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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 June 2022, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

If ∑k=131(31Ck)(31Ck−1)−∑k=130(30Ck)(30Ck−1)=α(60!)(30!)(31!)\sum_{k=1}^{31}\left({}^{31}C_k\right)\left({}^{31}C_{k-1}\right)-\sum_{k=1}^{30}\left({}^{30}C_k\right)\left({}^{30}C_{k-1}\right)=\frac{\alpha(60!)}{(30!)(31!)}, where α∈R\alpha\in\mathbb{R}, then the value of 16α16\alpha is equal to
  1. (1)1411Official answer
  2. (2)1320
  3. (3)1615
  4. (4)1855

Official answer

Option 1

NTA final key.

Chapter
Binomial Theorem
Topic
Binomial Coefficients
Idea tested
Product Sums with Constant Index Difference

Same topic in other shifts

All Binomial Coefficients questions
  1. 2 Apr 2026, Shift 1 · Q7The number of elements in the set…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q6If for 3≤r≤303 \le r \le 30, (30C30−r)+3(30C31−r)+3(30C32−r)+(30C33−r)=mCr\binom{30}{C_{30-r}} + 3\binom{30}{C_{31-r}} + 3\binom{30}{C_{32-r}} + \binom{30}{C_{33-r}} = ^m C_r, then mm…MediumSingle correct
  3. 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
  4. 5 Apr 2026, Shift 1 · Q23If the sum of the coefficients of x7x^7 and x14x^{14} in the expansion of (1x3−x4)n\left(\frac{1}{x^3} - x^4\right)^n, x≠0x \neq 0, is zero, then…MediumNumerical value
  5. 6 Apr 2026, Shift 1 · Q8If the coefficients of the middle terms in the binomial expansions of (1+αx)26(1+\alpha x)^{26} and (1−αx)28(1-\alpha x)^{28}, α≠0\alpha\neq 0, are…EasySingle correct
  6. 8 Apr 2026, Shift 2 · Q8If…HardSingle 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.