Consider two physical quantities A and B rela | vedclass

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(B) According to the principle of homogeneity of dimensions,quantities added or subtracted must have the same dimensions.Since $B$ is subtracted by $x

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$L^2 M^{-1} T^1$

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(B) According to the principle of homogeneity of dimensions,quantities added or subtracted must have the same dimensions.Since $B$ is subtracted by $x^2$,the dimension of $B$ must be equal to the dimension of $x^2$.$[B] = [x^2] = L^2$.Now,the equation is $E = \frac{B - x^2}{At}$. Rearranging for $A$,we get $A = \frac{B - x^2}{Et}$.Substituting the dimensions: $[A] = \frac{[L^2]}{[E][t]}$.Given $[E] = M^1 L^2 T^{-2}$ and $[t] = T^1$,we have $[A] = \frac{L^2}{(M^1 L^2 T^{-2})(T^1)} = \frac{L^2}{M^1 L^2 T^{-1}} = M^{-1} T^1$.Finally,the dimension of $AB$ is $[A][B] = (M^{-1} T^1)(L^2) = L^2 M^{-1} T^1$.

List-$I$	List-$II$
$A$. Meter $(L)$	$I$. $\sqrt{\frac{hc}{G}}$
$B$. Second $(S)$	$II$. $\sqrt{\frac{Gh}{c^5}}$
$C$. Kilogram $(M)$	$III$. $\sqrt{\frac{L^2c^3}{Gh}}$
$D$. Kelvin $(K)$	$IV$. $\sqrt{\frac{Gh}{c^3}}$

Consider two physical quantities $A$ and $B$ related to each other as $E = \frac{B - x^2}{At}$,where $E, x,$ and $t$ have dimensions of energy,length,and time respectively. The dimension of $AB$ is

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