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Suppose a block of constant cross section area $A$ and length $L$ has its ends maintained at temperature $0^{\circ}C$ and $100^{\circ}C$ . And the thermal conductivity of block varies as $K = K_0(1 + \alpha x)$ where $x$ is distance from the end which is at $100^{\circ}C$ and $\alpha$ is a positive constant

Then the temperature in the middle of rod at steady state will be (options in $^{\circ}C$