For $ \alpha, \beta, \gamma \in \mathbb{R} $, if $$ \lim_{x \to 0} \frac{x^2 \sin \alpha x + (\gamma - 1)e^{x^2} - 3}{\sin 2x - \beta x} = 3, $$ then $ \beta + \gamma - \alpha $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
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 –