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Friday, 9 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 3 April 2025, Shift 1, Maths Q8

Question 8 of 75 in this shift, Maths question 8 of 25, Section A.

If ∑r=19(r+32r)⋅9Cr=α(32)9−β\sum_{r=1}^{9}\left(\frac{r+3}{2^r}\right)\cdot {}^9C_r = \alpha\left(\frac{3}{2}\right)^9 - \beta, α,β∈N\alpha, \beta \in \mathbb{N}, then (α+β)2(\alpha + \beta)^2 is equal to
  1. (1)27
  2. (2)18
  3. (3)9
  4. (4)81Official answer

Official answer

Option 4

NTA final key.

Chapter
Binomial Theorem
Topic
Binomial Coefficients
Idea tested
Binomial Coefficients with AP Multiplier

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 42 of the 174 JEE Main shifts held from 2017 to 2026.