List of top Mathematics Questions on Applications of Determinants and Matrices

If \[ A = \begin{pmatrix} 2 & 3 \\ 3 & 5 \end{pmatrix} \] then the value of \[ |A^{2025} - 3A^{2024} + A^{2023}| \] is:

If \[ \begin{vmatrix} 0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} = \begin{vmatrix} 1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} \] then the value of $ \cos^2 \alpha + \cos^3 \beta + \cos^2 \gamma $ is:

If $ A $ is a square matrix of order 3 and $ |A| = 6 $, it is given that \[ \left| \text{adj} \left( 3 \, \text{adj} \left( A^2 \, \text{adj} (2A) \right) \right) \right| = 2^m \cdot 3^n \] where $ m $ and $ n $ are natural numbers. Then find $ m + n $. Here, $ \text{adj}(X) $ denotes the adjoint of matrix $ X $, and $ |X| $ denotes the determinant of matrix $ X $.

If $ A = \left[ \begin{array}{cc} \alpha & 2 \\ 1 & 2 \end{array} \right] $, $ B = \left[ \begin{array}{cc} 1 & 1 \\ 1 & 1 \end{array} \right] $ and $ A^2 - 4A + 2I = 0, B^2 - 2B + I = 0 $, then $ \text{adj}(A^3 - B^3) $ is equal to

Let A = $\begin{bmatrix} \log_5 128 & \log_4 5 \log_5 8 & \log_4 25 \end{bmatrix}$ \). If $A_{ij}$ is the cofactor of $ a_{ij} $, $ C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk} $, and $ C = [C_{ij}] $, then $ 8|C| $ is equal to:

For the system of linear equations$\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta$ which one of the following statements is NOT correct ?

The system of the equations
$x + y + z = 6$
$x + 2y + \alpha z = 5 $
$x + 2y + 6z = $$ \beta$ has

The number of distinct real roots of the equation, $\begin{vmatrix}\cos x&\sin x &\sin x\\ \sin x&\cos x&\sin x\\ \sin x&\sin x&\cos x\end{vmatrix}= 0$ in the interval $ \left[- \frac{\pi}{4}, \frac{\pi}{4}\right]$ is :

Given below is a frequency distribution with median 46. In this distribution, some of the frequencies are missing. Determine the missing frequencies.

Marks: 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80
No. of students: 12, 30, x, 65, y, 25, 18

Total number of students = 229

If A and B are 2×2 matrices, which of the following is true?

The digits A,B,C are such that the three-digit numbers A88, 6B8, 86C are divisible by 72. Then the determinant vmatrix A & 6 & 8
8 & B & 6
8 & 8 & C vmatrix is divisible by