co – ordinates of the point thus obtained are
  • A
    (3,3)
  • B
    (–3,–3)
    Correct
  • C
    (–3,3)
  • D
    (3,–3)
14
If the value of a third order determinant is 11 , then the value of the square of the determinant formed by the cofactors will be
  • A
    121
  • B
    14641
    Correct
  • C
    1331
  • D
    11
15
The system of equationsx+2y =5 , 4x+8y =20 has
  • A
    none of these.
  • B
    no solution
  • C
    a unique solution
  • D
    infinitely many solutions
    Correct