Determinants - ISC Class 12 Mathematics Questions with Answers
43 past-paper questions on Determinants from ISC Class 12 Mathematics papers (2027-2017), newest first. Open one to see its answer.
- If $x, y, z$ are distinct non zero real numbers, prove that… 2027 · 3 marks · Short answer
- 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 following is correct? 2027 · 1 mark · MCQ
- Using properties of determinants, solve for $x$: $\begin{vmatrix} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{vmatrix} = 0$ 2026 · 4 marks · Numerical
- The system of linear equations $x + y + z = 6$, $x + \lambda y + 2z = 7$ and $3x + y + z = 12$ has a unique solution if: 2026 · 1 mark · MCQ
- If $A$ is a square matrix of order $3$ and its determinant is $|A| = -3$, then the value of $|-4A|$ is: 2026 · 1 mark · MCQ
- Using properties of determinant, show that… 2026 · 2 marks · Derivation
- Solve for $x$: $\begin{vmatrix} 1 & -2 & 5 \\ 2 & x & -1 \\ 0 & 4 & 2x \end{vmatrix} = 86$. 2026 · 1 mark · Short answer
- Consider the matrix $A$ of order $3 \times 3$ with $|A| = 5$. If any two columns are interchanged in $A$, then $|A|$ is: 2026 · 1 mark · MCQ
- Using determinants, find the value of $x$ if the points $(x, -2)$, $(5, 2)$ and $(8, 8)$ are collinear. 2026 · 2 marks · Numerical
- Find the value of $\mu$ if the following system of equations is consistent: $2x + 3y - 8 = 0$, $7x - 5y + 3 = 0$… 2025 · 1 mark · MCQ
- If $A$ is a skew-symmetric matrix of order $3 \times 3$, then $\det(A) = 0$. 2025 · 1 mark · Assertion-reason
- Using the properties of determinants, prove that… 2025 · 4 marks · Derivation
- If $D = \begin{vmatrix} p & p & p \\ p & p+x & p \\ p & p & p+y \end{vmatrix}$ for $p \neq 0, x \neq 0, y \neq 0$ then $D$ is… 2025 · 1 mark · MCQ
- To raise money for an orphanage, students of three schools A, B and C organised an exhibition in their residential colony, where… 2025 · 6 marks · Short answer
- … 2025 · 1 mark · MCQ
- If $x + y + z = 0$ then show that $\begin{vmatrix} 1 & 1 & 1 \\ x & y & z \\ x^3 & y^3 & z^3 \end{vmatrix} = 0$, using properties… 2025 · 4 marks · Derivation
- Each triangular face of the pyramid of Peace of Kazakhstan is made up of 25 smaller triangles as shown in figure below: Using the… 2025 · 1 mark · Short answer
- Rajesh wants to purchase some fruits from fruit market. 4 kilograms (kgs) apples, 3 kgs grapes and 2 kgs oranges cost him ₹ 600… 2025 · 6 marks · Long answer
- For what value of $\alpha$, is the matrix $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \alpha & 2 & -3 \end{bmatrix}$ not… 2025 · 1 mark · Numerical
- If the value of 3rd order determinant is $5$, then the value of determinant formed by replacing its element by its co-factor is: 2025 · 1 mark · MCQ
- If $\operatorname{adj}(A) = \begin{bmatrix} 2 & 3 & 5 \\ x & 5 & 1 \\ 3 & 3 & 4 \end{bmatrix}$ and $|A| = 4$, then the value of… 2025 · 1 mark · MCQ
- The existence of unique solution of the system of equations $x + y = \lambda$ and $5x + ky = 2$ depends on: 2025 · 1 mark · MCQ
- Find the value of the determinant given below, without expanding it at any stage… 2024 · 2 marks · Numerical
- If… 2023 · 1 mark · MCQ
- If $A$ is a square matrix of order 3, then $|2A|$ is equal to: 2023 · 1 mark · MCQ
- If $A$ is a $3 \times 3$ matrix such that… 2023 · 1 mark · MCQ
- Evaluate the following determinant without expanding. $\begin{vmatrix} 5 & 5 & 5 \\ a & b & c \\ b+c & c+a & a+b \end{vmatrix}$ 2023 · 2 marks · Short answer
- What will be the value of $x$ for the determinant equation… 2022 · 2 marks · MCQ
- The value of $\begin{vmatrix} 1 & \log_a b \\ \log_b a & 1 \end{vmatrix}$ is: 2022 · 2 marks · MCQ
- Ramu purchased 5 pens, 3 bags and 1 instrument box and paid ₹ 16. From the same shop Venkat purchased 2 pens , 1 bag and 3… 2022 · 8 marks · Case based
- If $\Delta = \begin{vmatrix} a & b & c \\ x & y & z \\ p & q & r \end{vmatrix}$, then… 2022 · 2 marks · MCQ
- Which of the following statements is correct: 2021 · 1 mark · MCQ
- For what value of $k$ inverse does not exist for the matrix $\begin{bmatrix} 1 & 2 \\ k & 6 \end{bmatrix}$: 2021 · 1 mark · MCQ
- If A is square matrix of order 3, with $|A| = 4$, then write the value of $|-2A|$. 2021 · 1 mark · Short answer
- Without expanding at any stage, find the value of the determinant… 2020 · 2 marks · Numerical
- Using properties of determinants, show that… 2020 · 4 marks · Derivation
- Using determinants, find the values of $k$, if the area of triangle with vertices $(-2, 0)$, $(0, 4)$ and $(0, k)$ is $4$ square… 2019 · 2 marks · Short answer
- Using properties of determinants prove that… 2019 · 4 marks · Derivation
- Without expanding at any stage, find the value of the determinant… 2018 · 2 marks · Short answer
- Use properties of determinants to solve for $x$: $\begin{vmatrix} x+a & b & c \\ c & x+b & a \\ a & b & x+c \end{vmatrix} = 0$… 2018 · 4 marks · Short answer
- Using properties of determinants, prove… 2018 · 4 marks · Derivation
- Without expanding at any stage, find the value of: $\begin{vmatrix} a & b & c \\ a+2x & b+2y & c+2z \\ x & y & z \end{vmatrix}$ 2018 · 2 marks · Numerical
- Using properties of determinants, prove that… 2017 · 5 marks · Derivation
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