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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 24 February 2021, Shift 2, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

If n≥2n\geq2 is a positive integer, then the sum of the series n+1C2+2(2C2+3C2+4C2+….+nC2){}^{n+1}C_2+2\left({}^{2}C_2+{}^{3}C_2+{}^{4}C_2+\ldots.+{}^{n}C_2\right) is :
  1. (1)n(n−1)(2n+1)6\frac{n(n-1)(2n+1)}{6}
  2. (2)n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6}Official answer
  3. (3)n(2n+1)(3n+1)6\frac{n(2n+1)(3n+1)}{6}
  4. (4)n(n+1)2(n+2)12\frac{n(n+1)^2(n+2)}{12}

Official answer

Option 2

NTA final key.

Chapter
Permutations and Combinations
Topic
Binomial Coefficients
Idea tested
Hockey Stick Identity

Same idea in other shifts

Asked 4× in all
  1. 4 Apr 2026, Shift 1 · Q9Let the smallest value of k∈Nk\in\mathbb{N}, for which the coefficient of x3x^3 in…MediumSingle correct
  2. 26 Jun 2022, Shift 2 · Q26If…MediumNumerical value
  3. 4 Sep 2020, Shift 1 · Q55The value of ∑r=02050−rC6\sum_{r=0}^{20} {}^{50-r}C_6 is equal to :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.