Question 7978 – GATE 2017 [Set-2]

                                     S → XY
                                     X → aX|a
                                     Y → aYb|ϵ

The production X→ aX | a can generate any number of a’s ≥ 1 and the production Y→ aYb | ϵ will generate equal number of a’s and b’s.

So the production S→XY can generate any number of a’s (≥1) in the beginning (due to X) and then Y will generate equal number of a’s and b’s.
So, the number of a’s will always be greater than number of b’s and number of b’s must be greater than or equal to 0 (as Y → ϵ, so number of b’s can be zero also).
Hence the language is {a^m bⁿ│m>n,n≥0}.