Step 1: Verifying the Assertion A
Given mass of hydrated oxalic acid = 3.1500 g
Molar mass of hydrated oxalic acid = 126 g/mol
Volume of solution = 250.0 mL = 0.250 L
To calculate molarity (M), we use the formula: \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \] Moles of solute: \[ \text{moles} = \frac{3.1500 \, \text{g}}{126 \, \text{g/mol}} = 0.0250 \, \text{mol} \] Thus, molarity: \[ M = \frac{0.0250 \, \text{mol}}{0.250 \, \text{L}} = 0.1 \, \text{M} \] So, Assertion A is correct.
Step 2: Verifying the Reason R
The molar mass of hydrated oxalic acid is indeed 126 g/mol, as given in the question. This confirms that Reason R is correct.
Thus, both Assertion A and Reason R are true, and Reason R explains Assertion A.
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: