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.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: