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Friday, 9 October

JEE Main Maths · Binomial Theorem

Sum of all Coefficients

Sum of all Coefficients (Binomial Theorem) was asked 3 times in 3 JEE Main shifts, 2017–2024, out of the 42 shifts Lumi analysed. 2 of the 3 had a numerical answer.

Times asked
3
in 3 shifts
Years
2017–2024
Usual format
Numerical value
Multi-step
Pattern
Frequent
repeats across shifts

How it is asked

  • Sum of coefficients of binomial-type series
  • Mean of selected binomial coefficients

Difficulty

Easy 0Medium 2Hard 1

Where it sits

Chapter: Binomial Theorem. Topic: Binomial Coefficients, 26 questions over 18 ideas.

Other repeat ideas in this topic

Every time it came

All 3 questions

Newest first, each with its options and official answer.

  1. 31 Jan 2024, Shift 2 · Q23Let the coefficient of xrx^r in the expansion of (x+3)n−1+(x+3)n−2(x+2)+(x+3)n−3(x+2)2+…+(x+2)n−1(x+3)^{n-1}+(x+3)^{n-2}(x+2)+(x+3)^{n-3}(x+2)^2+\ldots+(x+2)^{n-1} be αr\alpha_r. If…HardNumerical value
  2. 11 Apr 2023, Shift 1 · Q21The mean of the coefficients of x,x2,…,x7x, x^2, \ldots, x^7 in the binomial expansion of (2+x)9(2+x)^9 is ______________.MediumNumerical value
  3. 2 Apr 2017 (offline) · Q67The value of (21C1−10C1)+(21C2−10C2)+(21C3−10C3)+(21C4−10C4)+…+(21C10−10C10)(^{21}C_1-{}^{10}C_1)+(^{21}C_2-{}^{10}C_2)+(^{21}C_3-{}^{10}C_3)+(^{21}C_4-{}^{10}C_4)+\ldots+(^{21}C_{10}-{}^{10}C_{10})…MediumSingle correct