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12th Standard Maths Application of Matrices and Determinants English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. If |adj(adj A)| = |A|9, then the order of the square matrix A is

    (a)

    3

    (b)

    4

    (c)

    2

    (d)

    5

  2. If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A = 

    (a)

    A-1

    (b)

    \(\frac { { A }^{ -1 } }{ 2 } \)

    (c)

    3A-1

    (d)

    2A-1

  3. If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

    (a)

    15

    (b)

    12

    (c)

    14

    (d)

    11

  4. If A, B and C are invertible matrices of some order, then which one of the following is not true?

    (a)

    adj A = |A|A-1

    (b)

    adj(AB) = (adj A)(adj B)

    (c)

    det A-1 = (det A)-1

    (d)

    (ABC)-1 = C-1B-1A-1

  5. If adj A = \(\left[ \begin{matrix} 2 & 3 \\ 4 & -1 \end{matrix} \right] \) and adj B = \(\left[ \begin{matrix} 1 & -2 \\ -3 & 1 \end{matrix} \right] \) then adj (AB) is

    (a)

    \(\left[ \begin{matrix} -7 & -1 \\ 7 & -9 \end{matrix} \right] \)

    (b)

    \(\left[ \begin{matrix} -6 & 5 \\ -2 & -10 \end{matrix} \right] \)

    (c)

    \(\left[ \begin{matrix} -7 & 7 \\ -1 & -9 \end{matrix} \right] \)

    (d)

    \(\left[ \begin{matrix} -6 & -2 \\ 5 & -10 \end{matrix} \right] \)

  6. The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

    (a)

    λ = 8

    (b)

    λ = 8, μ ≠ 36

    (c)

    λ ≠ 8

    (d)

    none

  7. If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2. is inconsistent then k is

    (a)

    -3, -\(\frac{1}{2}\)

    (b)

    -\(\frac{1}{2}\)

    (c)

    1

    (d)

    2

  8. Cramer's rule is applicable only when ______

    (a)

    Δ ≠ 0

    (b)

    Δ = 0

    (c)

    Δ =0, Δx =0

    (d)

    Δx = Δy = Δz =0

  9. In the system of equations with 3 unknowns, if Δ = 0, and one of Δx, Δy of Δz is non zero then the system is ______

    (a)

    Consistent

    (b)

    inconsistent

    (c)

    consistent with one parameter family of solutions

    (d)

    consistent with two parameter family of solutions

  10. In a square matrix the minor Mij and the' co-factor Aij of and element aij are related by _____

    (a)

    Aij = -Mij

    (b)

    Aij = Mij

    (c)

    Aij = (-1)i+j Mij

    (d)

    Aij =(-1)i-j Mij

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