Determinants Test

Determinants

This is Determinants Test-01 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Let a =\(\begin{gathered} \left[ {\begin{array}{*{20}{c}} 1&{a(b + c)}&{bc} \\ 1&{b(c + a)}&{ca} \\ 1&{c(a + b)}&{ab} \end{array}} \right] \\ \\\\\\ \end{gathered} \) , then Det. A is
  • A
    none of these
  • B
    ab +bc+ca
  • C
    0
    Correct
  • D
    1+ab+bc+ca
2
\(\left| {\begin{array}{*{20}{c}} 1&1&1 \\ e&0&{\sqrt 2 } \\ 2&2&2 \end{array}} \right| = \)is equal to
  • A
    2
  • B
    0
    Correct
  • C
    3e
  • D
    none of these
3
If A B be two square matrices such that AB=O, then
  • A
    Det.=A =0
  • B
    BA
  • C
    Det.B=0
  • D
    Det. A=0 or Det. B =0
    Correct
4
A square matrix A is invertible iff det A is equal to
  • A
    non zero
    Correct
  • B
    0
  • C
    –1
  • D
    1
5
If A and B are square matrices of order 3 , then
  • A
    \(\left| B \right| = 0\)\({\text{AB }} = {\text{ O}}\; \Rightarrow \left| A \right| = 0\)
    Correct
  • B
    none of these
  • C
    \({\text{AB }} = {\text{ O}}\;\, \Rightarrow \left| A \right| = 0\) and \(\left| B \right| = 0\)
  • D
    adj(AB) = adj A adj B
6
The value of the determinant \(\left| {\begin{array}{*{20}{c}} 1&x&{{x^3}} \\ 1&y&{{y^3}} \\ 1&z&{{z^3}} \end{array}} \right|\) is
  • A
    (x–y)(y–z)(z–x)(x+y+z)
    Correct
  • B
    none of these
  • C
    2(x–y)(y–z)(z–x)
  • D
    (x–y)(y–z)(z–x)
7
One root of the equation \(\left| {\begin{array}{*{20}{c}} {3x - 8}&3&3 \\ 3&{3x - 8}&3 \\ 3&3&{3x - 8} \end{array}} \right|\) =0 is
  • A
    5/3
  • B
    \(8\)
  • C
    \(\frac{1}{3}\)
  • D
    \(\frac{2}{3}\)
    Correct
8
\(\begin{gathered} A = \left| {\begin{array}{*{20}{c}} {\frac{1}{a}}&{{a^2}}&{bc} \\ {\frac{1}{b}}&{{b^2}}&{ac} \\ {\frac{1}{c}}&{{c^2}}&{ab} \end{array}} \right| \\ \\ \end{gathered} \)is equal to
  • A
    –1
  • B
    0
    Correct
  • C
    1
  • D
    none of these.
9
If A ,B andC be the three square matrices such that A = B + C , then Det A is equal to
  • A
    det B
  • B
    none of these
    Correct
  • C
    det B + detC
  • D
    det C
10
If 1 , \(\omega ,\,{\omega ^2}\) are cube roots of unity , then \(\left| {\begin{array}{*{20}{c}} 1&{{\omega ^n}}&{{\omega ^{2n}}} \\ {{\omega ^{2n}}}&1&{{\omega ^n}} \\ {{\omega ^n}}&{{\omega ^{2n}}}&1 \end{array}} \right|\) has value
  • A
    none of these.
  • B
    –1
  • C
    1
  • D
    0
    Correct
11
If \(\omega \)is non real cube root of unity , then\(\left| {\begin{array}{*{20}{c}} 2&{2\omega }&{ - {\omega ^2}} \\ 1&1&1 \\ 1&{ - 1}&0 \end{array}} \right|\) is equal to
  • A
    0
    Correct
  • B
    –1
  • C
    none of these
  • D
    1
12
\(\left| {\begin{array}{*{20}{c}} {1 + a}&b&c \\ a&{1 + b}&c \\\ a&b&{1 + c} \end{array}} \right|\) =
  • A
    none of these.
  • B
    abc
  • C
    a+b+c
  • D
    1+a+b+c
    Correct
13
The determinant \(\left| {\begin{array}{*{20}{c}} a&{bc}&{a(b + c)} \\ b&{ac}&{b(c + a)} \\ c&{ab}&{c(a + b)} \end{array}} \right|\) =
  • A
    (ab + bc + ca ) (a–b) (b–c) (c–a)
    Correct
  • B
    none of these
  • C
    abc( ab+bc +ca )
  • D
    abc (a–b) (b–c) (c–a)
14
The value of the determinant \(\left| {\begin{array}{*{20}{c}} 1&0&0 \\ 2&{\cos x}&{\sin x} \\ 3&{\sin x}&{\cos x} \end{array}} \right|\) is
  • A
    sin2x
  • B
    0
  • C
    1.
  • D
    cos2x
    Correct
15
If A = \(\left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 2&{\cos x}&{\sin x} \\ 3&{\sin x}&{ - \cos x} \end{array}} \right]\) then det. A is equal to
  • A
    cos2x
  • B
    –1
    Correct
  • C
    1
  • D
    sin2x