The reaction proceeds as follows: 1. The anisole (methoxybenzene) undergoes nitration with \( \text{HNO}_3/\text{H}_2\text{SO}_4 \) to form the product (A), which is 4-nitroanisole. 2. Subsequently, bromination with \( \text{Br}_2 \) (in the presence of excess iron) results in the brominated product (B), 4-bromo-2-nitroanisole.
Thus, the major products are (A) and (B) as represented in option (2).
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: