Step 1: Vasco da Gama, the renowned Portuguese navigator, reached India in 1498, paving the way for a sea route to the Indian subcontinent.
Step 2: Junagadh, located in Saurashtra, was one of the princely states that initially hesitated to join India post-independence but eventually became a part of the country.
Step 3: The United Nations (UN) played a crucial role in supporting decolonisation after World War II, assisting numerous regions in their struggles for independence.
Step 4: Kolkata became the first Indian city to launch a metro railway system, with its inaugural service beginning in 1984.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]