Which of the following sets have different dimensions ?

The correct option is Dipole moment, electric flux, electric field.

To determine which set of physical quantities has different dimensions, let us analyze the dimensional formulas for each option step-by-step:

1. Option 1: Pressure, Young's modulus, stress
- Pressure is force per unit area:
$\text{Pressure}=\frac{\text{Force}}{\text{Area}}$
Its dimensional formula is:
$\left[{\text{MLT}}^{-2}\right]/\left[{\text{L}}^2\right]=\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$
- Stress is restoring force per unit area, which shares the same definition and dimensions as pressure:
$\left[\text{Stress}\right]=\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$
- Young's modulus is stress divided by strain. Since strain is dimensionless (ratio of change in length to original length), Young's modulus has the same dimensions as stress:
$\left[\text{Young's modulus}\right]=\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$
Therefore, all three quantities in this set have the same dimensions.

2. Option 2: Emf, potential difference, electric potential
- Electric potential is defined as work done per unit charge:
$V=\frac{W}{q}$
Its dimensional formula is:
$\left[{\text{ML}}^2{\text{T}}^{-2}\right]/\left[\text{AT}\right]=\left[{\text{ML}}^2{\text{T}}^{-3}{\text{A}}^{-1}\right]$
- Potential difference is the difference in electric potential between two points, so it has the same dimensions:
$\left[\text{Potential difference}\right]=\left[{\text{ML}}^2{\text{T}}^{-3}{\text{A}}^{-1}\right]$
- Electromotive force (Emf) is the potential difference of a source when no current is flowing, which also shares the same dimensions:
$\left[\text{Emf}\right]=\left[{\text{ML}}^2{\text{T}}^{-3}{\text{A}}^{-1}\right]$
Therefore, all three quantities in this set have the same dimensions.

3. Option 3: Heat, work done, energy
- Work done is force multiplied by displacement:
$W=F\cdot d$
Its dimensional formula is:
$\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
- Energy represents the capacity to do work and shares the same unit (Joule) and dimensions as work:
$\left[\text{Energy}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
- Heat is a form of energy transfer, which also shares the same dimensions:
$\left[\text{Heat}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
Therefore, all three quantities in this set have the same dimensions.

4. Option 4: Dipole moment, electric flux, electric field
- Electric dipole moment is charge multiplied by distance:
$p=q\cdot d$
Its dimensional formula is:
$\left[\text{LTA}\right]$
- Electric field is force per unit charge:
$E=\frac{F}{q}$
Its dimensional formula is:
$\left[{\text{MLT}}^{-2}\right]/\left[\text{AT}\right]=\left[{\text{MLT}}^{-3}{\text{A}}^{-1}\right]$
- Electric flux is electric field multiplied by area:
${\Phi }_E=E\cdot A$
Its dimensional formula is:
$\left[{\text{MLT}}^{-3}{\text{A}}^{-1}\right]\cdot \left[{\text{L}}^2\right]=\left[{\text{ML}}^3{\text{T}}^{-3}{\text{A}}^{-1}\right]$
Since all three quantities in this set have different dimensional formulas, this is the correct set.