Matrices and Determinants is an important topic in the Mathematics section in WBJEE exam. Practising this topic will increase your score overall and make your conceptual grip on WBJEE exam stronger.
This article gives you a full set of WBJEE PYQs for Matrices and Determinants with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Matrices and Determinants questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.
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WBJEE PYQs for Matrices and Determinants with Solutions
1.
If \[ A = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \] and \(\theta = \frac{2\pi}{7}\), then \(A^{100} = A \times A \times \ldots\) (100 times) is equal to:- \(\begin{pmatrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \end{pmatrix}\)
- \(\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}\)
- \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
- \(\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}\)
2.
If for a matrix \( A \), \( |A| = 6 \) and \( \text{adj } A = \begin{bmatrix} 1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0 \end{bmatrix} \), then \( k \) is equal to:- \( -1 \)
- \( 1 \)
- \( 2 \)
- \( 0 \)
3.
If
\[ \begin{vmatrix} x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3} \end{vmatrix} = (x - y)(y - z)(z - x)\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right), \] then the value of \(k\) is:- k =−3
- k = 3
- k = 1
- k =−1
4.
If
\[ \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix} \cdot A \cdot \begin{pmatrix} -3 & 2 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \]
then \(A\) is:- \(\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}\)
- \(\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}\)
- \(\begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}\)
- \(\begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix}\)
5.
Let
\[ A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 2 \\ 1 \\ 7 \end{bmatrix}. \]
For the validity of the result \(AX = B\), \(X\) is:- \(\begin{bmatrix} -1 \\ 1 \\ 7 \end{bmatrix}\)
- \(\begin{bmatrix} 1 \\ 2 \\ 4 \end{bmatrix}\)
- \(\begin{bmatrix} 3 \\ -1 \\ -1 \end{bmatrix}\)
- \(\begin{bmatrix} 4 \\ 2 \\ 1 \end{bmatrix}\)
6.
Let
\[ A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}. \]
Which of the following is true?- \( A \) is a null matrix
- \( A \) is skew-symmetric
- \( A^{-1} \) does not exist
- \( A^2 = I \)
7.
If the matrix \[ \begin{pmatrix} 0 & a & a\\ 2b & b & -b\\ c & -c & c \end{pmatrix} \] is orthogonal, then the values of \( a, b, c \) are:- \( a = \pm \frac{1}{\sqrt{3}}, b = \pm \frac{1}{\sqrt{6}}, c = \pm \frac{1}{\sqrt{2}} \)
- \( a = \pm \frac{1}{\sqrt{2}}, b = \pm \frac{1}{\sqrt{6}}, c = \pm \frac{1}{\sqrt{3}} \)
- \( a = \pm \frac{1}{\sqrt{2}}, b = \pm \frac{-1}{\sqrt{6}}, c = \pm \frac{-1}{\sqrt{3}} \)
- \( a = \pm \frac{1}{\sqrt{3}}, b = \pm \frac{1}{\sqrt{6}}, c = \pm \frac{1}{\sqrt{3}} \)
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