Given below are two statements: one is labelled as Assertion (A)...

The exponent of an exponential function must be a dimensionless quantity. Therefore, the term $\beta t$ is dimensionless.

$[\beta][t] = [M^0 L^0 T^0] \Rightarrow [\beta][T] = 1 \Rightarrow [\beta] = [T^{-1}]$.

Thus, the Reason (R) is false.

According to the principle of homogeneity, the dimensions of the left-hand side must equal the dimensions of the right-hand side. The term $(1 - e^{-\beta t})$ is a dimensionless number.

$[x] = \dfrac{[\alpha]}{[\beta]} \Rightarrow [L] = \dfrac{[\alpha]}{[T^{-1}]} \Rightarrow [\alpha] = [L][T^{-1}] = [L T^{-1}]$.

Thus, the Assertion (A) is true.

Therefore, Assertion (A) is true but Reason (R) is false.

Answer: Assertion (A) is true but Reason (R) is false.