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Saturday, 31 October

JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2026, Shift 1, Maths Q9

Question 9 of 75 in this shift, Maths question 9 of 25, Section A.

Let the smallest value of k∈Nk\in\mathbb{N}, for which the coefficient of x3x^3 in (1+x)3+(1+x)4+(1+x)5+…+(1+x)99+(1+kx)100, x≠0(1+x)^3+(1+x)^4+(1+x)^5+\ldots+(1+x)^{99}+(1+kx)^{100},\ x\neq0, is (43n+1014)(100C3)\left(43n+\frac{101}{4}\right)\left({}^{100}C_3\right) for some n∈Nn\in\mathbb{N}, be pp. Then the value of p+np+n is:
  1. (1)1010
  2. (2)1111Official answer
  3. (3)1212
  4. (4)1313

Official answer

Option 2

NTA final key.

Chapter
Binomial Theorem
Topic
Binomial Coefficients
Idea tested
Hockey Stick Identity

Same idea in other shifts

Asked 4× in all
  1. 26 Jun 2022, Shift 2 · Q26If…MediumNumerical value
  2. 24 Feb 2021, Shift 2 · Q71If 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)…MediumSingle correct
  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.