Matrices Test

Matrices

This is Matrices 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
For what value of \(\lambda \) the following system of equations does not have a solution ?x + y + z = 6, 4x + \(\lambda \)y - \(\lambda \)z = 0, 3 x + 2y – 4 z = - 5
  • A
    1.
  • B
    0
  • C
    3
    Correct
  • D
    -3
2
The value of\(\lambda \), for which system of equations. x + y + z = 1, x + 2y + 2z = 3, x + 2y + \(\lambda \)z = 4, have no solution is
  • A
    1
  • B
    3.
  • C
    0
  • D
    2
    Correct
3
The system of equations,x + y = 2 and 2x + 2y = 3 has
  • A
    no solution
    Correct
  • B
    finitely many solutions
  • C
    a unique solution
  • D
    infinitely many solutions
4
The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have
  • A
    no solution
    Correct
  • B
    infinitely many solutions.
  • C
    only two solutions
  • D
    only one solution
5
If the system of equationsx + 4 ay + az = 0, x + 3by + bz = 0 andx + 2 cy +cz = 0 have a non-zero solution,then a, b, c are in
  • A
    A.P.
  • B
    none of these
  • C
    H.P.
    Correct
  • D
    G.P.
6
The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, \(\alpha \)x + 2 y + 3z = 1 has a unique solution for
  • A
    all rational \(\alpha \)
  • B
    \(\alpha \)not equal to 0
  • C
    all integral \(\alpha \)
    Correct
  • D
    all real \(\alpha \)
7
If \(\left[ {\begin{array}{*{20}{c}} 0&0&0 \\ 1&0&0 \\ 0&1&0 \end{array}} \right]\)
  • A
    \({A^3} = O\)
    Correct
  • B
    \({A^2} = A\)
  • C
    \({A^2} = I\)
  • D
    \({A^2} = O\)
8
The matrix of the transformation ‘reflection in the line x + y = 0 ‘ is
  • A
    \(\left[ {\begin{array}{*{20}{c}} 0&{ - 1} \\ { - 1}&0 \end{array}} \right]\)
    Correct
  • B
    \(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]\)
  • C
    \(\left[ {\begin{array}{*{20}{c}} { - 1}&0 \\ 0&{ - 1} \end{array}} \right]\)
  • D
    \(\left[ {\begin{array}{*{20}{c}} 0&1 \\ 1&0 \end{array}} \right]\)
9
If A = [x y z], \(B = \left[ {\begin{array}{*{20}{c}} a&h&g \\ h&b&f \\ g&f&c \end{array}} \right]\)and \(C = {[xyz]^t}\), then ABC is
  • A
    not defined
  • B
    \(1 \times 1\) matrix
    Correct
  • C
    none of these.
  • D
    \(3 \times 3\) matrix
10
Rank of a non-zero matrix is always
  • A
    greater than 1
  • B
    equal to 1
  • C
    \( \geqslant 1\).
    Correct
  • D
    0
11
The value of k for which the system of equations, x + k y + 3 z = 0, 3 x + k y – 2 z = 0, 2 x + 3 y – 4 z = 0, have a non-trival solution is
  • A
    \(\frac{2}{{33}}\)
  • B
    \(\frac{{33}}{2}\)
    Correct
  • C
    none of these
  • D
    33
12
If \(A = \left[ {\begin{array}{*{20}{c}} 1&2&{ - 1} \\ { - 1}&1&2 \\ 2&{ - 1}&1 \end{array}} \right]\)thendet.(adj (adj A)) =
  • A
    \({14^2}\)
  • B
    \({14^3}\)
  • C
    \({14^4}\)
    Correct
  • D
    13
13
The system of equations, 3 x + y – z = 0, 5 x + 2y – 3z = 2, 15 x + 6 y – 9 z = 5 has
  • A
    a unique solution
  • B
    two distinct solutions
  • C
    infinitely many solutions.
  • D
    no solution
    Correct
14
The number of solutions of 2x + y = 4, x – 2y = 2, 3 x + 5y = 6 is
  • A
    none
  • B
    One
    Correct
  • C
    Two
  • D
    infinitely many
15
The system of equations, x + 2y = 5 ,4x + 8y = 20 has
  • A
    a unique solution
  • B
    no solution
  • C
    infinitely many solutions
    Correct
  • D
    none of these.