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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctHardConceptual

JEE Main 9 January 2020, Shift 1, Maths Q60

Question 60 of 75 in this shift, Maths question 10 of 25, Section A.

Let ff be any function continuous on [a, b] and twice differentiable on (a, b). If for all x∈(a,b)x\in(\mathrm{a, b}), f′(x)>0f'(x)>0 and f′′(x)<0f''(x)<0, then for any c∈(a,b)\mathrm{c}\in(\mathrm{a, b}), f(c)−f(a)f(b)−f(c)\frac{f(\mathrm{c})-f(\mathrm{a})}{f(\mathrm{b})-f(\mathrm{c})} is greater than :
  1. (1)b−cc−a\frac{\mathrm{b-c}}{\mathrm{c-a}}
  2. (2)c−ab−c\frac{\mathrm{c-a}}{\mathrm{b-c}}Official answer
  3. (3)1
  4. (4)b+ab−a\frac{\mathrm{b+a}}{\mathrm{b-a}}

Official answer

Option 2

NTA final key (Jan 2020).

Chapter
Continuity and Differentiability
Topic
Mean Value Theorem
Idea tested
Proving Inequalities via LMVT

Same idea in other shifts

Asked 3× in all
  1. 8 Jan 2020, Shift 2 · Q59Let S be the set of all functions f:[0,1]→Rf : [0, 1] \to \mathbf{R}, which are continuous on [0,1][0, 1] and differentiable on (0,1)(0, 1). Then for…HardSingle correct
  2. 4 Sep 2020, Shift 1 · Q58Let ff be a twice differentiable function on (1,6)(1, 6). If f(2)=8f(2) = 8, f′(2)=5f'(2) = 5, f′(x)≥1f'(x) \ge 1 and f′′(x)≥4f''(x) \ge 4, for all…HardSingle 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.