Identify correct statement/s:
(A) \( -\text{OCH}_3 \) and \( -\text{NHCOCH}_3 \) are activating groups.
(B) \( -\text{CN} \) and \( -\text{OH} \) are meta directing groups.
(C) \( -\text{CN} \) and \( -\text{SO}_3\text{H} \) are meta directing groups.
(D) Activating groups act as ortho- and para-directing groups.
(E) Halides are activating groups.
Choose the correct answer from the options given below:
- (A) True: \( -\text{OCH}_3 \) and \( -\text{NHCOCH}_3 \) are electron-donating groups, thus activating the aromatic ring.
- (B) True: \( -\text{CN} \) and \( -\text{OH} \) are both meta directing groups.
- (C) False: \( -\text{SO}_3\text{H} \) is actually a meta directing group, but \( -\text{CN} \) is a meta directing group too, making the statement true.
- (D) True: Activating groups usually act as ortho-para directing groups.
- (E) False: Halides are deactivating and ortho-para directing.
Thus, the correct answer is \( \text{(A)}, \text{(B)}, \text{and (E)} \).
Final Answer: (1) (A), (B) and (E) only.
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: