Expansion of (1+x)2n is 1+2nC1x+2nC2x2+.......+ 2nCrxr+2nCr+1xr+1+......+2nC2nx2n As given 2nCr+2=2nC3 ⇒
(2n)!
(r+2)!(2n−r−2)!
=
(2n)!
(3r)!(2n−3r)!
⇒(3r)!(2n−3r)!=(r+2)!(2n−r−2)!...(1) Now, put value of n from the given choices. Choice (a) put n=2r+1 in (1) LHS:(3r)!(4r+2−3r)!=(3r)!(r+2)! RHS:(r+2)!(3r)! ⇒LHS=RHS