Match List - I with List - II:
Choose the correct answer from the options given below:
We will match the structure in List I with its corresponding IUPAC name in List II.
- (A) The structure corresponds to 4-Methylpent-1-ene. This is because the longest chain is 5 carbons, with a methyl group at position 4 and a double bond at position 1.
- (B) The structure corresponds to 4,4-Dimethylheptane. The central carbon is attached to two methyl groups, and the longest chain has 7 carbon atoms.
- (C) The structure corresponds to 3-Ethyl-5-methylheptane. It is a heptane chain with an ethyl group at position 3 and a methyl group at position 5.
- (D) The structure corresponds to 2-Methyl-1,3-pentadiene. It is a pentadiene chain with a methyl group at position 2 and double bonds at positions 1 and 3. Thus, the correct matching is (A)-(I)}, (B)-(III), (C)-(II), (D)-(IV).
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: