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Friday, 9 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 18 March 2021, Shift 1, Maths Q70

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

If f(x)={1∣x∣; ∣x∣≥1ax2+b; ∣x∣<1f(x)=\begin{cases}\dfrac{1}{|x|} & ;\ |x|\ge1\\ ax^2+b & ;\ |x|<1\end{cases} is differentiable at every point of the domain, then the values of a and b are respectively :
  1. (1)12,12\frac{1}{2},\frac{1}{2}
  2. (2)−12,32-\frac{1}{2},\frac{3}{2}Official answer
  3. (3)52,−32\frac{5}{2},-\frac{3}{2}
  4. (4)12,−32\frac{1}{2},-\frac{3}{2}

Official answer

Option 2

NTA final key.

Chapter
Continuity and Differentiability
Topic
Continuity and Differentiability
Idea tested
Finding Unknowns using Differentiability

Same idea in other shifts

Asked 3× in all
  1. 30 Jan 2024, Shift 2 · Q8Let aa and bb be real constants such that the function ff defined by…MediumSingle correct
  2. 8 Apr 2023, Shift 2 · Q25Let kk and mm be positive real numbers such that the function…MediumNumerical value

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 42 of the 174 JEE Main shifts held from 2017 to 2026.