a
(a)

\(y=x^2 \cos ^2 2 \pi\left(\frac{\beta \gamma}{\alpha}\right)\)

The argument of a trigonometric ratio is always dimensionless.

\(\frac{\beta \gamma}{\alpha}=\left[ M ^0 L ^0 T ^0\right] \text { or } \beta \gamma=\alpha \Rightarrow \gamma=\frac{ T }{ L ^2}\)

\(\text { and } y=x^2 \Rightarrow\left[ L ^2\right]\)

\(\alpha= s ^{-1} \Rightarrow\left[ T ^{-1}\right], \beta=\left[ LT ^{-1}\right]^{-1} \Rightarrow\left[ L ^{-1} T \right]\)

\(y=m^2\)

\(\gamma= ms ^{-2}\)