Choose the correct option from the following sentences which uses a more definite modal auxiliary.
Neeraj Chopra may not participate in the world championship due to an ankle injury.
The modal auxiliary "cannot" expresses a more definite restriction on participation, implying that participation is impossible rather than just uncertain. "May not" and "might not" indicate possibilities, whereas "should not" suggests advice rather than certainty.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]