Recall the definitions

• Extensive variables depend on the amount of substance or size of the system. Examples: mass, volume, internal energy.
• Intensive variables do not depend on the amount of substance. Examples: pressure, temperature, density.

Check statement (A)

Statement (A): Internal energy, volume $(V)$ and mass $(M)$ are extensive variables.

• Internal energy $\to$ extensive
• Volume $\to$ extensive
• Mass $\to$ extensive

Hence, (A) is correct.

Check statement (B)

Statement (B): Pressure $(P)$, temperature $(T)$ and density $(\rho)$ are intensive variables.

• Pressure $\to$ intensive
• Temperature $\to$ intensive
• Density $\to$ intensive

Hence, (B) is correct.

Check statement (C)

Statement (C): Volume $(V)$, temperature $(T)$ and density $(\rho)$ are intensive variables.

• Volume is not intensive; it is extensive.
• Temperature is intensive.
• Density is intensive.

Since volume is wrongly classified, (C) is false.

Check statement (D)

Statement (D): Mass $(M)$, temperature $(T)$ and internal energy are extensive variables.

• Mass $\to$ extensive
• Temperature $\to$ intensive, not extensive
• Internal energy $\to$ extensive

Since temperature is wrongly classified, (D) is false.

Select the correct option

Correct statements are (A) and (B) only.

Therefore, the correct option is: $\boxed{\text{B}}$

Comparison with stored answer

Stored correct answer: B

My derived answer: B

So, the answer matches the stored correct answer.