JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 17 March 2021, Shift 2, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

The value of

\lim_{n\to\infty}\frac{[r]+[2r]+\ldots+[nr]}{n^2}

, where r is a non-zero real number and

[r]

denotes the greatest integer less than or equal to r, is equal to :

(1) $r$
(2) $\frac{r}{2}$ Official answer
(3) $2r$
(4) $0$

Official answer

Option 2

NTA final key.

Chapter: Limits and Derivatives
Topic: Integral as Limit of Sum
Idea tested: Greatest Integer Function Sums

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.