Mark and name the following on the outline map of the world with suitable index:
An industrial region in South Africa - Kimberley.
List-I: Basis | List-II: Industry Type |
---|---|
(A) Ownership | (III) Private sector |
(B) Capital investment | (IV) Cottage industry |
(C) Use of their products | (I) Consumer goods |
(D) Raw materials used by them | (II) Mineral based |
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]