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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 1 February 2024, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let f(x)={x−1,x is even,2x,x is odd,f(x)=\begin{cases}x-1, & x \text{ is even,}\\ 2x, & x \text{ is odd,}\end{cases} x∈Nx\in\mathbf{N}. If for some a∈Na\in\mathbf{N}, f(f(f(a)))=21f(f(f(a)))=21, then lim⁡x→a−{∣x∣3a−[xa]}\lim_{x\to a^-}\left\{\frac{|x|^3}{a}-\left[\frac{x}{a}\right]\right\}, where [t][t] denotes the greatest integer less than or equal to tt, is equal to :
  1. (1)121121
  2. (2)144144Official answer
  3. (3)169169
  4. (4)225225

Official answer

Option 2

NTA final key.

Chapter
Limits and Derivatives
Topic
L'Hopital's Rule
Idea tested
Handling Greatest Integer Functions

Same idea in other shifts

Asked 3× in all
  1. 17 Mar 2021, Shift 1 · Q70The value of lim⁡x→0+cos⁡−1(x−[x]2)⋅sin⁡−1(x−[x]2)x−x3\lim_{x\to0^{+}}\frac{\cos^{-1}(x-[x]^{2})\cdot\sin^{-1}(x-[x]^{2})}{x-x^{3}}, where [x][x] denotes the greatest integer…MediumSingle correct
  2. 3 Sep 2020, Shift 1 · Q58Let [t][t] denote the greatest integer ≤t\le t. If for some λ∈R−{0,1}\lambda\in\mathbf{R}-\{0,1\},…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.