JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q87

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MathematicsSingle correct+4 / -1Question 87 of 90

A number $x$ is chosen at random from the set {1, 2, 3, 4, ....., 100}. Define the event : A = the chosen number $x$ satisfies
$\frac{(x-10)(x-50)}{(x-30)}\ge0$
Then P(A) is :

0.71

0.70

0.51

0.20

Answer and worked solution

Official answer: A

Sign of $\dfrac{(x-10)(x-50)}{x-30}$ :

$10\le x<30$ : non-negative, 20 numbers.
$x=50$ : zero, 1 number.
$51\le x\le100$ : positive, 50 numbers.

The rest are negative or undefined. $P(A)=\frac{71}{100}=0.71$ .

Topics:Classical probability Inequalities and modulus

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JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 87