JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 September 2020, Shift 2, Maths Q59

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

If the tangent to the curve,

y=f(x)=x\log_e x

(x>0)

at a point

(c, f(c))

is parallel to the line - segment joining the points

(1, 0)

and

(e, e)

, then c is equal to :

(1) $e^{\left(\frac{1}{e-1}\right)}$ Official answer
(2) $e^{\left(\frac{1}{1-e}\right)}$
(3) $\frac{e-1}{e}$
(4) $\frac{1}{e-1}$

Official answer

Option 1

NTA final key (Sep 2020).

Chapter: Application of Derivatives
Topic: Mean Value Theorem
Idea tested: Finding the Mean Value Point

Same topic in other shifts

All Mean Value Theorem questions

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3 Aug 2021, Shift 2 · Q70Let $f : \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $f(0) = 2$ . If $\left|\frac{df}{dx}\right| \le 3$ , for all…MediumSingle correct
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
4 Sep 2020, Shift 1 · Q58Let $f$ 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…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.