Match the LIST-I with LIST-II.
Choose the correct answer from the options given below :
Let's analyze the molecular structures: ICl\(^-\): This ion has a central iodine atom with 2 bonding pairs and 3 lone pairs, resulting in a 2 : 3 ratio (option III). H\(_2\)O:
The oxygen atom has 2 lone pairs and 2 bonding pairs, which gives the ratio 2 : 2 (option IV). SO\(_2\):
The sulfur atom has 2 bonding pairs and 1 lone pair, leading to a 4 : 1 ratio (option II).
XeF\(_4\): The xenon atom has 4 bonding pairs and 2 lone pairs, giving the ratio 4 : 2 (option I).
Therefore, the correct matching is: A-III, B-IV, C-II, D-I.
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: