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

12th Standard

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Business Maths

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

    Answer all the questions

    10 x 1 = 10
  1. If A = (1 2 3), then the rank of AAT is ________.

    (a)

    0

    (b)

    2

    (c)

    3

    (d)

    1

  2. if T = \(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right) \) is a transition probability matrix, then at equilibrium A is equal to ________.

    (a)

    \(\frac { 1 }{ 4 } \)

    (b)

    \(\frac { 1 }{ 5 } \)

    (c)

    \(\frac { 1 }{ 6 } \)

    (d)

    \(\frac { 1 }{ 8 } \)

  3. If \(\rho (A)\) = r  then which of the following is correct?

    (a)

    all the minors of order r which does not vanish

    (b)

    A has at least one minor of order r which does not vanish

    (c)

    A has at least one (r+1) order minor which vanishes

    (d)

    all (r+1) and higher order minors should not vanish

  4. If the rank of the matrix  \(\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right) \)  is 2. Then \(\lambda \) is ________.

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    only real number

  5. If \(\rho (A)=\rho (A,B)\) then the system is ________.

    (a)

    Consistent and has infinitely many solutions

    (b)

    Consistent and has a unique solution

    (c)

    Consistent

    (d)

    inconsistent

  6. If \(\rho(A) \neq \rho(A, B)\), then the system is _______.

    (a)

    Consistent and has infinitely many solutions

    (b)

    Consistent and has a unique solution

    (c)

    inconsistent

    (d)

    consistent

  7. Rank of a null matrix is _______.

    (a)

    0

    (b)

    -1

    (c)

    \(\infty \)

    (d)

    1

  8. For what value of k, the matrix \(A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right) \) has no inverse?

    (a)

    \(\frac { 3 }{ 10 } \)

    (b)

    \(\frac { 10 }{ 3 } \)

    (c)

    3

    (d)

    10

  9. The value of \(\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right| \)

    (a)

    52

    (b)

    0

    (c)

    513

    (d)

    59

  10. If A is a singular matrix, then Adj A is ___________

    (a)

    non-singular

    (b)

    singular

    (c)

    symmetric

    (d)

    not defined

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