List of top Questions asked in AP EAPCET- 2022

If the rank of the matrix \[ A = \begin{bmatrix} 1 & 2 & 1 & -1 \\ -1 & 2 & 3 & 5 \\ 0 & 1 & k & k \end{bmatrix} \] is 2 and \( k \) is a real number, then \( k \) is a root of which of the following quadratic equations?

Evaluate: \[ \sum_{k=1}^{6} \left[ \sin\left( \frac{2\pi k}{7} \right) - i \cos\left( \frac{2\pi k}{7} \right) \right] \]

If \( (x - iy)^{1/3} = a - ib \), then the value of \( \frac{x}{2a} + \frac{y}{2b} \) is:

If \( x = -5 + 2\sqrt{-4} \), then the value of \( x^4 + 9x^3 + 35x^2 - x + 4 \) is:

If the solution of the system of simultaneous equations \[ \frac{1}{x} + \frac{2}{y} - \frac{3}{z} = 1, \quad \frac{2}{x} - \frac{4}{y} + \frac{3}{z} = 1, \quad \frac{3}{x} + \frac{6}{y} - \frac{6}{z} = 4 \] is \( x = \alpha, y = \beta, z = \gamma \), then the value of \( \alpha^2 + \gamma^2 \) is: