100 Super Revision Test – CBSE Class 12 Determinants (2026)
Preparing for CBSE Class 12 Mathematics becomes much easier when you revise using well-structured practice questions. Determinants is one of the most scoring chapters in the Class 12 Maths syllabus, and almost every year, 6–8 marks come directly from this topic.
This 100 Super Revision Test is designed to help you:
- Revise every important concept of Determinants
- Practice all types of questions asked in Class 12 board exams
- Strengthen your speed and accuracy
- Build confidence for both Term Exams and Pre-Boards 2026
Before attempting the questions, make sure you revise:
- Properties of Determinants
- Cofactor and Minors
- Adjoint of a Matrix
- Inverse using Adjoint Method
- Applications of Determinants (Area of Triangle)
Note: Important/high-weight questions are highlighted. Try solving before checking final answers below.
- Define determinant of a square matrix.
- Find \(\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix} \).
- Evaluate \( \begin{vmatrix} 2 & 5 \\ 1 & 3 \end{vmatrix} \).
- If two rows of a determinant are interchanged, what happens to its sign?
- If two rows are identical, what is the value of the determinant?
- Evaluate \( \begin{vmatrix} 2 & 0 \\ 0 & 2 \end{vmatrix} \).
- Prove that \( \begin{vmatrix} a & b \\ b & a \end{vmatrix} = a^2 - b^2 \).
- Find determinant of \( I_2 \).
- Find \( |3I_2| \).
- Find \( |0I_2| \).
- Evaluate \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{vmatrix} \).
- Find determinant of a diagonal matrix with diagonal entries 2, 3, 4.
- If \(|A| = 5\), find \(|2A|\).
- What happens to \(|A|\) if a row is multiplied by constant \(k\)?
- Show that determinant of upper triangular matrix equals product of its diagonal elements.
- Prove that \( \begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^2 & b^2 & c^2 \end{vmatrix} = (b - a)(c - a)(c - b) \).
- Find \( \begin{vmatrix} x & 1 \\ 1 & x \end{vmatrix} \).
- Find \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \).
- For \( \begin{vmatrix} 2 & 3 \\ 4 & 6 \end{vmatrix} \), comment on its value.
- Find determinant of \( \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix} \).
- Find determinant of \( \begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{vmatrix} \).
- Find \( |A| \) if \( A = \begin{bmatrix} 1 & 2 & 0 \\ 0 & 1 & 3 \\ 0 & 0 & 2 \end{bmatrix} \).
- If \( |A| = 4 \), find \( |A^{-1}| \).
- Expand \( \begin{vmatrix} 2 & 1 & 0 \\ 0 & 3 & 2 \\ 1 & 0 & 1 \end{vmatrix} \) along first column.
- Find determinant of \( \begin{vmatrix} 1 & 2 & 1 \\ 0 & 1 & 2 \\ 1 & 1 & 1 \end{vmatrix} \).
- Find determinant of a zero matrix of order 3.
- Find determinant of \( A' \) if \( |A| = 5 \).
- Show that \( |A'| = |A| \).
- If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), find \( |A'| \).
- Find \( |AB| \) if \( |A|=2, |B|=3 \).
- Find \( |A^{-1}| \) if \( |A|=2 \).
- Find the area of triangle with vertices (1,2), (3,5), (6,7) using determinants.
- Show that points (1,2), (2,4), (3,6) are collinear using determinant.
- Find condition for collinearity of (x1, y1), (x2, y2), (x3, y3).
- If one row is multiplied by zero, what is determinant?
- Find \( \begin{vmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{vmatrix} \).
- Find \( \begin{vmatrix} 2 & -3 \\ 1 & 4 \end{vmatrix} \).
- Find determinant of \( \begin{vmatrix} 1 & 0 & -2 \\ 3 & 1 & 0 \\ 0 & 2 & 1 \end{vmatrix} \).
- Find \( \begin{vmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{vmatrix} \).
- Prove that rotation matrix determinant = 1.
- Find \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{vmatrix} \).
- Find \( \begin{vmatrix} 2 & 0 & 0 \\ 1 & 3 & 0 \\ 4 & 5 & 6 \end{vmatrix} \).
- If \( |A|=k \\), find \\( |A^T| \).
- Evaluate \( \begin{vmatrix} 3 & 2 & 0 \\ 0 & 1 & 4 \\ 1 & 0 & 5 \end{vmatrix} \).
- Find determinant of \( \begin{vmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{vmatrix} \).
- Prove that \( |kA| = k^n|A| \) for an \(n×n\) matrix.
- Find \( |2A| \) if \( |A| = 3 \) and order of A = 2.
- Find \( |2A| \) if \( |A| = 3 \) and order of A = 3.
- Find \( |0A| \).
- Prove that determinant is linear in each row.
- Find \( |A| \) if A = [[1,2,3],[2,3,4],[3,4,5]].
- Show that if any two rows are proportional, \(|A| = 0\).
- Find \( |A| \) if \( A = [[a,b,c],[b,c,a],[c,a,b]] \).
- Find \( |A| \) if \( A = [[1,1,1],[x,y,z],[x^2,y^2,z^2]] \).
