Corrected Pairs:
The terms in Group ‘A’ refer to key historical events and figures in Indian history. The incorrect pair in item (b) is corrected as Sheikh Abdullah played a significant role in the merger of Kashmir with India, not Shaikh Abdulla.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]