Read the following statements carefully: I. The magnetic flux...

Let us evaluate each statement:

Statement I is incorrect. The magnetic flux is given by $\Phi = BA \cos\theta$, where $\theta$ is the angle between the area vector (normal to the plane) and the magnetic field. When the plane of the coil is parallel to the magnetic field, $\theta = 90^{\circ}$, making the flux zero (minimum), not maximum.

Statement II is incorrect. The SI unit of magnetic flux is the weber (Wb), which is equivalent to tesla square metre ($\text{T m}^2$), not $\text{T m}^{-2}$.

Statement III is correct. Magnetic flux is defined as the dot product of the magnetic field vector and the area vector ($\Phi = \vec{B} \cdot \vec{A}$), which yields a scalar quantity.

Statement IV is correct. The dimensional formula for magnetic field $B$ is $[\text{M T}^{-2} \text{A}^{-1}]$. Multiplying by area $[\text{L}^2]$ gives the dimensional formula for magnetic flux as $[\text{M L}^2 \text{T}^{-2} \text{A}^{-1}]$.

Therefore, exactly two statements (III and IV) are correct.

Answer: Only two