A box contains 90 discs which are numbered from 1 to 90.

Total number of discs = 90

(i) Total number of two-digit numbers between 1 and 90 = 81

$P$ (getting a two-digit number) $=\frac{81}{90}=\frac{9}{10}$

(ii) Perfect squares between 1 and 90 are 1, 4, 9, 16, 25, 36, 49, 64, and 81. Therefore, total number of perfect squares between 1 and 90 is 9.

$P($ getting a perfect square $)=\frac{9}{90}=\frac{1}{10}$

(iii) Numbers that are between 1 and 90 and divisible by 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, and 90. Therefore, total numbers divisible by 5 = 18

Probability of getting a number divisible by $5=\frac{18}{00}=\frac{1}{5}$