JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q20

Question 20 of 90 in this shift, Maths question 20 of 30, Section A.

Let a function

f : \mathbb{R} \rightarrow \mathbb{R}

be defined as :

f(x) = \begin{cases} \int_0^x (5 - |t-3|)\,dt, & x > 4 \\ x^2 + bx, & x \le 4 \end{cases}

where

b \in \mathbb{R}

. If

f

is continuous at

x = 4

, then which of the following statements is NOT true?

(1) $f$ is not differentiable at $x = 4$
(2) $f'(3) + f'(5) = \dfrac{35}{4}$
(3) $f$ is increasing in $\left(-\infty, \dfrac{1}{8}\right) \cup (8, \infty)$ Official answer
(4) $f$ has a local minima at $x = \dfrac{1}{8}$

Official answer

Option 3

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Piecewise Differentiability

Same idea in other shifts

Asked 7× in all

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.