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(D) The dimensional formula of the coefficient of thermal conductivity $[k]$ is $[M^1 L^1 T^{-3} K^{-1}]$.The dimensional formula of the universal gra

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$+\frac{1}{2}$

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(D) The dimensional formula of the coefficient of thermal conductivity $[k]$ is $[M^1 L^1 T^{-3} K^{-1}]$.The dimensional formula of the universal gravitational constant $[G]$ is $[M^{-1} L^3 T^{-2}]$.Taking the ratio,$\frac{[k]}{[G]} = \frac{[M^1 L^1 T^{-3} K^{-1}]}{[M^{-1} L^3 T^{-2}]} = [M^{1-(-1)} L^{1-3} T^{-3-(-2)} K^{-1}] = [M^2 L^{-2} T^{-1} K^{-1}]$.Comparing this with the given dimensional formula $[M^{2a} L^{4b} T^{2c} K^d]$:$2a = 2 \implies a = 1$$4b = -2 \implies b = -\frac{1}{2}$$2c = -1 \implies c = -\frac{1}{2}$$d = -1$Now,calculating the required expression: $\frac{a+b}{c+b} - d = \frac{1 + (-1/2)}{-1/2 + (-1/2)} - (-1) = \frac{1/2}{-1} + 1 = -\frac{1}{2} + 1 = \frac{1}{2}$.

$A$ physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula $[M^{2a} L^{4b} T^{2c} K^d]$. Then the value of $\frac{a+b}{c+b}-d$ is

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