



The total number of compounds from below when treated with hot KMnO4 giving benzoic acid is:
Identify product [A], [B], and [C] in the following reaction sequence.
The major product of the following reaction is: 
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Amine is a type of compound which is derived from ammonia (NH3). According to Organic chemistry, they are basically classified as the functional groups of the organic nitrogen compounds that contain nitrogen atoms with a lone pair.
It is formed when one hydrogen atom in ammonia is substituted by an alkyl or aromatic group. Amino acids and methyl amine are the best examples that why aromatic amines include aniline.
Amines that have two organic substitutes either alkyl or aryl ones or both and are bound to the nitrogen together with one hydrogen are termed as secondary amines. For Example, Dimethylamine.
Tertiary Amines are the amines where the nitrogen consists of three organic substitutes. For example, Trimethylamine and EDTA.