Question

A number is selected at random from integers 1 to 100. Find the probability that it is
(i) a perfect square (ii) not a perfect cube.

• A. (i)$\frac{1}{20}$ (ii) $\frac{14}{25}$
• B. (i)$\frac{1}{15}$ (ii) $\frac{14}{25}$
• C. (i)$\frac{1}{10}$ (ii) $\frac{24}{25}$
• D. None of these

Answer 1

Answer: (C)

(i)$\frac{1}{10}$ (ii) $\frac{24}{25}$

Total Numbers $=1,\mathrm{2...100}$

$=100$

Perfect Squares

$=1^2,2^2,3^2..{.10}^2$

$=1,4,\mathrm{9...100}$

$=10$ numbers

$\therefore$ Pralal $=\frac{10}{100}=\frac{1}{10}$

Perfect Cube $=1^3,2^3,3^3...$

$=1,8,27,64$

$=4$

$\therefore$ P (Not Perfect cube) $=1-\frac{4}{100}$

$=\frac{24}{25}$