The question asks us to identify the pair that is not correctly matched. Let`s analyze each option to determine if it is correctly matched or not.

Option 1: Power of creating a new state Parliament - This is a correctly matched pair. The power to create a new state Parliament is granted to the central government under the Indian Constitution.

Option 2: Power of state altering the name of the state legislature - This is the pair that is not correctly matched. The power to alter the name of the state legislature is not mentioned in the Indian Constitution. The state legislature has the power to make laws for the state, but the power to alter its name does not lie with the state government.

Option 3: Equality before law guaranteed to both Indian citizens and non-citizens - This is a correctly matched pair. The concept of equality before the law is a fundamental right guaranteed to all individuals, whether they are Indian citizens or non-citizens.

Option 4: Equality of opportunity guaranteed only to Indian citizens - This is a correctly matched pair. The concept of equality of opportunity is a fundamental right guaranteed specifically to Indian citizens.

In conclusion, option 2 is the pair that is not correctly matched. The power of the state to alter the name of the state legislature is not