An alpha particle moves along a circular path of radius 0.5 mm in a magnetic field of \( 2 \times 10^{-2} \, \text{T} \). The de Broglie wavelength associated with the alpha particle is nearly
(Planck’s constant \( h = 6.63 \times 10^{-34} \, \text{Js} \))
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: