List of top Mathematics Questions on solution of system of linear inequalities in two variables asked in KEAM

If \( Z = 1 + i \) and \( Z - 24\overline{Z} = \lambda Z^2 \), find \( \lambda \).

If \( \overrightarrow{a} \) and \( \overrightarrow{b} \) are two unit vectors and if \( \frac{\pi}{4} \) is the angle between \( \overrightarrow{a} \) and \( \overrightarrow{b} \), then \[ (\overrightarrow{a} + (\overrightarrow{a} \cdot \overrightarrow{b})\overrightarrow{b}) \cdot (\overrightarrow{a} - (\overrightarrow{a} \cdot \overrightarrow{b})\overrightarrow{b}) \] is: