JEE Main 2025 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q23

Question 23 of 75 in this shift, Maths question 23 of 25, Section B.

For

t>-1

, let

\alpha_t

and

\beta_t

be the roots of the equation

\left((t+2)^{1/7}-1\right)x^2+\left((t+2)^{1/6}-1\right)x+\left((t+2)^{1/21}-1\right)=0

. If

\lim_{t\to-1^+}\alpha_t=a

and

\lim_{t\to-1^+}\beta_t=b

, then

72(a+b)^2

is equal to ________.

Official answer

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Simplifying with Standard Limits Before L'Hopital

Same idea in other shifts

Asked 6× in all

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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.