`{:("List-I","List-2"),((a)"Pressure ",(e)ML^(2)T^(-2)I^(-1)),((b)"Latent heat", (f) M^(0)L^(0)T^(-1)),((c)"Velocity gradient" ,(g) ML^(-1)T^(-2)),((d) "Magnetic flux" ,(h) M^(0)L^(2)T^(-2)):}`

Options

A. a - h`" "` b- f `" "`c -g `" "` d-e
B. a - g`" "` b- h `" "`c -e `" "` d-f
C. a - g`" "` b- h `" "`c -f `" "` d-e
D. a - f`" "` b- g `" "`c -e`" "` d-h

Answer

To solve the problem of matching the physical quantities in List-I with their corresponding dimensional formulas in List-II, we will analyze each physical quantity one by one and determine its dimensional formula.

### Step 1: Identify the dimensional formula for Pressure
- Pressure is defined as force per unit area.
- The dimensional formula for force is \( M L T^{-2} \) (mass × acceleration).
- Area has the dimensional formula \( L^2 \).
- Therefore, the dimensional formula for pressure is:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{M L T^{-2}}{L^2} = M L^{-1} T^{-2} \]
- So, the dimensional formula for Pressure is \( M L^{-1} T^{-2} \).

### Step 2: Identify the dimensional formula for Latent Heat
- Latent heat is defined as the amount of heat required to change the state of a unit mass of a substance without changing its temperature.
- The dimensional formula for energy (or heat) is \( M L^2 T^{-2} \).
- Since latent heat is energy per unit mass, we divide by mass:
\[ \text{Latent Heat} = \frac{M L^2 T^{-2}}{M} = L^2 T^{-2} \]
- Thus, the dimensional formula for Latent Heat is \( M^0 L^2 T^{-2} \).

### Step 3: Identify the dimensional formula for Velocity Gradient
- Velocity gradient is defined as the change in velocity per unit distance.
- The dimensional formula for velocity is \( L T^{-1} \).
- Therefore, the dimensional formula for velocity gradient is:
\[ \text{Velocity Gradient} = \frac{L T^{-1}}{L} = T^{-1} \]
- Thus, the dimensional formula for Velocity Gradient is \( M^0 L^0 T^{-1} \).

### Step 4: Identify the dimensional formula for Magnetic Flux
- Magnetic flux is defined as the product of the magnetic field and the area perpendicular to the field.
- The dimensional formula for magnetic field is \( M T^{-2} I^{-1} \) (force per unit charge per unit length).
- Therefore, the dimensional formula for magnetic flux is:
\[ \text{Magnetic Flux} = \text{Magnetic Field} \times \text{Area} = (M T^{-2} I^{-1}) \times (L^2) = M L^2 T^{-2} I^{-1} \]
- Thus, the dimensional formula for Magnetic Flux is \( M L^2 T^{-2} I^{-1} \).

### Step 5: Match the quantities with their dimensional formulas
Now we can match the physical quantities with their corresponding dimensional formulas:
- (a) Pressure → \( M L^{-1} T^{-2} \) → Matches with (g)
- (b) Latent Heat → \( M^0 L^2 T^{-2} \) → Matches with (h)
- (c) Velocity Gradient → \( M^0 L^0 T^{-1} \) → Matches with (f)
- (d) Magnetic Flux → \( M L^2 T^{-2} I^{-1} \) → Matches with (e)

### Final Matching
- a → g
- b → h
- c → f
- d → e

Thus, the correct matches are:
- a g
- b h
- c f
- d e