Match the following:
List-I (Metal in drinking water) | List-II (Maximum prescribed concentration in ppm) |
---|---|
A) Mn | I) \( 0.05 \) |
B) Zn | II) \( 3.0 \) |
C) Cd | III) \( 0.005 \) |
D) Cu | IV) \( 5.0 \) |
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: