Which of the following is a dimensionless quantity ?

The correct option is Strain.

To understand why strain is a dimensionless quantity, let us analyze the definition and dimensions of each option step-by-step:

1. Strain:
Strain is defined as the ratio of the change in dimension to the original dimension of an object when a deforming force is applied. For example, tensile strain is given by the formula:

$\text{Strain}=\frac{\mathrm{Change\; in\; length}\left(\mathrm{\Delta L}\right)}{\mathrm{Original\; length}\left(L\right)}$
Since both the numerator and the denominator represent length (measured in meters), their dimensions cancel out. Therefore, strain is a ratio of two similar quantities and has no units or dimensions.
Its dimensional formula is:

$\left[M^0{L}^0{T}^0\right]$

2. Stress:
Stress is defined as the restoring force restoring per unit area of a body. Its dimensional formula is:

$\text{Stress}=\frac{\text{Force}}{\text{Area}}=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}=\left[M{L}^{-1}{T}^{-2}\right]$
Thus, stress has physical dimensions.

3. Specific heat:
Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). Its formula is:

$s=\frac{Q}{m\mathrm{\Delta T}}$
Its dimensional formula is:

$\left[M^0{L}^2{T}^{-2}{K}^{-1}\right]$
Thus, specific heat has physical dimensions.

4. Quantity of heat:
Heat is a form of energy. Therefore, its dimensional formula is the same as that of work or energy:

$\left[M{L}^2{T}^{-2}\right]$
Thus, quantity of heat has physical dimensions.

Consequently, only Strain is a dimensionless quantity.