In any culture (I suppose) the life of an adult should be mainly his own problem.
What you describe is a typical behavior of parents, especially mothers, who need to be in control of their children for too long.
On one hand, you need to be understanding with her and her emotional needs. Until recently, you were the most part of her life. If you go away (even emotionally, let alone physically), there will be a huge void in her life. To minimize this impact, you need to reassure her that you will not forget her, you will always love her etc.
On the other hand, you must learn to be (and to build yourself as) an individual. You must have a discussion (probably quite many) with your mother to tell her that your needs now are more different than some years ago, when you were still a child. It is normal for a man of 24 to need the presence of another girl / woman in his life.
I wanted to take up a job and move out as soon as I graduated but my parents were so aghast at the idea that I had to give it up.
I understand that you finished your studies, do not have a job, and your parents keep you more or less as a hostage. I guess that even in the Indian culture, that is questionable. In "western" cultures, that is almost an abomination. While it can happen for various reasons (mainly financial) that people share an apartment with their parents, total restriction of getting a job, moving out or having a visiting friend are not common.
Bottom line - you are in a difficult situation because of:
- "mother" reasons;
- Indian culture reasons.
However, with good communication and with a lot of calm and good arguments, you may find a way out.
As a coincidence, I had a discussion with a friend not longer then two evenings ago. Both our complaints were about the same thing: mothers not willing / not able to let go of their children. Actually, the mother of my friend is already a grandmother, taking care of he child of her daughter (my friend), but still, my friend is still "the baby" of her mother.
Also, I had to move, for job reasons, to another country. It was much easier to make make my mother accept the fact after moving. Getting her acceptance before leaving was impossible.
Effectively communicating that I am not withholding information
Actually, you do not need to be only defensive, protecting yourself from the accusations of your parents. You need to be pro-active, and take your life into your own hands.
One way to do that is exactly what you already planned doing: get a job, move to another apartment, continue with your life. Invite your parents to visit you after you move. Even ask them for advice on how to choose an apartment, or help you pack / move. Your mother could still prepare some food for you, if you have a busy schedule - you just go and take it with you to your new apartment. In that way, she will not feel out of the loop, and she will be able to let go with more ease.