← CBSE Class 12 PYQ

Determinants

CBSE Class 12 · Mathematics · 30 past questions

17 of 30 · show all

Q3 2026

If $A = \begin{bmatrix} 0 & 2 & 1 \\ -2 & -1 & -2 \\ 1 & -1 & 0 \end{bmatrix}$, find $A^{-1}$ and use it to…
Q4 2026

For a square matrix A, (3A)$^{-1}$ =
Q6 2026

If $A^2 = 4A + 3I$ and $A^{-1} = xA + yI$, then the value of $(x + y)$ is…
Q7 2026

If…
Q8 2026

On the inauguration day of a new showroom, a lucky draw was organized and some vouchers of ₹ 1,000 and ₹ 500… (with a figure)
Q9 2025

If $A = \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$, then $A^{-1}$ is
Q11 2025

A school wants to allocate students into three clubs : Sports, Music and Drama, under following conditions…
Q12 2025

Given $A = \begin{bmatrix} -4 & 4 & 4 \\ -7 & 1 & 3 \\ 5 & -3 & -1 \end{bmatrix}$ and…
Q17 2024

If $A = \begin{bmatrix} 1 & -2 & 0 \\ 2 & -1 & -1 \\ 0 & -2 & 1 \end{bmatrix}$, find $A^{-1}$ and use it to…
Q18 2024

Let $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ be a square matrix such that adj $A = A$. Then…
Q19 2024

If $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 5 \end{bmatrix}$, then $A^{-1}$ is…
Q21 2024

Solve the following system of equations, using matrices: $\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4$…
Q22 2023

If $A \cdot (\operatorname{adj} A) = \begin{bmatrix} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{bmatrix}$, then…
Q24 2023

If for a square matrix A, $A^2 - 3A + I = O$ and $A^{-1} = xA + yI$, then the value of $x + y$ is…
Q25 2023

If $|A| = 2$, where A is a $2 \times 2$ matrix, then $|4A^{-1}|$ equals…
Q26 2023

Let A be a $3 \times 3$ matrix such that $|\text{adj } A| = 64$. Then $|A|$ is equal to…
Q30 2023

If $A=\begin{bmatrix}-3&-2&-4\\2&1&2\\2&1&3\end{bmatrix}$…