#### 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