To determine the dimensions of mass when force (F), velocity (V), and time (T) are taken as fundamental units, we start by expressing mass in terms of these units.$\\$The dimensional formula for force is given by:$\\ [F] = MLT^{-2} \\$The dimensional formula for velocity is given by:$\\ [V] = LT^{-1} \\$We need to express mass (M) in terms of F, V, and T. Assume:$\\ M = F^a V^b T^c \\$Substitute the dimensional formulas:$\\ M = (MLT^{-2})^a (LT^{-1})^b (T)^c \\$Equating the dimensions on both sides, we have:$\\ M^1 L^0 T^0 = M^a L^{a+b} T^{-2a-b+c} \\$By comparing the powers of M, L, and T, we get:$\\ 1 = a \\ 0 = a + b \\ 0 = -2a - b + c \\$From $1 = a,$ we have $a = 1. \\$Substitute $a = 1$ into $0 = a + b: \\ 0 = 1 + b \\ b = -1 \\$Substitute $a = 1$ and $b = -1$ into $0 = -2a - b + c: \\ 0 = -2(1) - (-1) + c \\ 0 = -2 + 1 + c \\ c = 1 \\$Thus, the dimensions of mass in terms of F, V, and T are:$\\ M = F^1 V^{-1} T^1 \\$Therefore, the correct option is:$\\$Option 4: $[FV^{-1}T]$