Find the IUPAC name of the compound.
The given compound is a substituted benzoic acid. We need to identify the positions of the substituents and name the compound according to the IUPAC rules. - The parent structure is benzoic acid, with a carboxyl group (-COOH) at position
1. - The other substituents are: - A bromine (Br) group attached at position
2. - A nitro (NO\(_2\)) group attached at position 3. Thus, the correct IUPAC name for this compound is 2-Bromo-3-nitrobenzoic acid.
Conc. HNO\(_3\)
Designate whether each of the following compounds is aromatic or not aromatic.
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:
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 maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank is _________ cm. (Take \( g = 10 \, {m/s}^2 \)).