Question

Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, $\left[x\right]={\mathrm{M}}^a{\mathrm{L}}^b{\mathrm{T}}^c$. The quantity mass
(a) can always be dimensionally represented in terms of L, T and x,
(b) can never be dimensionally represented in terms of L, T and x,
(c) may be represented in terms of L, T and x if a = 0,
(d) may be represented in terms of L, T and x if $a\ne 0$.

Answer 1

(d) may be represented in terms of L, T and x if $a\ne 0$

If a = 0, then we cannot represent mass dimensionally in terms of L, T and x, otherwise it can be represented in terms of L, T and x.