$(a)\;K_{1}K_{4}=K_{2}K_{3}\qquad(b)\;K_{1}K_{2}=K_{3}K_{4}\qquad(c)\;K_{1}K_{3}=K_{2}K_{1}\qquad(d)\;None$

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Answer : $\;K_{1}K_{2}=K_{3}K_{4}$

Explanation :

Since no heat flows through the central rod , temperatures at C and D are the same .

The above is like a wheatstone Network .

$\large\frac{L_{1}}{K_{1}A_{1}} \;. \large\frac{L_{2}}{K_{2}A_{2}} = \large\frac{L_{3}}{K_{3}A_{3}} \; . \large\frac{L_{4}}{K_{4}A_{4}}$

$L_{1}=L_{2}=L_{3}=L_{4}$

$A_{1}=A_{2}=A_{3}=A_{4}$

$K_{1}K_{2}=K_{3}K_{4}$

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