Modulus of resilience is a property of a material that measures its ability to store energy without undergoing permanent deformation. It is an important parameter to consider when designing structures or components that are subjected to impact or shock loading.

The modulus of resilience is defined as the maximum amount of energy that can be absorbed by a material without causing permanent deformation. In other words, it represents the ability of a material to absorb energy elastically and return to its original shape after the load is removed.

Here is a detailed explanation of each option:

a) Property to resist shocks:
While it is true that materials with high resilience can resist shocks to some extent, the modulus of resilience specifically refers to the material's ability to store energy without undergoing permanent deformation. Therefore, option 'a' is not the correct answer.

b) Property to withstand heavy pressure:
Withstanding heavy pressure is more related to the material's strength or hardness, rather than its resilience. The modulus of resilience focuses on the energy absorption capacity of the material, not its ability to withstand pressure. Hence, option 'b' is not the correct answer.

c) Property to store energy without undergoing paramount deformation:
This is the correct answer. The modulus of resilience quantifies the amount of energy a material can absorb elastically without causing permanent deformation. It is a measure of the material's ability to store energy and return to its original shape after the load is removed.

d) An index of elasticity:
While elasticity is related to the material's ability to deform under stress and return to its original shape, the modulus of resilience specifically measures the ability to store energy without permanent deformation. Therefore, option 'd' is not the correct answer.

In conclusion, the modulus of resilience is a property of a material that reflects its ability to store energy without undergoing permanent deformation. It is an important parameter to consider when designing materials and structures that are subjected to impact or shock loading.

The maximum energy that can be absorbed per unit volume within elastic limit.
or
area under the elastic region in stress vs strain diagram.