Consider the efficiency of Carnot's engine is given by $\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}$, where $\alpha$ and $\beta$ are constants. If $T$ is temperature, $k$ is Boltzman constant, $\theta$ is angular displacement and $x$ has the dimensions of length. Then, choose the incorrect option.
JEE MAIN 2022, Diffcult
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$[\alpha \beta]=[\eta]=[\sin \theta]=$ Dimensionless
$\left[\eta^{-1} \sin \theta\right]=[\alpha \beta]=\text { D.L. }$
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