AP EAMCET · Maths · Quadratic Equation
Given \(f(x)=x^2-5 x+4\). Out of first 20 natural numbers, if a number \(x\) is chosen at random, then the probability that the chosen \(x\) satisfies the inequality \(f(x)>10\) is
- A \(\frac{1}{2}\)
- B \(\frac{3}{4}\)
- C \(\frac{7}{10}\)
- D \(\frac{13}{20}\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{10}\)
Step-by-step Solution
Detailed explanation
\(x^2 - 5x + 4 > 10\) \(x^2 - 5x - 6 > 0\) \((x-6)(x+1) > 0\) \(x 6\) Natural numbers from 1 to 20 satisfying \(x > 6\): \(\{7, 8, ..., 20\}\) Favorable outcomes \( = 14\) Total outcomes \( = 20\) Probability \( = \frac{14}{20} = \frac{7}{10}\)
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