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Solutions
Final arrangement:

Clues: One person was born between Vikram and Nisha. Arjun was born three persons before Nisha. Arjun is older than Vikram but not just older. Nisha was born in the month having an even number of days.
Inference: From the above conditions there are two possibilities i.e., Case 1 and Case 2.

Clues: Two persons were born between Deepak and Ananya. Neither Deepak nor Ananya was born in the month in which Vikram was born. Deepak is not just older than Arjun and Nisha. Ananya was not the first person to be born.
Inference: From the above conditions we get the following arrangement:

Clue: Rajesh was born two persons before Rahul.
Inference: From the above conditions Case 2 is cancelled here as there is no place for Rajesh and Rahul.

Inference: Only one person remains i.e., Priya. So, the Final arrangement is:

The statements given in options I and II both are true