I saw . . . . . . . . one-rupee coin lying on . . . . . . . . ground.

Even though the word 'one' begins with the vowel 'o', it's pronounced as 'won' and thus has the sound of consonant 'w'. Thus, we use 'a' instead of 'an'. Use 'a' article in the first blank. In the second blank, article "the" will be used because article 'the' is used to refer to something specific. Here 'ground' is specific.