JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 17 March 2021, Shift 1, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

The value of

\lim_{x\to0^{+}}\frac{\cos^{-1}(x-[x]^{2})\cdot\sin^{-1}(x-[x]^{2})}{x-x^{3}}

, where

[x]

denotes the greatest integer

\leq x

is :

(1) $\frac{\pi}{4}$
(2) $0$
(3) $\frac{\pi}{2}$ Official answer
(4) $\pi$

Official answer

Option 3

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 Feb 2024, Shift 2 · Q9Let $f(x)=\begin{cases}x-1, & x \text{ is even,}\\ 2x, & x \text{ is odd,}\end{cases}$ $x\in\mathbf{N}$ . If for some $a\in\mathbf{N}$ ,…MediumSingle correct
3 Sep 2020, Shift 1 · Q58Let $[t]$ denote the greatest integer $\le t$ . If for some $\lambda\in\mathbf{R}-\{0,1\}$ ,…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.