Question

Probability of getting positive integral roots of the equation x${}^2$ - n = 0 for the integer n, 1 $\le$ n $\le$ 40 is

• A. $\frac{1}{5}$
• B. $\frac{1}{10}$
• C. $\frac{3}{20}$
• D. $\frac{1}{20}$

Answer 1

Answer: (C)

$x^2-n=0\Rightarrow x=\sqrt{n}$
For each integral value of x $\in$ [1, 40], There is a positive root. Hence for 40 integral values of x from 1 to 40, there are 40 positive roots, out of which only six roots 1, 2, 3, 4, 5 and 6 are positive integral roots. Hence, probability of getting positive integral roots =$\frac{6}{40}=\frac{3}{20}$