Determinants in past papers.

CBSE Board Examination 2026

• Board 2026 Q4Comparing the determinants $\Delta_1$ and $\Delta_2$
  Evaluating 3 × 3 determinants1 mark
• Board 2026 Q5A value of $x$ making a trigonometric determinant equal 1
  Evaluating 2 × 2 determinants1 mark
• Board 2026 Q33Find $A^{-1}$ and solve a system, or the values of $x$ that make a matrix singular
  Inverse by adjoint, linear system; singular matrix5 marks

CBSE Board Examination 2025

• Board 2025 Q6$\det(4\,\text{adj}\,A)$ when $\det A = 4$⁠, order 2
  Determinant of k adj A1 mark
• Board 2025 Q15Which property of invertible matrices is not correct?
  Properties of the inverse and adjoint1 mark
• Board 2025 Q35Students in the Sports, Music and Drama clubs by the matrix method
  System of linear equations by the matrix method5 marks

CBSE Board Examination 2024

• Board 2024 Q12Value of a $2 \times 2$ determinant in $x$
  Evaluating a 2 × 2 determinant1 mark
• Board 2024 Q19$|A| \in [2, 4]$ for a matrix in $\cos\theta$
  Value of a 3 × 3 determinant1 mark
• Board 2024 Q32Find $A^{-1}$ and solve a system of three equations, or find unknown entries from $A^{-1}$
  Inverse by adjoint; solving a linear system5 marks

CBSE Board Examination 2023

• Board 2023 Q1$A^{-1} = xA + yI$ when $A^2 - 3A + I = O$
  Inverse of a matrix from a matrix equation1 mark
• Board 2023 Q2$|4A^{-1}|$ for a $2 \times 2$ matrix with $|A| = 2$
  Determinant of kA and of the inverse1 mark
• Board 2023 Q3$|A|$ when $|\text{adj}\,A| = 64$ for a $3 \times 3$ matrix
  Determinant of the adjoint1 mark
• Board 2023 Q33Find $(AB)^{-1}$ from $A$ and $B^{-1}$⁠, or solve a system by the matrix method
  Inverse of a product; system by matrix method5 marks

CBSE Sample Paper 2026-27

• Sample 2026-27 Q5$|\text{adj}(PQ)|$ for $2 \times 2$ matrices $P$ and $Q$
  Adjoint of a matrix: |adj A| = |A|ⁿ⁻¹1 mark
• Sample 2026-27 Q38Case study: fruit baskets, prices by the matrix inverse
  System of equations by the matrix inverse4 marks

CBSE Sample Paper 2025-26

• Sample 2025-26 Q4$A(\operatorname{adj} A)$ when $|\operatorname{adj} A| = 27$⁠, order 4
  Adjoint: |adj A| = |A|ⁿ⁻¹ and A(adj A) = |A|I1 mark
• Sample 2025-26 Q5Inverse of the diagonal matrix $\operatorname{diag}(3, 2, 5)$
  Inverse of a diagonal matrix1 mark
• Sample 2025-26 Q6Determinant of $\cos 67^\circ$⁠, $\sin 67^\circ$⁠, $\sin 23^\circ$⁠, $\cos 23^\circ$
  Value of a 2 × 2 determinant1 mark

CBSE Sample Paper 2024-25

• Sample 2024-25 Q1$|A| + |\operatorname{adj} A|$ when $A\,(\operatorname{adj} A) = 2025\,I$
  Adjoint: |A| and |adj A| from A(adj A)1 mark
• Sample 2024-25 Q4$\det(B^{-1}AB)^2$ when $\det(A) = 5$
  Determinant of a product of matrices1 mark
• Sample 2024-25 Q6$x_1y_2$ when $(x_1, y_1)$⁠, $(x_2, y_2)$⁠, $(x_1 + x_2, y_1 + y_2)$ are collinear
  Collinear points: area of a triangle is zero1 mark
• Sample 2024-25 Q33Path $y = ax^2 + bx + c$ of a headed football by the matrix method
  System of three equations by the matrix method5 marks

CBSE Sample Paper 2023-24

• Sample 2023-24 Q2Which statement about $|AB^{-1}|$⁠, $(AB)^{-1}$⁠, $(A + B)^{-1}$ is not correct
  Properties of determinants and inverses1 mark
• Sample 2023-24 Q3$k$ when the triangle $(-3, 0)$⁠, $(3, 0)$⁠, $(0, k)$ has area 9
  Area of a triangle using determinants1 mark
• Sample 2023-24 Q10$|A|$ for a $3 \times 3$ skew symmetric matrix in $x$
  Determinant of a skew symmetric matrix1 mark
• Sample 2023-24 Q13$|\operatorname{adj}(2A)|$ when $A$ is of order 3 and $|A| = -2$
  Determinant of the adjoint of kA1 mark
• Sample 2023-24 Q34Matrix method: $\frac2x + \frac3y + \frac{10}{z} = 4$⁠, $\frac4x - \frac6y + \frac5z = 1$⁠, $\frac6x + \frac9y - \frac{20}{z} = 2$
  Matrix method: equations in 1/x, 1/y, 1/z5 marks

CBSE Sample Paper 2022-23

• Sample 2022-23 Q2$|AA'|$ when $|A'| = -3$
  Determinant of a product and of a transpose1 mark
• Sample 2022-23 Q12$x$ from an equation of two $2 \times 2$ determinants
  Equation in 2 × 2 determinants1 mark
• Sample 2022-23 Q13$|\operatorname{adj} A|$ when $|A| = 5$⁠, order 3
  Determinant of the adjoint1 mark
• Sample 2022-23 Q35Find $A^{-1}$ and solve $2x - 3y + 5z = 11$⁠, $3x + 2y - 4z = -5$⁠, $x + y - 2z = -3$
  Inverse by the adjoint; solving a system by A⁻¹5 marks

CBSE Sample Paper 2020-21

• Sample 2020-21 Q6Value of $a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23}$
  Cofactors: one row's elements, another's cofactors1 mark
• Sample 2020-21 Q20$|A|$ when $A^2 = 2A$⁠. Or: show $A^2 - 5A + 7I = O$ and find $A^{-1}$
  |kA| and |AB|; inverse from a matrix equation2 marks
• Sample 2020-21 Q36$A^{-1}$ and a system with matrix $A'$⁠, or $AB = 6I$ and a system
  Inverse of a matrix; solving a system of equations5 marks

Questions that also use Determinants

Their main topic is in another chapter.

• Board 2022 T2 Q14Case study: two transmission wires along lines $l_1$ and $l_2$
  Two lines: coplanar and point of intersection4 marks
• Sample 2026-27 Q26Find $PQ$ and $QP$ and the inverse of the product, if it exists
  Matrix products; inverse of a product matrix3 marks
• Sample 2025-26 Q32Find $AB$ and hence solve a system of three equations
  Inverse from AB = I; solving a system of equations5 marks
• Sample 2022-23 Q10$(AB^{-1})^{-1}$ for non-singular $A$⁠, $B$
  Inverse of a product of matrices1 mark
• Sample 2020-21 Q5$A^2$ for $a_{ij} = 1$ ($i \ne j$⁠), $0$ ($i = j$⁠). Or: $|\text{adj}\,A|$ when $|A| = -4$
  Constructing a matrix; |adj A| = |A|ⁿ⁻¹1 mark