Hello Student,

Obviously you can apply for master of computer application without attending TANCET examination as well. Actually there are two ways, you can look for private colleges which can basically provide admission in management quota on the basis of your merrit in bachelor degree. You can check out option private MCA colleges from the link below

https://it.careers360.com/colleges/list-of-bca-mca-colleges-in-india?state=Tamil%20Nadu&ownership=Private&degree=M.C.A.&fee=100000-500000

However there are also other kinds of MCA entrance examinations, like NIMCET. Some top institutes like BHU JNU DU conducts there on examination to provide admission in MCA.