@Umesh_Awasthi, that is not correct. A connection is established between 2 pairs of IPs and ports, say <source_IP:source_port> and <dest_IP:dest_port>. Typically destination port is fixed, for example 80 (HTTP). The source IP can open 2^16 simultaneous connections to <dest_IP:80>, from <source_IP:10000>, <source_IP:10001> etc (the source port is usually randomly picked from a high range), and excluding other limitations another source IP could open the same amount of connections.
The maximum limit of connections comes from the maximum number of file descriptors available to the process, most commonly. Then, there will be other limitations, such as the available memory to handle the connections internally (how much memory does your process use per connection?).