\(4\text{HNO}_3(\text{l}) + 3\text{KCl}(\text{s}) \rightarrow \text{Cl}_2(\text{g}) + \text{NOCl}(\text{g}) + 2\text{H}_2\text{O}(\text{g}) + 3\text{KNO}_3(\text{s})\)
\(\because 110 \, \text{g of KNO}_3 \Rightarrow \text{moles of KNO}_3 = \frac{110}{101} = 1.089 \, \text{mol}\)
As, \(4 \, \text{mol of HNO}_3 \text{ produces } 3 \, \text{mol of KNO}_3\).
\(\text{Hence, the moles of HNO}_3 \text{ required to produce } 1.089 \text{ moles of KNO}_3 =\)
\(=43×1.089=1.452 mol\)
\(\text{Hence, mass of HNO}_3 \text{ required} = 1.452 \times 63\)
\(≃ 91.5 g\)
So, the correct option is (C): \(91.5\ \text{g}\)
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: