(A) The graph between magnetic susceptibility and magnetising field is as shown in (III).
(B) For \( x < a \), the magnetic field due to a current-carrying wire is given by: \[ B = \frac{\mu_0 I x}{2 \pi a^2}, \] matching graph (IV).
(C) For \( x > a \), the magnetic field due to a current-carrying wire is given by: \[ B = \frac{\mu_0 I}{2 \pi x}, \] matching graph (I).
(D) The magnetic field inside a solenoid varies with distance as shown in (II).
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: