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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 September 2020, Shift 1, Maths Q59

Question 59 of 75 in this shift, Maths question 9 of 25.

If the function f(x)={k1(x−π)2−1,x≤πk2cos⁡x,x>πf(x)=\begin{cases}k_1(x-\pi)^2-1, & x\le\pi\\ k_2\cos x, & x>\pi\end{cases} is twice differentiable, then the ordered pair (k1,k2)(k_1, k_2) is equal to :
  1. (1)(12,1)\left(\frac{1}{2},1\right)Official answer
  2. (2)(1,1)(1,1)
  3. (3)(12,−1)\left(\frac{1}{2},-1\right)
  4. (4)(1,0)(1,0)

Official answer

Option 1

NTA final key (Sep 2020).

Chapter
Continuity and Differentiability
Topic
Continuity and Differentiability
Idea tested
Existence of Higher Order Derivatives

Same idea in other shifts

Asked 3× in all
  1. 6 Apr 2024, Shift 1 · Q8If f(x)={x3sin⁡(1x),x≠00,x=0f(x)=\begin{cases} x^3\sin\left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases}, thenMediumSingle correct
  2. 24 Jun 2022, Shift 2 · Q17If y=tan⁡−1(sec⁡x3−tan⁡x3)y = \tan^{-1}\left(\sec x^3 - \tan x^3\right), π2<x3<3π2\frac{\pi}{2} < x^3 < \frac{3\pi}{2}, thenHardSingle 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.