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 carbamylamine test is used to detect the presence of primary amines (1° amines).
Reaction Mechanism:
- When a primary amine (either aliphatic or aromatic) is treated with chloroform (CHCl₃) in the presence of an alkali (such as potassium hydroxide, KOH), it undergoes a reaction to form an isocyanate.
- This is a characteristic test for primary amines, as secondary and tertiary amines do not undergo this reaction.
The reaction can be represented as follows:
\[ \text{RNH}_2 \xrightarrow{\text{CHCl}_3 + \text{KOH}} \text{RNC} \] Where:
- RNH₂ represents the primary amine group.
- CHCl₃ is chloroform, which reacts with the amine in the presence of an alkaline medium.
- KOH is potassium hydroxide, which is used to generate the basic condition needed for the reaction.
- RNC represents the isocyanate product formed.
Note:
- The reaction is specific to primary amines (1° amines), both aliphatic and aromatic. Secondary (2°) and tertiary (3°) amines do not respond to this test. Thus, if an isocyanate (RNC) is formed, it indicates the presence of a primary amine.
This test is useful in organic chemistry to distinguish primary amines from other types of amines.
Amines are usually formed from amides, imides, halides, nitro compounds, etc. They exhibit hydrogen bonding which influences their physical properties. In alkyl amines, a combination of electron releasing, steric and H-bonding factors influence the stability of the substituted ammonium cations in protic polar solvents and thus affect the basic nature of amines. Alkyl amines are found to be stronger bases than ammonia. Amines being basic in nature, react with acids to form salts. Aryldiazonium salts, undergo replacement of the diazonium group with a variety of nucleophiles to produce aryl halides, cyanides, phenols and arenes.
The total number of compounds from below when treated with hot KMnO4 giving benzoic acid is:
Two blocks of masses \( m \) and \( M \), \( (M > m) \), are placed on a frictionless table as shown in figure. A massless spring with spring constant \( k \) is attached with the lower block. If the system is slightly displaced and released then \( \mu = \) coefficient of friction between the two blocks.
(A) The time period of small oscillation of the two blocks is \( T = 2\pi \sqrt{\dfrac{(m + M)}{k}} \)
(B) The acceleration of the blocks is \( a = \dfrac{kx}{M + m} \)
(\( x = \) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \( \dfrac{m\mu |x|}{M + m} \)
(D) The maximum amplitude of the upper block, if it does not slip, is \( \dfrac{\mu (M + m) g}{k} \)
(E) Maximum frictional force can be \( \mu (M + m) g \)
Choose the correct answer from the options given below:
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: