Our Cognos 11 install folder shows we have 11.0.2 version (ca_srv_win64_184.108.40.20642816) . So I started installing the same version of Framework (ca_model_win32_220.127.116.1142816).
But after going through cmplst files we came to know our Cognos 11 is 11.0.0 and Framework is 11.0.2. This is causing the issue. I removed the Framework and installed 11.0.0 version which fixed the issue.
Thank you all for your inputs and I am sorry for the confusion.