Spot the error and rewrite the correct sentence :
He prescribe medicine alongwith a few exercises to his patients.
The errors in the given sentence are:
1. "prescribe" should be "prescribes" to match the singular subject "He".
2. "alongwith" should be "along with", as "alongwith" is incorrect usage in English.
Corrected Sentence: He prescribes medicine along with a few exercises to his patients.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]