JEE Main 2022MathematicsPermutation CombinationHardNumerical

JEE Main 2022Permutation Combination Question with Solution

JEE Main 2022 (26 Jun Shift 2)

Question

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ______.

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Show full solutionCorrect answer: 150
Correct answer
150

Step-by-step explanation

Prime factorisation of 36=2×2×3×3

So, for number having G.C.D with 36 to be 2, the number should be odd multiple of 2 and does not have factor 3 and 9

Odd multiple of 2 are

102,106,110,114.998  225 numbers

No. of multiples of 3 are

102,114,126.990 75 numbers

Which also include multiple of 9

Hence, Required =225-75=150

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About this question

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.