JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q19

MathematicsSingle correct+4 / -1Question 19 of 90

Let S = {1, 2, 3, ..., 2022}. Then the probability, that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, is :

\dfrac{128}{1011}

\dfrac{166}{1011}

\dfrac{127}{337}

\dfrac{112}{337}

Answer and worked solution

Official answer: D

Count. $2022=2\cdot3\cdot337$ , $\varphi(2022)=1\cdot2\cdot336=672$ .

Probability $\frac{672}{2022}=\frac{112}{337}$ .

(D)

Topics:Classical probability Number systems

JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 19