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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q72

Question 72 of 90 in this shift, Maths question 12 of 30, Section A.

lim⁡n→∞∑k=1nn(n2+k2)(n4+n2k2+k4)\lim_{n\to\infty} \sum_{k=1}^{n} \frac{n(n^2+k^2)}{(n^4+n^2k^2+k^4)} is equal to
  1. (1)π3\frac{\pi}{\sqrt{3}}
  2. (2)2π33\frac{2\pi}{3\sqrt{3}}
  3. (3)π23\frac{\pi}{2\sqrt{3}}Official answer
  4. (4)π3\frac{\pi}{3}

Official answer

Option 3

NTA final key.

Chapter
Integrals
Topic
Integral as Limit of Sum
Idea tested
Algebraic Manipulation to Extract 1/n

Same topic in other shifts

All Integral as Limit of Sum questions
  1. 9 Apr 2024, Shift 1 · Q28Let…HardNumerical value
  2. 30 Jan 2024, Shift 1 · Q10The value of lim⁡n→∞∑k=1nn3(n2+k2)(n2+3k2)\lim_{n\to\infty}\sum_{k=1}^{n}\frac{n^3}{(n^2+k^2)(n^2+3k^2)} is :MediumSingle correct
  3. 13 Apr 2023, Shift 1 · Q7Among (S1) : lim⁡n→∞1n2(2+4+6+……+2n)=1\lim_{n\to\infty}\frac{1}{n^2}(2+4+6+\ldots\ldots+2n)=1 (S2) :…MediumTwo statements
  4. 25 Jul 2022, Shift 1 · Q27If…MediumNumerical value
  5. 25 Jul 2022, Shift 2 · Q7…MediumSingle correct
  6. 26 Jul 2022, Shift 1 · Q10If a=lim⁡n→∞∑k=1n2nn2+k2\mathrm{a} = \lim_{n \to \infty} \sum_{k=1}^{n} \dfrac{2n}{n^2 + k^2} and f(x)=1−cos⁡x1+cos⁡xf(x) = \sqrt{\dfrac{1 - \cos x}{1 + \cos x}},…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.