What are the dimensions of energy, and which of the following options correctly represents them: (a) MLT, (b) LT2/m, (c) ML2T⁻², (d) m2L3T?

Work done ($W$) is defined as force ($F$) multiplied by distance ($d$):

$$W = F \times d$$

Force ($F$) is defined as mass ($m$) multiplied by acceleration ($a$):

$$F = m \times a$$

The dimensions of mass are M.
The dimensions of acceleration are length (L) divided by time squared (T$^2$), so:

$$[a] = \frac{\text{L}}{\text{T}^2} = \text{L T}^{-2}$$

Therefore, the dimensions of force are:

$$[F] = [\text{m}] \times [a] = \text{M} \times \text{L T}^{-2} = \text{M L T}^{-2}$$

Now substitute the dimensions of force and distance into the work done formula:

$$[W] = [F] \times [d]$$ $$[W] = (\text{M L T}^{-2}) \times \text{L}$$ $$[W] = \text{M L}^2 \text{ T}^{-2}$$

The dimensions of energy are $\text{M L}^2 \text{ T}^{-2}$.
Let's check the options:

(a) MLT

(b) LT$^2$/m (which is M$^{-1}$ L T$^2$)

(c) ML$^2$T$^{-2}$

(d) m$^2$L$^3$T (assuming 'm' is mass, this would be M$^2$L$^3$T)

Option (c) matches our calculated dimensions.

The correct combination of dimensions for energy is $\boxed{\text{c) ML}^2\text{T}^{-2}}$.