1. Check statement (A):

   • "Weight of a substance is the amount of matter present in it."
   • The amount of matter present in a substance is called mass, not weight.
   • Weight is the force with which gravity pulls an object.
   • Hence, (A) is false.

2. Check statement (B):

   • "Mass is the force exerted by gravity on an object."
   • This is actually the definition of weight, not mass.
   • Hence, (B) is false.

3. Check statement (C):

   • "Volume is the amount of space occupied by a substance."
   • This is the correct definition of volume.
   • Hence, (C) is true.

4. Check statement (D):

   • In the Celsius scale, temperatures below $0^\circ \mathrm{C}$ are possible.
   • In the Kelvin scale used in classical thermodynamics, temperature cannot be negative because $0\,\mathrm{K}$ is absolute zero.
   • Hence, (D) is true.

5. Check statement (E):

   • Precision means the closeness of repeated measurements of the same quantity to one another.
   • This is correct.
   • Hence, (E) is true.

6. Collect the correct statements:

   • True statements are (C), (D), and (E) only.

7. Match with the options:

   • Option C = (C), (D) and (E) Only

Therefore, the correct answer is Option C.