Learn

Friday, 9 October

JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2023, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let a1,a2,a3,…,ana_1,a_2,a_3,\ldots,a_n be nn positive consecutive terms of an arithmetic progression. If d>0d>0 is its common difference, then lim⁡n→∞dn(1a1+a2+1a2+a3+⋯+1an−1+an)\lim_{n\to\infty}\sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+\cdots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right) is
  1. (1)1Official answer
  2. (2)0
  3. (3)d\sqrt d
  4. (4)1d\frac{1}{\sqrt d}

Official answer

Option 1

NTA final key.

Chapter
Sequences and Series
Topic
AP and GP
Idea tested
Method of Differences (Vn Method)

Same idea in other shifts

Asked 4× in all
  1. 5 Apr 2026, Shift 2 · Q5If the sum of the first 10 terms of the series…HardSingle correct
  2. 2 Apr 2025, Shift 2 · Q22If the sum of the first 10 terms of the series…HardNumerical value
  3. 9 Apr 2024, Shift 1 · Q5If the sum of the series 11⋅(1+d)+1(1+d)(1+2d)+…+1(1+9d)(1+10d)\frac{1}{1\cdot(1+d)}+\frac{1}{(1+d)(1+2d)}+\ldots+\frac{1}{(1+9d)(1+10d)} is equal to 55, then 50d50d is equal…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 42 of the 174 JEE Main shifts held from 2017 to 2026.