Compare the Limits

Calculus Level 4

{a=limx0ln(cos(2x))3x2b=limx0sin2(2x)x(1ex)c=limx1xxlnx \large \begin{cases} a = \displaystyle\lim_{x\rightarrow 0} \dfrac{\ln(\cos(2x))}{3x^2} \\ \\ b = \displaystyle\lim_{x\rightarrow 0} \dfrac{\sin^2(2x)}{x(1-e^x)} \\ \\ c = \displaystyle\lim_{x\rightarrow 1} \dfrac{\sqrt{x} - x }{\ln x} \end{cases}
Then , a,b,c a , b , c satisfy which of the following relation :

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