Determinants Test

Determinants

This is Determinants Test-04 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 and B are invertible matrices of order 3 , then det (adj A) =
  • A
    \({(det\,A)^2}\)
  • B
    none of these
  • C
    \({A^{ - 1}}\).
    Correct
  • D
    1
2
If A is a square matrix of order 2 , then det (adj A) =
  • A
    \(2{A^2}\)
  • B
    \(\left| A \right|.\).
    Correct
  • C
    \({A^2} = O\)
  • D
    I
3
If A is a non singular matrix of order 3 , then \(\left| {adj({A^3})} \right|\) =
  • A
    \({\left| A \right|^6}\)
    Correct
  • B
    \({\left| A \right|^8}\)
  • C
    none of these
  • D
    \({\left| A \right|^9}\)
4
If \({I_3}\) is the identity matrix of order 3 , then \(I_3^{ - 1}\) is
  • A
    \({I_3}\)
    Correct
  • B
    none of these
  • C
    \(3{I_3}\)
  • D
    0
5
The roots of the equation \(\left| {\begin{array}{*{20}{c}} 1&4&{20} \\ 1&{ - 2}&5 \\ 1&{2x}&{5{x^2}} \end{array}} \right| = 0\) are
  • A
    –1 , 2
    Correct
  • B
    –1, – 2
  • C
    1 , 2
  • D
    1 , –2
6
The value of det A where A=\(\left[ {\begin{array}{*{20}{c}} 1&{\sin \theta }&1 \\ { - \sin \theta }&1&{\sin \theta } \\ { - 1}&{ - \sin \theta }&1 \end{array}} \right]\) lies in the interval
  • A
    (1,2)
  • B
    \(\left[ {1,2} \right]\;\)
    Correct
  • C
    none of these
  • D
    \(\left[ {0,2} \right]\)
7
\(\left| {\begin{array}{*{20}{c}} {{a_1}}&{{b_1}}&{{c_1}}&{{d_1}} \\ 0&{{a_2}}&{{b_2}}&{{c_2}} \\ 0&0&{{a_3}}&{{b_3}} \\ 0&0&0&{{a_4}} \end{array}} \right|\) is equal to
  • A
    none of these
  • B
    \({a_1} + {a_2} + {a_3} + {a_4}\)
  • C
    \({a_1}{a_2}{a_3}{a_4}\)
    Correct
  • D
    0
8
If A is a non singular matrix and A’ denotes the transpose of A , then
  • A
    \(\left| A \right| + \left| {A'} \right| \ne 0\)
    Correct
  • B
    \(\left| A \right| \ne \left| {A'} \right|\)
  • C
    none of these
  • D
    \(\left| {AA'} \right| \ne \left| {{A^2}} \right|\)
9
If A and B are square matrices of order 3 , such that Det.A = –1 , Det.B =3 then the determinant of 3AB is equal to
  • A
    81
  • B
    -81
    Correct
  • C
    –9
  • D
    –27
10
A square matrix A is called singular iff det. A is
  • A
    0
    Correct
  • B
    non–zero
  • C
    Negative
  • D
    Positive
11
For a singular matrix ,\(\left| A \right| = 0.\) The value of det. \(\left[ {\begin{array}{*{20}{c}} a&0&0&0 \\ 2&b&0&0 \\ 4&6&c&0 \\ 6&8&{10}&d \end{array}} \right]\) is
  • A
    none of these
  • B
    a +b +c +d
  • C
    0
  • D
    abcd
    Correct
12
The system AX = B of n equations in n unknowns has infinitely many solutions if
  • A
    det. \(A{\text{ }} \ne 0\)
  • B
    if det. \(A{\text{ }} = \;\;0{\text{ }},{\text{ }}\left( {{\text{ }}adj{\text{ }}A{\text{ }}} \right){\text{ }}B{\text{ }} \ne {\text{ }}O\)
  • C
    if det. A = 0 , ( adj A ) B =O
    Correct
  • D
    if det. \(A \ne \;0{\text{ }},{\text{ }}\left( {{\text{ }}adj{\text{ }}A{\text{ }}} \right){\text{ }}B{\text{ }} \ne {\text{ }}O\)
13
Let A be a skew – symmetric matrix of order n then
  • A
    none of these.
  • B
    \(\left| A \right|\) = 0 if n is odd
    Correct
  • C
    \(\left| A \right|\) = 0 if n is even
  • D
    \(\left| A \right|\) = 0 for all n \( \in \;\)N
14
For an invertible square matrix of order 3 with real entries \({A^{ - 1}} = \,{A^2}\) , then det. A =
  • A
    3
  • B
    none of these
  • C
    \(\frac{1}{3}\)
  • D
    1
    Correct
15
The value of the determinant of a skew symmetric matrix of even order is
  • A
    0
  • B
    Negative
  • C
    A non zero perfect square.
    Correct
  • D
    none of these