Learn

Saturday, 31 October

JEE Main 2025 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q22

Question 22 of 75 in this shift, Maths question 22 of 25, Section B.

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number nn be denoted by Wn\mathrm{W}_n. Let the probability P(Wn)\mathrm{P}(\mathrm{W}_n) of choosing the word Wn\mathrm{W}_n satisfy P(Wn)=2P(Wn−1)\mathrm{P}(\mathrm{W}_n) = 2\mathrm{P}(\mathrm{W}_{n-1}), n>1n > 1. If P(CDBEA)=2α2β−1\mathrm{P(CDBEA)} = \frac{2^{\alpha}}{2^{\beta} - 1}, α,β∈N\alpha, \beta \in \mathbb{N}, then α+β\alpha + \beta is equal to : ______

Official answer

183

NTA final key.

Chapter
Probability
Topic
AP and GP
Idea tested
GP Sum of n terms

Same idea in other shifts

Asked 10× in all
  1. 6 Apr 2026, Shift 1 · Q24For the functions f(θ)=αtan⁡2θ+βcot⁡2θf(\theta)=\alpha\tan^2\theta+\beta\cot^2\theta, and g(θ)=αsin⁡2θ+βcos⁡2θg(\theta)=\alpha\sin^2\theta+\beta\cos^2\theta,…HardNumerical value
  2. 29 Jan 2024, Shift 1 · Q7If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is…MediumSingle correct
  3. 28 Jul 2022, Shift 2 · Q86If 6312+10311+20310+4039+...+102403=2n⋅m\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+...+\frac{10240}{3}=2^n\cdot m, where m is odd, then m⋅nm\cdot n…MediumNumerical value
  4. 25 Jun 2022, Shift 1 · Q4Let f:N→Rf:\mathbf{N}\to\mathbf{R} be a function such that f(x+y)=2f(x) f(y)f(x+y)=2f(x)\,f(y) for natural numbers xx and yy. If f(1)=2f(1)=2, then the value…MediumSingle correct
  5. 25 Jun 2022, Shift 1 · Q8If 12⋅310+122⋅39+…+1210⋅3=K210⋅310\frac{1}{2\cdot3^{10}}+\frac{1}{2^2\cdot3^9}+\ldots+\frac{1}{2^{10}\cdot3}=\frac{K}{2^{10}\cdot3^{10}}, then the remainder when K is…MediumSingle correct
  6. 25 Jun 2022, Shift 1 · Q30The greatest integer less than or equal to the sum of first 100 terms of the sequence…MediumNumerical value
  7. 9 Jan 2020, Shift 2 · Q57Let ana_n be the nthn^{\mathrm{th}} term of a G.P. of positive terms. If ∑n=1100a2n+1=200\sum_{n=1}^{100}a_{2n+1}=200 and ∑n=1100a2n=100\sum_{n=1}^{100}a_{2n}=100,…MediumSingle correct
  8. 5 Sep 2020, Shift 1 · Q57If 210+29⋅31+28⋅32+....+2⋅39+310=S−2112^{10}+2^{9}\cdot3^{1}+2^{8}\cdot3^{2}+....+2\cdot3^{9}+3^{10}=S-2^{11}, then S 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.