Q. Probability of getting positive integral roots of the equation $x^{2} - n = 0$ for the integer $n,\ 1 \leq n \leq 40$ is
A) $\frac{1}{5}$
B) $\frac{1}{10}$
C) $\frac{3}{20}$
D) $\frac{1}{20}$
Explanation
(c)
Given, $x^{2} - n = 0$
$\Rightarrow \ x = \pm \sqrt{n}$
$\therefore\ n = 1,\ 4,\ 9,\ 16,\ 25,\ 36$
$\therefore$Required probability $= \frac{6}{40} = \frac{3}{20}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.