Institute for net/jre, gate, it-jam, jest, tifr and gre in physical scieng the number of degrees of freedom of a rigid body in d space-dimensions is (a) 2d (b)

Dof = d(d+1)/2

This will definately give you intuitively knowledge. I have shown for 1,2,3-dimensional space. Then I generalised. This will surely help you to build the concept. Now you can remem...

see attached file... it's very helpful for you dear

dear it's fixed formula.

this is the direct formula.. d(d+1)/2 for rigid body...