Assertion (A): If x and y are the distance along x and y axes...

Assertion (A): "If $x$ and $y$ are distances along $x$ and $y$ axes respectively, then the dimensions of ($\frac{d^3 y}{d x^3}$) is $M⁰ L^{-2} T^{0 . "}$ - Here, $y$ has dimensions of length (L). - $x$ also has dimensions of length (L). - Differentiating once: ($\frac{d y}{d x} \rightarrow$L / L=) dimensionless. - Differentiating twice: ($\frac{d^2 y}{d x^2} \rightarrow$) dimension $=1 / L$. - Differentiating thrice: ($\frac{d^3 y}{d x^3} \rightarrow$) dimension $=1 / L²=L^{-2}$. So, dimensions = $M⁰ L^{-2} T⁰$. (1) Assertion (A) is true.