JEE Main 2019MathematicsSequences and SeriesMediumMCQ

JEE Main 2019 — Sequences and Series Question with Solution

JEE Main 2019 (08 Apr Shift 1)

Question

The sum of all natural numbers n such that 100<n<200 and H.C.F. 91,n>1 is

Choose an option

Show full solutionCorrect option: C
Correct answer
C3121

Step-by-step explanation

Since, H.C.F. of 91, n>1.

Hence, n should be multiple of 7 or 13 or both.

Hence, when n is multiple of 7,

Number of terms=14, t1=105, l=196

∴S1=142105+196=7×301=2107

When n is multiple of 13,

Number of terms =8, t1=104, l=195

∴S2=82×299=1196

When n is multiple of 91

∴ Number of term =1 

S3=182

∴ Required sum =2107+1196-182=3121

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About this question

This is a previous-year question from JEE Main 2019, 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.