The dimensions of angular momentum, latent heat and capacitance are, respectively.

Let's find the dimensions of angular momentum, latent heat, and capacitance step by step.

First, angular momentum is given by the formula: angular momentum = radius × linear momentum. Radius has the dimension of length, so its dimension is $$L$$. Linear momentum is mass × velocity. Mass has dimension $$M$$, and velocity is distance over time, so its dimension is $$LT^{-1}$$. Therefore, linear momentum has dimension $$M \times LT^{-1} = MLT^{-1}$$. Now, angular momentum = radius × linear momentum = $$L \times MLT^{-1} = ML^2T^{-1}$$.

Second, latent heat is the heat energy absorbed or released per unit mass during a phase change. Heat energy has the same dimension as work, which is force × distance. Force is mass × acceleration, so force has dimension $$M \times LT^{-2} = MLT^{-2}$$. Work = force × distance = $$MLT^{-2} \times L = ML^2T^{-2}$$. Latent heat = heat energy / mass = $$ML^2T^{-2} / M = L^2T^{-2}$$.

Third, capacitance is defined as charge divided by voltage. Charge has dimension $$AT$$ (since current I is charge per time, so charge = current × time). Voltage (potential difference) is work done per unit charge, so voltage = work / charge = $$ML^2T^{-2} / AT = ML^2T^{-3}A^{-1}$$. Therefore, capacitance = charge / voltage = $$AT / (ML^2T^{-3}A^{-1}) = AT \times M^{-1}L^{-2}T^{3}A = M^{-1}L^{-2}T^{4}A^{2}$$.

So, the dimensions are:

• Angular momentum: $$ML^2T^{-1}$$
• Latent heat: $$L^2T^{-2}$$
• Capacitance: $$M^{-1}L^{-2}T^{4}A^{2}$$

Now, comparing with the options:

• Option A: $$ML^2T^1A^2$$ (incorrect angular momentum exponent for T), $$L^2T^{-2}$$ (correct latent heat), $$M^{-1}L^{-2}T^2$$ (incorrect capacitance exponent for T)
• Option B: $$ML^2T^{-2}$$ (incorrect angular momentum exponent for T), $$L^2T^2$$ (incorrect latent heat exponent for T), $$M^{-1}L^{-2}T^4A^2$$ (correct capacitance)
• Option C: $$ML^2T^{-1}$$ (correct angular momentum), $$L^2T^{-2}$$ (correct latent heat), $$ML^2TA^2$$ (incorrect capacitance exponents and sign)
• Option D: $$ML^2T^{-1}$$ (correct angular momentum), $$L^2T^{-2}$$ (correct latent heat), $$M^{-1}L^{-2}T^4A^2$$ (correct capacitance)

Hence, the correct answer is Option D.