- Find \( |A| \) if \( A = [[1,p,q],[p,1,r],[q,r,1]] \).
- Find determinant of \( \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 10 \end{vmatrix} \).
- Find \( |A| \) for A = [[2,1,1],[1,2,1],[1,1,2]].
- Prove: \( |A| = (a+b+c)(a^2+b^2+c^2 - ab - bc - ca) \) for \(A = [[1,1,1],[a,b,c],[a^2,b^2,c^2]]\).
- Find determinant of [[a, b+c, c+b], [b, c+a, a+c], [c, a+b, b+a]].
- Find determinant of [[1,0,-1],[0,1,0],[1,1,1]].
- Find \( |A| \) if \( A = [[1,0,1],[0,1,1],[1,1,0]] \).
- Find determinant when two rows are equal.
- Prove that \( |A| = 0 \) if one row is sum of other two.
- Find determinant of \( [[2,3,4],[0,1,5],[0,0,6]] \).
- Find determinant of \( [[1,2,3],[2,4,6],[3,6,9]] \).
- Prove that \( |A| = 0 \) if rows are proportional.
- Find \( |A| \) when \( A = [[1,2,3],[4,5,6],[7,8,10]] \).
- Find \( |A| \) for \( A = [[x,1,1],[1,x,1],[1,1,x]] \).
- Find determinant of \( [[2,1,0],[1,2,1],[0,1,2]] \).
- Find determinant of [[1,2,3],[1,3,4],[1,4,5]].
- Find determinant of \( [[x,0,0],[0,x,0],[0,0,x]] \).
- If \( |A| = 2 \), find \( |3A^{-1}| \).
- Find determinant of [[2,0,1],[3,4,0],[1,2,3]].
- Find determinant of [[1,3,1],[0,2,4],[2,1,3]].
- Find determinant of [[1,0,0],[2,3,0],[1,4,5]].
- Find determinant of [[0,1,2],[1,2,3],[4,5,6]].
- Find determinant of [[1,2,1],[3,2,1],[1,1,1]].
- Find determinant of [[x,1,0],[1,x,1],[0,1,x]].
- Find determinant of [[1,1,1],[1,2,3],[1,3,6]].
- Find \( |A| \) when \( A = [[a,b,c],[b,c,a],[c,a,b]] \).
- Find \( |A| \) for A = [[1,p,q],[p,1,r],[q,r,1]].
- Find determinant of [[a,b,1],[b,1,a],[1,a,b]].
- Find \( |A| \) for [[1,2,3],[0,1,4],[5,6,0]].
- Find \( |A| \) for [[a,b,0],[0,a,b],[b,0,a]].
- If \( A = [[1,1,1],[1,2,3],[1,4,9]] \), find \( |A| \).
- Find determinant of [[x,1,1],[1,x,1],[1,1,x]].
- Find determinant of [[1,a,a^2],[1,b,b^2],[1,c,c^2]].
- Find determinant of [[1,2,3],[2,4,5],[3,5,7]].
- Find determinant of [[2,1,0],[0,3,1],[0,0,4]].
- Find determinant of [[1,2,0],[0,1,3],[4,0,1]].
- Find determinant of [[1,0,2],[3,1,4],[0,2,5]].
- Find determinant of [[2,1,3],[0,4,5],[1,0,6]].
- Find determinant of [[3,0,1],[1,2,0],[4,1,5]].
- If \(|A| = 3\) and \(|B| = 2\), find \(|A^2B'|\).
- If \(A\) is singular, what is \(|A|\)?
- If \(|A| = 0\), what type of matrix is A?
- If \(|A| = 1\), what type of transformation does it represent?
- Find \(|\nabla f|\) using determinant for function f(x,y,z).
Final Answers (Key):
- Definition based.
- = -2
- = 1
- Sign changes.
- 0
- 4
- \(a^2 - b^2\)
- 1
- 9
- 0
- -38
- 24
- 8
- k|A|
- Product of diagonals.
- \((b-a)(c-a)(c-b)\)
- \(x^2 - 1\)
- \(ad - bc\)
- 0
- 0
- 1
- 2
- 1/4
- 4
- 2
- 0
- 5
- 5
- 6
- 6
- 1/2
- Area = 0
- 0 (collinear)
- Formula determinant = 0
- 0
- 0
- 11
- 1
- 1
- -38
- 36
- k|A|
- 12
- 24
- 0
- True
- 0
- 0
- 6
- 8
- \((a+b+c)(a^2+b^2+c^2-ab-bc-ca)\)
- 0
- 2
- 1
- 0
- 72
- 0
- 0
- 3
- \(x^3-3x+2\)
- 4
- 3
- 2
- 0
- \(27\)
- \(x^3 - 3x + 2\)
- \((b-a)(c-a)(c-b)\)
- 5
- 24
- 18
- 7
- 9
- 5
- 12
- 18
- 12
- 12
- 1
- 0
- Singular
- Identity transformation
- Jacobian determinant based
🧠 Revise these daily before exams — they cover all CBSE 2026 Determinants concepts: properties, expansion, triangle area, and matrix relation.