JEE Main 2021 — Sequences And Series Question with Solution
From: JEE Main 2021 (Online) 22th July Evening Shift
Question
The sum of all the elements in the set {n {1, 2, ....., 100} | H.C.F. of n and 2040 is 1} is equal to _____________.
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Show full solutionCorrect answer: 1251
Correct answer
1251
Step-by-step explanation
2040 = 23 3 5 17
n should not be multiple of 2, 3, 5 and 17.
Sum of all n = (1 + 3 + 5 + ...... + 99) (3 + 9 + 15 + 21 + ...... + 99) (5 + 25 + 35 + 55 + 65 + 85 + 95) (17)
= 2500 (3 + 99) 365 17
2500 867 365 17
= 1251
n should not be multiple of 2, 3, 5 and 17.
Sum of all n = (1 + 3 + 5 + ...... + 99) (3 + 9 + 15 + 21 + ...... + 99) (5 + 25 + 35 + 55 + 65 + 85 + 95) (17)
= 2500 (3 + 99) 365 17
2500 867 365 17
= 1251
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This is a previous-year question from JEE Main 2021, covering the Sequences And Series 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.