The binary mixture of Terephthal-bis-p-n-hexadecylaniline (TB16A) and cholesteryl nonanoate (CN) exhibits I - N* -TGB(A)- TGB(c*)- Sm A - Sm I - Sm F - Sm. G - K Phases in the concentration region between 95 to 98% of TB 16A at higher temperature range. The 90% of TB 16A exhibits I - N* - TGB(A) -TGB(C) - Sm A - Sin I - Sm F - K phases. The mixtures of concentration between 50 to 80% of TB 16A exhibits I - Sm A -Sm I - K phases. The frustrated blue phase is also observed in the mixtures of lower concentration of TB 16A in CN at higher temperature. Optical, DSC and X-ray studies were carried out for the identification of the different phases. The phase diagram of the Chen-Lubensky model in this context is discussed.