
If A and B are two events such that \( P(A \cap B) = 0.1 \), and \( P(A|B) \) and \( P(B|A) \) are the roots of the equation \( 12x^2 - 7x + 1 = 0 \), then the value of \(\frac{P(A \cup B)}{P(A \cap B)}\)
Minerals are the naturally occurring, homogeneous inorganic solid substances. They are having a definite chemical composition and crystalline structure, hardness and color. For example, copper pyrite, calamine, etc.

Impurities in an ore are called gauge. The removal of a gauge from the ore is called concentration ore.
Several steps are involved in the extraction of pure metal from ores. Major steps are as follows –