Latent heat is the energy absorbed or released during a phase change per unit mass. Hence, it is specific energy:
\[ \text{Latent Heat} = \frac{\text{Energy}}{\text{Mass}}. \]
The dimensional formula of energy is:
\[ \text{Energy} = [ML^2T^{-2}]. \]
Divide by mass:
\[ \text{Latent Heat} = \frac{[ML^2T^{-2}]}{[M]} = [M^0L^2T^{-2}]. \]
Final Answer: \([M^0L^2T^{-2}]\).
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to: