Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=\begin{cases}\frac{\lambda|x^2-5x+6|}{\mu(5x-x^2-6)}, & x 2\\ \mu, & x=2\end{cases}$ where $[x]$ is the greatest integer less than or equal to $x$. If $f$ is continuous at $x=2$, then $\lambda+\mu$ is equal to :

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q65

Question 65 of 90 in this shift, Maths question 5 of 30, Section A.

Let

f:\mathbf{R}\to\mathbf{R}

be defined as

f(x)=\begin{cases}\frac{\lambda|x^2-5x+6|}{\mu(5x-x^2-6)}, & x<2\\ e^{\frac{\tan(x-2)}{x-[x]}}, & x>2\\ \mu, & x=2\end{cases}

where

[x]

is the greatest integer less than or equal to

x

. If

f

is continuous at

x=2

, then

\lambda+\mu

is equal to :

(1) $1$
(2) $2e-1$
(3) $e(e-2)$
(4) $e(-e+1)$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Continuity at a Point

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Asked 8× 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 108 of the 174 JEE Main shifts held from 2017 to 2026.