Can orbitals 6f,6g,7d,7f exist?Give reason for your answer.

yes these orbitals can exist. Rules are algorithms, by which we generate possible quantum numbers. The lowest value of n is 1 (NOT zero). For n = 1, the only possible value for quantum number l is 0, and m = 0. Each set of quantum numbers is called a state. Thus, for n = 1, there is only one state (1,0,0). The states are represented by symbols, and special symbols have been used to represent the quantum number l as follows:

           l = 0, 1, 2, 3, 4, ...
      symbol = s, p, d, f, g, ...

The three quantum numbers (q.n.) n, l, m follow the rules:

 for the principal q.n.  n
         azimuthal q.n.  l = 0, 1, 2, ..., n-1
          magnetic q.n.  m = -l, -(l-1), ..., (l-1), l

So, these orbitals are possible.