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A physical quantity of the dimensions of length that can be formed out of c, G and $e^{2}/(4\pi\varepsilon_{0})$ is [ c is velocity of light, G is universal constant of gravitation and e is charge]
Explanation
Let dimensions of length is related as, $L = [c]^{x}[G]^{y}[e^{2}/(4\pi\varepsilon_{0})]^{z}$ $L = [LT^{-1}]^{x}[M^{-1}L^{3}T^{-2}]^{y}[ML^{3}T^{-2}]^{z}$. $[L] = [L^{x+3y+3z}M^{-y+z}T^{-x-2y-2z}]$ Comparing both sides $-y + z = 0 \Rightarrow y = z$. $x + 3y + 3z = 1$. $-x - 4z = 0 ( \because y = z)$ From (i), (ii) & (iii) $z = y = 1/2$, $x = -2$. Hence, $L = c^{-2}[G \cdot e^{2}/(4\pi\varepsilon_{0})]^{1/2}$