Questions and Solutions

Class: 12 Subject: Math Type: Mcq Year: 2022

Question 1:

If for a square matrix A, \(A^2 - 3A + I = O\) and \(A^{-1} = xA + yI\), then the value of \(x + y\) is:

  • A. -2
  • B. 2
  • C. 3
  • D. -3
Class: 12 Subject: Math Type: Mcq Year: 2022

Question 2:

If \(A=\begin{bmatrix}3&4\\ 5&2\end{bmatrix}\) and \(2A+B\) is a null matrix, then B is equal to:

  • A. \(\begin{bmatrix}6&8\\ 10&4\end{bmatrix}\)
  • B. \(\begin{bmatrix}-6&-8\\ -10&-4\end{bmatrix}\)
  • C. \(\begin{bmatrix}5&8\\ 10&3\end{bmatrix}\)
  • D. \(\begin{bmatrix}-5&-8\\ -10&-3\end{bmatrix}\)
Class: 12 Subject: Math Type: Mcq Year: 2022

Question 3:

If \(A = \begin{bmatrix}2&-3\\ 4&-2\end{bmatrix}\), then the inverse of A is:

  • A. \(\frac{1}{8}\begin{bmatrix}2&3\\ -4&2\end{bmatrix}\)
  • B. \(\frac{1}{8}\begin{bmatrix}-2&-3\\ 4&-2\end{bmatrix}\)
  • C. \(\frac{1}{8}\begin{bmatrix}-2&3\\ -4&-2\end{bmatrix}\)
  • D. \(\frac{1}{8}\begin{bmatrix}-2&3\\ -4&2\end{bmatrix}\)
Class: 12 Subject: Math Type: Mcq Year: 2022

Question 4:

If A is a square matrix such that \(A^2 = A\), then A is:

  • A. Singular
  • B. Identity
  • C. Invertible
  • D. Idempotent
Class: 12 Subject: Math Type: Mcq Year: 2023

Question 5:

For two matrices A and B, given that \( A^{-1} = \frac{1}{4}B \), then the inverse of \( 4A \) is:

  • A. 4B
  • B. B
  • C. \( \frac{1}{4}B \)
  • D. \( \frac{1}{16}B \)
Class: 12 Subject: Math Type: Mcq Year: 2023

Question 6:

If X, Y and XY are matrices of order \(2\times3\), \(m\times n\) and \(2\times5\) respectively, then number of elements in matrix Y is:

  • A. 6
  • B. 10
  • C. 15
  • D. 35
Class: 12 Subject: Math Type: Mcq Year: 2024

Question 7:

If \( A = \begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} \), then \( A^{-1} \) is:

  • A. \( \begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix} \)
  • B. \( \begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix} \)
  • C. \( \begin{bmatrix}-1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{bmatrix} \)
  • D. \( \begin{bmatrix}-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} \)
Class: 12 Subject: Math Type: Mcq Year: 2024

Question 8:

Let \( A = \begin{bmatrix}1&-2&-1\\ 0&4&-1\\ -3&2&1\end{bmatrix} \), \( B = \begin{bmatrix}-2\\ -5\\ -7\end{bmatrix} \), \( C = [987] \). Which of the following is defined?

  • A. Only AB
  • B. Only AC
  • C. Only BA
  • D. All AB, AC and BA
Class: 12 Subject: Math Type: Mcq Year: 2024

Question 9:

If \( A = \begin{bmatrix}7 & 0 & x \\ 0 & 7 & 0 \\ 0 & 0 & y\end{bmatrix} \) is a scalar matrix, then \( y^x \) is equal to:

  • A. 0
  • B. 1
  • C. 7
  • D. \( \pm7 \)
Class: 12 Subject: Math Type: Mcq Year: 2024

Question 10:

If A and B are invertible matrices, then which of the following is not correct?

  • A. \( (A + B)^{-1} = B^{-1} + A^{-1} \)
  • B. \( (AB)^{-1} = B^{-1}A^{-1} \)
  • C. \( \text{adj}(A) = |A|A^{-1} \)
  • D. \( |A|^{-1} = |A^{-1}| \)