The silver mirror test is a chemical test used to identify aldehydes. Aldehydes, when treated with ammoniacal silver nitrate (Tollens’ reagent), reduce silver ions to metallic silver, forming a mirror-like deposit.
- Formic acid (A) is an aldehyde and will react with Tollens’ reagent.
- Formaldehyde (B) is also an aldehyde and will give a positive silver mirror test.
- Benzaldehyde (C) is another aldehyde and will also give a positive silver mirror test.
- Acetone (D) is a ketone and does not reduce Tollens’ reagent, so it will not give a silver mirror.
Thus, the correct answer is (2), A, B, and C only.
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: