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JEE Math Practice Question

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

  1. A.$$\frac{128}{1011}$$
  2. B.$$\frac{166}{1011}$$
  3. C.$$\frac{127}{337}$$
  4. D.$$\frac{112}{337}$$

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