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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctHardConceptual

JEE Main 30 January 2024, Shift 1, Maths Q9

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

Let g:R→Rg:\mathbf{R}\to\mathbf{R} be a non constant twice differentiable function such that g′(12)=g′(32)g'\left(\frac{1}{2}\right)=g'\left(\frac{3}{2}\right). If a real valued function ff is defined as f(x)=12[g(x)+g(2−x)]f(x)=\frac{1}{2}[g(x)+g(2-x)], then
  1. (1)f′′(x)=0f''(x)=0 for atleast two xx in (0,2)(0,2)Official answer
  2. (2)f′′(x)=0f''(x)=0 for exactly one xx in (0,1)(0,1)
  3. (3)f′′(x)=0f''(x)=0 for no xx in (0,1)(0,1)
  4. (4)f′(32)+f′(12)=1f'\left(\frac{3}{2}\right)+f'\left(\frac{1}{2}\right)=1

Official answer

Option 1

NTA final key.

Chapter
Application of Derivatives
Topic
Rolle's Theorem
Idea tested
Higher-Order Derivative Roots

Same idea in other shifts

Asked 4× in all
  1. 4 Apr 2024, Shift 2 · Q25Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a thrice differentiable function such that f(0)=0,f(1)=1,f(2)=−1,f(3)=2f(0)=0, f(1)=1, f(2)=-1, f(3)=2 and f(4)=−2f(4)=-2. Then, the…HardNumerical value
  2. 28 Jul 2022, Shift 1 · Q23Let f:[0,1]→Rf:[0,1]\to\mathbf{R} be a twice differentiable function in (0,1)(0,1) such that f(0)=3f(0)=3 and f(1)=5f(1)=5. If the line y=2x+3y=2x+3 intersects…MediumNumerical value
  3. 31 Aug 2021, Shift 2 · Q68Let ff be any continuous function on [0,2][0, 2] and twice differentiable on (0,2)(0, 2). If f(0)=0f(0) = 0, f(1)=1f(1) = 1 and f(2)=2f(2) = 2, then :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.