Surely, you can do engineering. To secure admission in a reputed engineering college, one must appear for (and crack) the relevant entrance test. For example, to get into an IIT, one must score valid marks in JEE entrance test. Many private engineering institutes conduct their own private entrance test.

Hi Pushpendra,

You can apply for any exam without your score but while counseling your 10+2th rank card is must. 

All the best!

please be specific about what do you want to apply for.