Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:
(iii) Find \( A^{-1} \), if possible, and write the formula to find \( \mathbf{X} \).
Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:
Solution and Explanation
Top Questions on Matrices
- If $A = \begin{bmatrix} 2 & 3 \\ -1 & 2 \end{bmatrix}$, then show that $A^2 - 4A + 7I = 0$.
- If $\begin{bmatrix} 2x-1 & 3x \\ 0 & y^2 - 1 \end{bmatrix}$ is a matrix, then the value of $(x - y)$ is:
- Let $A$ be a square matrix of order 3. If $|A| = 5$, then $|adj A|$ is:
- The matrix $A = \begin{bmatrix} \sqrt{5} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{bmatrix}$ is an:
- If $A$ and $B$ are two square matrices each of order 3 with $|A| = 3$ and $|B| = 5$, then $|2AB|$ is:
Questions Asked in CBSE CLASS XII exam
- Let $f: A \to B$ be defined by $f(x) = \frac{x - 2}{x - 3}$, where $A = \mathbb{R} - \{3\}$ and $B = \mathbb{R} - \{1\}$. Discuss the bijectivity of the function.
- CBSE CLASS XII - 2025
- Relations and functions
- Solve the differential equation \[ \frac{dy}{dx} = \cos x - 2y \]
- CBSE CLASS XII - 2025
- Differential Equations
Three friends A, B, and C move out from the same location O at the same time in three different directions to reach their destinations. They move out on straight paths and decide that A and B after reaching their destinations will meet up with C at his pre-decided destination, following straight paths from A to C and B to C in such a way that \( \overrightarrow{OA} = \hat{i}, \overrightarrow{OB} = \hat{j} \), and \( \overrightarrow{OC} = 5 \hat{i} - 2 \hat{j} \), respectively.
Based upon the above information, answer the following questions:
(i) Complete the given figure to explain their entire movement plan along the respective vectors.}
(ii) Find vectors \( \overrightarrow{AC} \) and \( \overrightarrow{BC} \).}
(iii) (a) If \( \overrightarrow{a} = 2 \hat{i} - \hat{j} + 4 \hat{k} \), distance of O to A is 1 km, and from O to B is 2 km, then find the angle between \( \overrightarrow{OA} \) and \( \overrightarrow{OB} \). Also, find \( | \overrightarrow{a} \times \overrightarrow{b} | \).}
(iii) (b) If \( \overrightarrow{a} = 2 \hat{i} - \hat{j} + 4 \hat{k} \), find a unit vector perpendicular to \( (\overrightarrow{a} + \overrightarrow{b}) \) and \( (\overrightarrow{a} - \overrightarrow{b}) \).- A woman discovered a scratch along a straight line on a circular table top of radius 8 cm. She divided the table top into 4 equal quadrants and discovered the scratch passing through the origin inclined at an angle \( \frac{\pi}{4} \) anticlockwise along the positive direction of x-axis. Find the area of the region enclosed by the x-axis, the scratch and the circular table top in the first quadrant, using integration.
- CBSE CLASS XII - 2025
- Integration
- (a) Find the point Q on the line \( \frac{2x + 4}{6} = \frac{y + 1}{2} = \frac{-2z + 6}{-4} \) at a distance of \( \frac{\sqrt{5}}{2} \) from the point \( P(1, 2, 3) \).
- CBSE CLASS XII - 2025
- Coordinate Geometry