A=\(\begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}\)if sum of diagonal elements of A13 is 3n then n equal to:
- 5
- 7
- 9
- 13
The Correct Option is B
Solution and Explanation
Top Questions on Matrices
Let \( A = \begin{bmatrix} \alpha & -1 \\6 & \beta \end{bmatrix},\ \alpha > 0 \), such that \( \det(A) = 0 \) and \( \alpha + \beta = 1 \). If \( I \) denotes the \( 2 \times 2 \) identity matrix, then the matrix \( (1 + A)^5 \) is:
Let $A = \begin{bmatrix} \cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta \end{bmatrix}$. If for some $\theta \in (0, \pi)$, $A^2 = A^T$, then the sum of the diagonal elements of the matrix $(A + I)^3 + (A - I)^3 - 6A$ is equal to
- If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:
Let $ A $ be a $ 3 \times 3 $ matrix such that $ | \text{adj} (\text{adj} A) | = 81.
$ If $ S = \left\{ n \in \mathbb{Z}: \left| \text{adj} (\text{adj} A) \right|^{\frac{(n - 1)^2}{2}} = |A|^{(3n^2 - 5n - 4)} \right\}, $ then the value of $ \sum_{n \in S} |A| (n^2 + n) $ is:- Let $ A $ be a matrix of order $ 3 \times 3 $ and $ |A| = 5 $. If $ |2 \, \text{adj}(3A \, \text{adj}(2A))| = 2^{\alpha} \cdot 3^{\beta} \cdot 5^{\gamma}, \quad \alpha, \beta, \gamma \in \mathbb{N} $ then $ \alpha + \beta + \gamma $ is equal to
Questions Asked in JEE Main exam
- Let \( f: \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) \] for all \( x, y \in \mathbb{R} \). If \( f(0) = 1 \), then the value of \( 24f^{(4)}\left(\frac{5\pi}{3}\right) \) is:
- JEE Main - 2025
- Differential Calculus
- The largest \( n \in \mathbb{N} \) such that \( 3^n \) divides 50! is:
- JEE Main - 2025
- Number Systems
For the reaction \( A \rightarrow \) products,
The reaction was started with 2.5 mol L\(^{-1}\) of A.- JEE Main - 2025
- Zero-order Reactions
Consider the following electrochemical cell at standard condition. \[ \text{Au(s) | QH}_2\text{ | QH}_X(0.01 M) \, \text{| Ag(1M) | Ag(s) } \, E_{\text{cell}} = +0.4V \] The couple QH/Q represents quinhydrone electrode, the half cell reaction is given below: \[ \text{QH}_2 \rightarrow \text{Q} + 2e^- + 2H^+ \, E^\circ_{\text{QH}/\text{Q}} = +0.7V \]
- JEE Main - 2025
- Electrochemical Cells
Consider the following compound (X):
The most stable and least stable carbon radicals, respectively, produced by homolytic cleavage of corresponding C - H bond are:- JEE Main - 2025
- Allotropes of carbon