Correct option is (c) \(\frac9{25}\)
Let two non-negative integers be x & y such that x = 5a + α and y = 5b + β where 0 ≤ α,β ≤ 4.
New, x2 + y2 = 25(a2 + b2) + 10(aα + bβ) + α2 + β2
⇒ α2 + β2 should be divisible by 5
\(\therefore\) (α, β) can have ordered pairs as
{(0,0), (1,2), (2,1), (1,3), (3,1), (2,4), (4,2), (3,4), (4,3)} = 9 ways
\(\therefore\) required probability is \(\frac 9{25}\).
