New ! Maths MCQ Practise Tests



Application of Matrices and Determinants One Mark Questions with Answer

12th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 25
    25 x 1 = 25
  1. 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

  2. If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then _____________

    (a)

    a2 + b2 + c2 = 1

    (b)

    abc ≠ 1

    (c)

    a + b + c =0

    (d)

    a2 + b2 + c2 + 2abc =1

  3. Let A be a 3 \(\times\) 3 matrix and B its adjoint matrix If |B| = 64, then |A| = ___________

    (a)

    ±2

    (b)

    ±4

    (c)

    ±8

    (d)

    ±12

  4. 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

  5. The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is ____________

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    infinitely many

  6. If A is a square matrix that IAI = 2, than for any positive integer n, |An| = _______

    (a)

    0

    (b)

    2n

    (c)

    2n

    (d)

    n2

  7. The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if __________

    (a)

    k ≠ 0

    (b)

    -1 < k < 1

    (c)

    -2 < k < 2

    (d)

    k = 0

  8. If A is a square matrix of order n, then |adj A| = ______________

    (a)

    |A|n-1

    (b)

    |A|n-2

    (c)

    |A|n

    (d)

    None

  9. 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

  10. 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

  11. If A is a matrix of order m \(\times\) n, then \(\rho\) (A) is _________

    (a)

    m

    (b)

    n

    (c)

    ≤ min (m,n)

    (d)

    ≥ min (m,n)

  12. The system of equations x + 2y + 3z = 1, x - y + 4z = 0, 2x + y + 7z = 1 has ___________

    (a)

    One solution

    (b)

    Two solution

    (c)

    No solution

    (d)

    Infinitely many solution

  13. If \(\rho\) (A) = \(\rho\) ([A/B]) = number of unknowns, then the system is _________--

    (a)

    consistent and has infinitely many solutions

    (b)

    consistent

    (c)

    inconsistent

    (d)

    consistent and has unique solution

  14. Which of the following is not an elementary transformation?

    (a)

    Ri ↔️ Rj

    (b)

    Ri ⟶ 2Ri + Rj

    (c)

    Cj ⟶ Cj + Ci

    (d)

    Ri ⟶ Ri + Cj

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

    (a)

    all the minors of order n which do not vanish

    (b)

    'A' has at least one minor of order r which does not vanish and all higher order minors vanish

    (c)

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

    (d)

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

  16. Every homogeneous system ______

    (a)

    Is always consistent

    (b)

    Has only trivial solution

    (c)

    Has infinitely many solution

    (d)

    Need not be consistent

  17. If \(\rho\) (A) ≠ \(\rho\) ([AIB]), then the system is _____________

    (a)

    consistent and has infinitely many solutions

    (b)

    consistent and has a unique solution

    (c)

    consistent

    (d)

    inconsistent

  18. In the non - homogeneous system of equations with 3 unknowns if \(\rho\) (A) = \(\rho\) ([AIB]) = 2, then the system has _______

    (a)

    unique solution

    (b)

    one parameter family of solution

    (c)

    two parameter family of solutions

    (d)

    in consistent

  19. Cramer's rule is applicable only when ______

    (a)

    Δ ≠ 0

    (b)

    Δ = 0

    (c)

    Δ =0, Δx =0

    (d)

    Δx = Δy = Δz =0

  20. In a homogeneous system if \(\rho\) (A) =\(\rho\) ([A|0]) < the number of unknouns then the system has ________

    (a)

    trivial solution

    (b)

    only non - trivial solution

    (c)

    no solution

    (d)

    trivial solution and infinitely many non - trivial solutions

  21. 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

  22. 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.

  23. If A = [2 0 1] then the rank of AAT is ______

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    0

  24. If A is a non-singular matrix then IA-1| = ______

    (a)

    \(\left| \frac { 1 }{ { A }^{ 2 } } \right| \)

    (b)

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

    (c)

    \(\left| \frac { 1 }{ A } \right| \)

    (d)

    \(\frac { 1 }{ |A| } \)

  25. 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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