To find the dimensional formula of surface tension using energy (E), velocity (V), and time (T) as fundamental quantities, we start by recalling the definition of surface tension.$\\$Surface tension $(\gamma)$ is defined as the force per unit length acting along the surface of a liquid.$\\$In terms of energy, surface tension can also be defined as energy per unit area.$\\$The dimensional formula for surface tension in terms of mass (M), length (L), and time (T) is:$\\ [\gamma] = [M^1L^0T^{-2}] \\$Now, we need to express this in terms of energy (E), velocity (V), and time (T).$\\$Recall the dimensional formulas for energy and velocity:$\\ [E] = [M^1L^2T^{-2}] \\ [V] = [L^1T^{-1}] \\$We want to express $[M^1L^0T^{-2}]$ in terms of $[E], [V],$ and $[T]. \\$Let's assume:$\\ [M^1L^0T^{-2}] = [E^aV^bT^c] \\$Equating the dimensions on both sides, we have:$\\$For mass (M):$\\ 1 = a \\$For length (L):$\\ 0 = 2a + b \\$For time (T):$\\ -2 = -2a - b + c \\$From the first equation, $a = 1. \\$Substitute $a = 1$ into the second equation:$\\ 0 = 2(1) + b \\ b = -2 \\$Substitute $a = 1$ and $b = -2$ into the third equation:$\\ -2 = -2(1) - (-2) + c \\ -2 = -2 + 2 + c \\ c = -2 \\$Thus, the dimensional formula of surface tension in terms of $[E], [V],$ and $[T]$ is:$\\ [E^1V^{-2}T^{-2}] \\$Therefore, the correct option is Option 2: $[EV^{-2}T^{-2}].$