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12th Standard Maths Application of Matrices and Determinants English Medium Free Online Test One Mark Questions with Answer Key 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 A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT = 

    (a)

    A

    (b)

    B

    (c)

    I

    (d)

    BT

  2. If A = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right] \) then the value of a23 is

    (a)

    0

    (b)

    -2

    (c)

    -3

    (d)

    -1

  3. If (AB)-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B-1 = 

    (a)

    \(\left[ \begin{matrix} 2 & -5 \\ -3 & 8 \end{matrix} \right] \)

    (b)

    \(\left[ \begin{matrix} 8 & 5 \\ 3 & 2 \end{matrix} \right] \)

    (c)

    \(\left[ \begin{matrix} 3 & 1 \\ 2 & 1 \end{matrix} \right] \)

    (d)

    \(\left[ \begin{matrix} 8 & -5 \\ -3 & 2 \end{matrix} \right] \)

  4. If A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA−1 =A, then λ is

    (a)

    17

    (b)

    14

    (c)

    19

    (d)

    21

  5. Which of the following is/are correct?
    (i) Adjoint of a symmetric matrix is also a symmetric matrix.
    (ii) Adjoint of a diagonal matrix is also a diagonal matrix.
    (iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).
    (iv) A(adjA) = (adjA)A = |A| I

    (a)

    Only (i)

    (b)

    (ii) and (iii)

    (c)

    (iii) and (iv)

    (d)

    (i), (ii) and (iv)

  6. Let A = \(\left[ \begin{matrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{matrix} \right] \) and 4B = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 1 & 3 & x \\ -1 & 1 & 3 \end{matrix} \right] \). If B is the inverse of A, then the value of x is

    (a)

    2

    (b)

    4

    (c)

    3

    (d)

    1

  7. If AT is the transpose of a square matrix A, then

    (a)

    |A| ≠ |AT|

    (b)

    |A| = |AT|

    (c)

    |A| + |AT| =0

    (d)

    |A| = |AT| only

  8. If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is

    (a)

    sinx cosx

    (b)

    1

    (c)

    2

    (d)

    none

  9. Every homogeneous system ______

    (a)

    Is always consistent

    (b)

    Has only trivial solution

    (c)

    Has infinitely many solution

    (d)

    Need not be consistent

  10. In the system of liner equations with 3 unknowns If \(\rho\)(A) = \(\rho\)([A|B]) =1, the system has ________

    (a)

    unique solution

    (b)

    inconsistent

    (c)

    consistent with 2 parameter -family of solution

    (d)

    consistent with one parameter family of solution.

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