JEE Main 2019MathematicsFunctionsMediumMCQ

JEE Main 2019 — Functions Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

For x∈R,  Let [x] denotes the greatest integer ≤x, then the sum of the series -13+-13-1100+-13-2100+.....+-13-99100 is

Choose an option

Show full solutionCorrect option: D
Correct answer
D-133

Step-by-step explanation

Greatest integer function
fx=x=0              ; 0≤x<1-1               ; -1≤ x <0-2                   ; -2≤x<-1

Given series
S=-13+-13-1100+-13-2100+-13-3100+…+-13-99100
General term Tr=-13-r100=-1        0≤r≤66-2               r>66
⇒S=∑r=066-1+∑r=6799-2=-67+-2×33
= -133

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About this question

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