Sriharikota Island is located near the mouth of the Pulicat Lake, hence the correct answer is option 'C'.

Located in the state of Andhra Pradesh, Sriharikota Island is a barrier island situated off the Bay of Bengal coast. It is known for being the primary site of the Indian Space Research Organisation's (ISRO) Satish Dhawan Space Centre, which is the main center for launching satellites into space.

The island is strategically located near the mouth of the Pulicat Lake, which is the second largest brackish water lake in India. The Pulicat Lake is separated from the Bay of Bengal by the barrier island and it serves as a natural boundary between the states of Andhra Pradesh and Tamil Nadu.

Here is a breakdown of the options and why they are incorrect:

a) Near Chilka lake: Chilka Lake is located in the state of Odisha, which is quite far from Sriharikota Island. Therefore, this option is incorrect.

b) Near the mouth of the Mahanadi: The Mahanadi River is also located in the state of Odisha, and it does not have any proximity to Sriharikota Island. Thus, this option is also incorrect.

d) Near the mouth of Godavari: The Godavari River is situated in Andhra Pradesh, but it is not in close proximity to Sriharikota Island. Therefore, this option is incorrect as well.

In conclusion, Sriharikota Island is located near the mouth of the Pulicat Lake, making option 'C' the correct answer. The island's strategic location near this brackish water lake has made it an ideal site for ISRO's space center, allowing for easy access to the Bay of Bengal for satellite launches.