If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula for C²LR is

The correct option is [M⁰L⁰T³I⁰].

To find the dimensional formula for $C^{2}LR$ (where $C$ is capacitance, $L$ is inductance, and $R$ is resistance), we can use well-known time constants in electrical circuits instead of deriving the dimensions of each quantity from scratch.

Let us recall the following relationships:
1. The time constant of an Inductor-Resistor ($L-R$) circuit is given by:
${\tau }_1=\frac{L}{R}$
This has the dimensions of time $\left[T\right]$.

2. The time constant of a Resistor-Capacitor ($R-C$) circuit is given by:
${\tau }_2=RC$
This also has the dimensions of time $\left[T\right]$.

Now, let us rewrite the expression $C^{2}LR$ in terms of these time constants:
$C^{2}LR=(RC{)}^2\times \left(\frac{L}{R}\right)$

Substituting the dimensions of $RC$ and $\frac{L}{R}$:
$\left[C^{2}LR\right]=[RC{]}^2\times \left[\frac{L}{R}\right]$
$\left[C^{2}LR\right]=[T{]}^2\times [T]=[T^3]$

Expressing this in the standard form with mass ($M$), length ($L$), time ($T$), and current ($I$), we get:
$\left[C^{2}LR\right]=\left[M^0{L}^0{T}^3{I}^0\right]$