An expression for a dimensionless quantity $P$ is given by $P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)$; where $\alpha$ and $\beta$ are constants, $x$ is distance ; $k$ is Boltzmann constant and $t$ is the temperature. Then the dimensions of $\alpha$ will be
  • A$[ M ^{0} L ^{-1} T ^{0} ]$
  • B$[ ML ^{0} T ^{-2}]$
  • C$[ MLT ^{-2}]$
  • D$[ ML ^{2} T ^{-2}]$
JEE MAIN 2022, Medium
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