Matrices Test

Matrices

This is Matrices 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
Two matrices A and B are multiplicative inverse of each other only if
  • A
    AB = BA
  • B
    AB = O, BA = I
  • C
    AB = BA = I
    Correct
  • D
    AB = BA = O
2
If A and B are square matrices of the same order, then\({(A + B)^2} = {A^2} + 2AB + {B^2}\) implies
  • A
    AB = BA
    Correct
  • B
    AB = O
  • C
    AB + BA = O
  • D
    none of these.
3
Let \(A = \left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 5&2&0 \\ { - 1}&6&1 \end{array}} \right]\), then adj (A) is
  • A
    \(\left[ {\begin{array}{*{20}{c}} 2&0&0 \\ { - 25}&2&0 \\ { - 32}&{36}&1 \end{array}} \right]\)
  • B
    \(\left[ {\begin{array}{*{20}{c}} 2&{ - 25}&{ - 32} \\ 0&2&{ - 36} \\ 0&0&1 \end{array}} \right]\)
  • C
    \(\left[ {\begin{array}{*{20}{c}} 2&{ - 5}&{32} \\ 0&1&6 \\ 0&0&2 \end{array}} \right]\)
  • D
    \(\left[ {\begin{array}{*{20}{c}} 2&0&0 \\ { - 5}&1&0 \\ {32}&{ - 6}&2 \end{array}} \right]\)
    Correct
4
The transformation ‘orthogonal projection on X-axis’ is given by the matrix
  • A
    \(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&0 \end{array}} \right]\)
    Correct
  • B
    \(\left[ {\begin{array}{*{20}{c}} 0&0 \\ 0&1 \end{array}} \right]\)
  • C
    \(\left[ {\begin{array}{*{20}{c}} 0&1 \\ 0&0 \end{array}} \right]\)
  • D
    \(\left[ {\begin{array}{*{20}{c}} 0&0 \\ 1&0 \end{array}} \right]\)
5
The equations, x + 4 y – 2 z = 3, 3 x + y + 5 z = 7, 2 x + 3y +z = 5 have
  • A
    infinitely many solutions
  • B
    no solution
    Correct
  • C
    none of these
  • D
    a unique solution
6
Let a, b, c, d, u, v be integers. If the system of equations, a x + b y = u, c x + dy = v, has a unique solution in integers, then
  • A
    ad – bc = - 1
  • B
    ad - bc need not be equal to \( \pm 1\).
    Correct
  • C
    ad – bc = 1
  • D
    ad – bc = \( \pm 1\)
7
The system of equations, x + y + z = 6, x + 2 y + 3 z = 14, x + 3 y + 5z = 20 has
  • A
    only finitely many solutions
  • B
    no solution.
    Correct
  • C
    infinitely many solutions
  • D
    a unique solution
8
If \({I_n}\) is the identity matrix of order n, the \({({I_n})^{ - 1}}\)
  • A
    =\({I_n}\)
    Correct
  • B
    = O
  • C
    \(n = {I_n}\)
  • D
    does not exist
9
If A and B are square matrices of the same order and AB = 3 I, then \({A^{ - 1}}\) is equal to
  • A
    3 B
  • B
    \(\frac{1}{3}B\)
  • C
    \(3{B^{ - 1}}\)
  • D
    none of these.
Answer
Not Available
10
If \(A = \left[ {\begin{array}{*{20}{c}} 1&1&3 \\ 5&2&6 \\ { - 2}&{ - 1}&{ - 3} \end{array}} \right]\). Then A is
  • A
    Nilpotent
    Correct
  • B
    Idempotent
  • C
    none of these.
  • D
    Symmetric
11
Let for any matrix M ,\({M^{ - 1}}\;exist. \) Which of the following is not true.
  • A
    \({\left( {{\text{ }}{M^{ - 1}}} \right)^{ - 1\;}} = {\left( {{M^{ - 1}}} \right)^1}\)
    Correct
  • B
    none of these
  • C
    \({\left( {{\text{ }}{M^{ - 1}}} \right)^{ - 1\;}} = ({M^)}\)
  • D
    \({\left( {{\text{ }}{M^{ - 1}}} \right)^{2\;}} = {\left( {{M^2}} \right)^{ - 1}}\)
12
The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y - kz = 4 has a unique solution if ,
  • A
    k = 0
  • B
    \( - {\text{ }}2{\text{ }} < {\text{ }}k{\text{ }} < {\text{ }}2\)
  • C
    \(k \ne 0\)
    Correct
  • D
    \( - {\text{ 1 }} < {\text{ }}k{\text{ }} < {\text{ 1}}\)
13
If\(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]\), then \({A^4}\) =
  • A
    \(\left[ {\begin{array}{*{20}{c}} 1&1 \\ 0&0 \end{array}} \right]\)
  • B
    \(\left[ {\begin{array}{*{20}{c}} 0&0 \\ 1&1 \end{array}} \right]\)
  • C
    \(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]\)
    Correct
  • D
    \(\left[ {\begin{array}{*{20}{c}} 0&1 \\ 1&0 \end{array}} \right]\)
14
The system of equations x + 2y = 11,-2 x – 4y = 22 has
  • A
    only one solution
  • B
    finitely many solution
  • C
    no solution
    Correct
  • D
    infinitely many solutions.
15
The equations2x + 3y = 7, 14 x + 21 y = 49 has
  • A
    a unique solution
  • B
    no solution
  • C
    infinitely many solutions
    Correct
  • D
    finitely many solutions.