c
(c) Both the cylinders are in parallel, for the heat flow from one end as shown.

Hence \({K_{eq}} = \frac{{{K_1}{A_1} + {K_2}{A_2}}}{{{A_1} + {A_2}}}\); where \(A_1\)

= Area of cross-section of inner cylinder = \(\pi\) \(R_2\) and \({A_2} = \)Area of cross-section of cylindrical shell \( = \pi \{ {(2R)^2} - {(R)^2}\} = 3\pi {R^2}\)

\(\Rightarrow {K_{eq}} = \frac{{{K_1}(\pi {R^2}) + {K_2}(3\pi {R^2})}}{{\pi {R^2} + 3\pi {R^2}}} = \frac{{{K_1} + 3{K_2}}}{4}\)