JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q58

Question 58 of 75 in this shift, Maths question 8 of 25.

Let

f

be a twice differentiable function on

(1, 6)

. If

f(2) = 8

f'(2) = 5

f'(x) \ge 1

and

f''(x) \ge 4

, for all

x \in (1, 6)

, then :

(1) $f(5) \le 10$
(2) $f(5) + f'(5) \ge 28$ Official answer
(3) $f'(5) + f''(5) \le 20$
(4) $f(5) + f'(5) \le 26$

Official answer

Option 2

NTA final key (Sep 2020).

Chapter: Application of Derivatives
Topic: Mean Value Theorem
Idea tested: Proving Inequalities via LMVT

Same idea in other shifts

Asked 3× in all

8 Jan 2020, Shift 2 · Q59Let S be the set of all functions $f : [0, 1] \to \mathbf{R}$ , which are continuous on $[0, 1]$ and differentiable on $(0, 1)$ . Then for…HardSingle correct
9 Jan 2020, Shift 1 · Q60Let $f$ be any function continuous on [a, b] and twice differentiable on (a, b). If for all $x\in(\mathrm{a, b})$ , $f'(x)>0$ and…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.