JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q8

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

If the probability that the random variable

X

takes the value

x

is given by

P(X = x) = k(x + 1)3^{-x},\ x = 0, 1, 2, 3\ldots

, where

k

is a constant, then

P(X \geq 3)

is equal to

(1) $\frac{7}{27}$
(2) $\frac{8}{27}$
(3) $\frac{4}{9}$
(4) $\frac{1}{9}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Probability
Topic: Arithmetico-Geometric Series
Idea tested: Sum of Infinite AGP

Same idea in other shifts

Asked 5× in all

27 Jan 2024, Shift 1 · Q24If $8=3+\dfrac{1}{4}(3+p)+\dfrac{1}{4^2}(3+2p)+\dfrac{1}{4^3}(3+3p)+\cdots\cdots\infty$ , then the value of p is ________.MediumNumerical value
29 Jul 2022, Shift 1 · Q24Let $a_1, a_2, a_3, \ldots$ be an A.P. If $\sum_{r=1}^{\infty} \frac{a_r}{2^r} = 4$ , then $4a_2$ is equal to __________.MediumNumerical value
26 Feb 2021, Shift 1 · Q78The sum of the infinite series $1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\ldots\ldots$ is equal to :EasySingle correct
25 Jul 2021, Shift 1 · Q84If the value of…MediumNumerical value

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.