Determinants

CBSE Class 12 · Mathematics · 30 past questions

1. Q1 2026

   If $\Delta_1 = \begin{vmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{vmatrix}$ and…

   Try it →
2. Q2 2026

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

   Try it →
3. Q3 2026

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

   Try it →
4. Q4 2026

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

   Try it →
5. Q5 2026

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

   Try it →
6. Q6 2026

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

   Try it →
7. Q7 2026

   If…

   Try it →
8. 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)

   Try it →
9. Q9 2025

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

   Try it →
10. Q10 2025

    If A is a square matrix of order 2 such that det (A) = 4, then det (4 adj A) is equal to…

    Try it →
11. Q11 2025

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

    Try it →
12. Q12 2025

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

    Try it →
13. Q13 2025

    If M and N are square matrices of order 3 such that det (M) = m and MN = mI, then det (N) is equal to…

    Try it →
14. Q14 2025

    Let A and B be two square matrices of order 3 such that $\det(A) = 3$ and $\det(B) = -4$. Find the value of…

    Try it →
15. Q15 2024

    $\begin{vmatrix} x+1 & x-1 \\ x^2+x+1 & x^2-x+1 \end{vmatrix}$ is equal to…

    Try it →
16. Q16 2024

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

    Try it →
17. Q17 2024

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

    Try it →
18. Q18 2024

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

    Try it →
19. Q19 2024

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

    Try it →
20. Q20 2024

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

    Try it →
21. Q21 2024

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

    Try it →
22. Q22 2023

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

    Try it →
23. Q23 2023

    Let A be the area of a triangle having vertices $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$. Which of the…

    Try it →
24. 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…

    Try it →
25. Q25 2023

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

    Try it →
26. Q26 2023

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

    Try it →
27. Q27 2023

    If $\begin{bmatrix} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & a & 1 \end{bmatrix}$ is non-singular matrix and $a \in A$…

    Try it →
28. Q28 2023

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

    Try it →
29. Q29 2023

    If (a, b), (c, d) and (e, f) are the vertices of $\triangle ABC$ and $\Delta$ denotes the area of…

    Try it →
30. Q30 2023

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

    Try it →