A random page from a book with 90 pages is opened. Find the probability of the page number being a perfect square.

The number of pages in the book is 90, which is taken as the total number of cases.

The favourable case has a number of perfect squares ranging from 1 to 90.

Given,

Total number of pages in the book, i.e. total number of cases = 90 

Now, from 1 to 90, the perfect squares are -  1, 4, 9, 16, 25, 36, 49, 64, 81.

Number of favourable cases, i.e. the number of perfect squares ranging from 1 to 90 = 9.

$\therefore \mathrm{P}(\mathrm{getting} \mathrm{a} \mathrm{perfect} \mathrm{square})=\frac{\mathrm{number} \mathrm{of} \mathrm{favourable} \mathrm{cases}}{\mathrm{total} \mathrm{number} \mathrm{of} \mathrm{cases}}=\frac{9}{90}=\frac{1}{10}$

Hence, the correct answer is $\frac{1}{10}$.