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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 February 2021, Shift 2, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as f(x)={−55x,if x<−52x3−3x2−120x,if −5≤x≤42x3−3x2−36x−336,if x>4,f(x)=\begin{cases}-55x, & \text{if } x<-5\\ 2x^3-3x^2-120x, & \text{if } -5\leq x\leq4\\ 2x^3-3x^2-36x-336, & \text{if } x>4,\end{cases} Let A = {x∈R:f is increasing}\{x\in\mathbf{R}: f \text{ is increasing}\}. Then A is equal to :
  1. (1)(−∞,−5)∪(4,∞)(-\infty,-5)\cup(4,\infty)
  2. (2)(−5,−4)∪(4,∞)(-5,-4)\cup(4,\infty)Official answer
  3. (3)(−∞,−5)∪(−4,∞)(-\infty,-5)\cup(-4,\infty)
  4. (4)(−5,∞)(-5,\infty)

Official answer

Option 2

NTA final key.

Chapter
Application of Derivatives
Topic
Monotonicity
Idea tested
Monotonicity in Piecewise Functions

Same idea in other shifts

Asked 2× in all
  1. 22 Jul 2021, Shift 2 · Q75Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as f(x)={−43x3+2x2+3x,x>03xex,x≤0f(x)=\begin{cases}-\frac{4}{3}x^3+2x^2+3x, & x>0\\ 3xe^x, & x\leq0\end{cases} Then ff is…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.