JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 August 2021, Shift 2, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

\sum_{\mathrm{r}=1}^{50}\tan^{-1}\frac{1}{2\mathrm{r}^2}=\mathrm{p}

, then the value of

\tan\mathrm{p}

is :

(1) $\frac{50}{51}$ Official answer
(2) $\frac{51}{50}$
(3) $\frac{101}{102}$
(4) $100$

Official answer

Option 1

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Telescoping Inverse Trig Series

Same idea in other shifts

Asked 5× in all

5 Apr 2026, Shift 1 · Q24If $\frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha$ , then $\tan\alpha$ is equal to ________.MediumNumerical value
28 Jun 2022, Shift 2 · Q18The value of $\lim_{n\to\infty} 6\tan\left\{\sum_{r=1}^{n}\tan^{-1}\left(\frac{1}{r^2+3r+3}\right)\right\}$ is equal to :MediumSingle correct
24 Feb 2021, Shift 1 · Q90 $\lim_{n \to \infty} \tan\left\{\sum_{r=1}^{n} \tan^{-1}\left(\frac{1}{1 + r + r^2}\right)\right\}$ is equal to ___________.MediumNumerical value
5 Sep 2020, Shift 1 · Q69If S is the sum of the first 10 terms of the series…MediumSingle correct

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.