Two non - negative integers are chosen at random from a set of non - negative integer with replacement. If the probability that sum of the squares divisible by 10 is P then 50P is

10 x10 = 100 ways.
x2 +y2 is divisible by 10 if unit digit of sum of squares
of unit digits of x and y is zero.
$\therefore$unit digits of x, y can be (0,0), (1,3), (3,1), (1,7),
(7,1), (2,4), (4,2), (2,6), (6,2), (3,9), (9,3), (4,8), (8,4),
(5,5), (6,8), (8,6), (7,9), (9,7).
$\therefore$18 cases are favourable, and$\mathrm{P}=\frac{18}{100}=\frac{9}{50}$
$\Rightarrow \therefore$50P = 9