Statement I:
The first ionisation enthalpy of group 14 elements is indeed higher than that of group 13 elements, as the number of valence electrons increases from group 13 to 14, leading to a higher ionisation energy.
Thus, Statement I is correct
Statement II: This statement is incorrect.
The melting points and boiling points of group 13 elements are generally lower than those of group 14 elements due to the stronger metallic bonding in group 14 elements.
Thus, Statement II is incorrect.
Therefore, the correct answer is (1).
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: