Which of the following amine(s) show(s) positive carbamylamine test?
The carbamylamine test is used to detect primary amines. It results in the formation of an isocyanide (carbamylamine).
Option A \( \text{NH}_2 \) (Phenylamine) is a primary amine and will give a positive result.
Option B \( \text{(CH}_3)_2\text{NH} \) (Dimethylamine) is a secondary amine and does not give a positive result.
Option C \( \text{CH}_3\text{NH}_2 \) (Methylamine) is a primary amine and will give a positive result.
Option D \( \text{(CH}_3)_3\text{N} \) (Trimethylamine) is a tertiary amine and does not give a positive result.
Option E \( \text{H}\text{NCH}_3 \) (Methylamine attached to a benzene ring) is a primary amine and will give a positive result.
Thus, the correct options are A and C.
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to: