← CBSE Class 12 PYQ

Determinants

CBSE Class 12 · Mathematics · 30 past questions

17 of 30 · show all

Q2 2026

One of the values of $x$ for which $\begin{vmatrix} \cos x & \sin x \\ -\cos x & \sin x \end{vmatrix} = 1$ is
Q3 2026

If $A = \begin{bmatrix} 0 & 2 & 1 \\ -2 & -1 & -2 \\ 1 & -1 & 0 \end{bmatrix}$, find $A^{-1}$ and use it to…
Q5 2026

If $\begin{vmatrix}-1 & -2 & 5\\ -2 & a & -1\\ 0 & 4 & 2a\end{vmatrix}$ = –86, then the sum of all possible…
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)
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…
Q16 2024

Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
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…
Q20 2024

If $\begin{vmatrix} -a & b & c \\ a & -b & c \\ a & b & -c \end{vmatrix} = kabc$, then the value of $k$ 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…
Q28 2023

If $|A| = |kA|$, where A is a square matrix of order 2, then sum of all possible values of k is
Q30 2023

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