Practicing Success
A natural number ‘n’ is selected at random from the set of first 100 natural numbers. The probability that $n+\frac{100}{n}≤50$ is equal to |
$\frac{9}{10}$ $\frac{39}{50}$ $\frac{9}{20}$ None of these |
$\frac{9}{20}$ |
$n+\frac{100}{n} \leq 50 $ $\Rightarrow n^2-50 n+100 \leq 0$ $\Rightarrow 25-5 \sqrt{21} \leq n \leq 25+5 \sqrt{21}$ ⇒ n = 3, 4, 5...., 47 Thus, favourable number of ways = (47 – 3 + 1) = 45 Thus, required probability = $\frac{45}{100}=\frac{9}{20}$ |