Two conductors have the same resistance at $0^\circ\text{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are:
Answer: (B) $\dfrac{\alpha_1 + \alpha_2}{2},\ \dfrac{\alpha_1 + \alpha_2}{2}$
Series: $R_0(1 + \alpha_1 t) + R_0(1 + \alpha_2 t) = 2R_0\left(1 + \dfrac{\alpha_1 + \alpha_2}{2}t\right)$, so $\alpha_s = \dfrac{\alpha_1 + \alpha_2}{2}$.
Parallel: $\dfrac1{R_p} = \dfrac1{R_0}\left[(1 + \alpha_1 t)^{-1} + (1 + \alpha_2 t)^{-1}\right] \approx \dfrac2{R_0}\left(1 - \dfrac{\alpha_1 + \alpha_2}{2}t\right)$, so $R_p \approx \dfrac{R_0}{2}\left(1 + \dfrac{\alpha_1 + \alpha_2}{2}t\right)$ and $\alpha_p = \dfrac{\alpha_1 + \alpha_2}{2}$ too.
Solution by Sreeraj P, M.Sc Physics