**Dimensions of Pressure, Stress, and Coefficient of Elasticity**

The dimensions of a physical quantity represent the powers to which the fundamental quantities are raised in its unit. In this case, we are asked to determine the dimensions of three quantities: pressure, stress, and coefficient of elasticity. Let's analyze each of them separately:

**1. Pressure:**
Pressure is defined as the force per unit area. Mathematically, it is expressed as P = F/A, where F is the force and A is the area. The dimensions of force are mass x acceleration (M x L x T^-2), and the dimensions of area are length squared (L^2). Therefore, the dimensions of pressure can be calculated as follows:

P = F/A = (M x L x T^-2)/(L^2) = M x L^-1 x T^-2

**2. Stress:**
Stress is a measure of the internal resistance of a material to external forces. It is defined as the force per unit area applied to a material. Mathematically, it is expressed as σ = F/A, where F is the force and A is the area. Since the dimensions of force and area are the same as in pressure, the dimensions of stress are also the same:

σ = F/A = (M x L x T^-2)/(L^2) = M x L^-1 x T^-2

**3. Coefficient of Elasticity:**
The coefficient of elasticity is a measure of the stiffness or rigidity of a material. It relates the stress applied to a material to the resulting strain (deformation) produced. Mathematically, it is expressed as E = σ/ε, where σ is the stress and ε is the strain. Since the dimensions of stress are the same as in pressure and stress, we can analyze the dimensions of strain to determine the dimensions of the coefficient of elasticity.

Strain is defined as the change in length divided by the original length. It is a dimensionless quantity. Therefore, the dimensions of the coefficient of elasticity can be calculated as follows:

E = σ/ε = (M x L^-1 x T^-2)/1 = M x L^-1 x T^-2

Therefore, the dimensions of pressure, stress, and the coefficient of elasticity are the same: M x L^-1 x T^-2. Hence, the correct option is D) Pressure, Stress, Coefficient of Elasticity.