JEE Main 2022 — Permutation Combination Question with Solution
JEE Main 2022 (26 Jun Shift 2)
Question
The total number of -digit numbers, whose greatest common divisor with is , is ______.
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Show full solutionCorrect answer: 150
Correct answer
150
Step-by-step explanation
Prime factorisation of
So, for number having G.C.D with to be , the number should be odd multiple of and does not have factor and
Odd multiple of are
No. of multiples of are
Which also include multiple of
Hence, Required
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This is a previous-year question from JEE Main 2022, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.