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

5 Apr 2026, Shift 2 · Q20Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x)=g''(x)$ for all $x \in \mathbf{R}$ , $f'(1)=2g'(1)=4$ and…MediumSingle correct
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

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.