Most candidates have a problem when they have wrong details related to the candidate's or the father's name.
Since you are applying for a graduate degree, you will be need to present the details of the XII marks sheet and certificate clearly. Correcting this mismatch now would help you in the long run when you apply for PG or a job a few years later when computerized and online forms etc would be much more commonly prevalent.
This is not a gross mistake if your mother's name is not complete. I would suggest, do not stop applying to the college for the admission process because the scrutiny and actual acceptance etc take time. By that time, you can get your XII marks sheet name corrected.
Please check mother's ID documents (PAN card or Aadhaar card) that has her name properly mentioned. If not you would have to meet a Notary who can get a legal affidavit done with your mother's name correctly mentioned including her initials.
The publish the correct name in two newspapers, one English and one local vernacular langauge and keep both the originals intact.
Then, if it is the CBSE board that you have completed, then you can fill out this form ((http://cbse.nic.in/faq/MM%202016%20Duplicate%20Form.pdf)) and get a the corrected certificate in hand by 15 days time. Futher details regard CBSE marksheet correction can be found in this link
If it is the state board, then forward an application request to the state board via your school principal. You would have to pay the appropriate fees as mentioned by your state board.
People ignore such small mistakes in important documents and may even get away but this simple mistake should not come in the way of getting a future enrollment or job.