Answer is (B) 2(k + 1)/n
n = 10k + r, k, r ∈ N, 0 ≤ r ≤ 9
Unit place of a2 will contain 0, 1, 4, 5, 6, 9 only.
Hence, a2 – 1 is divisible by 10 only if unit place of a2 contain 1.
If unit place of a2 is 1, then unit place of a will be 1 or 9.
n = 10k + 9
Number of a whose unit place is 1 or 9 = 2(k + 1)
Therefore,
pn = 2(k + 1)/n