In my view, one of Chhatrapati Shivaji Maharaj’s most remarkable contributions to the Maratha Empire and India’s defense was the creation of a formidable naval force.
In conclusion, the establishment of a strong naval force by Shivaji Maharaj was instrumental in defending his empire and asserting India’s control over its seas.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]