JEE Main 2020 (Online) 6th September Evening Slot | Application of Derivatives Question 112 | Mathematics

If the tangent to the curve, y = f (x) = xlog_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 :

$${{e - 1} \over e}$$

$${e^{\left( {{1 \over {1 - e}}} \right)}}$$

$${e^{\left( {{1 \over {e - 1}}} \right)}}$$

$${1 \over {e - 1}}$$

JEE Main 2020 (Online) 6th September Morning Slot

MCQ (Single Correct Answer)

-1

The position of a moving car at time t is
given by f(t) = at² + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t₁ , t₂ ] is attained at the point :

$${{\left( {{t_1} + {t_2}} \right)} \over 2}$$

$${{\left( {{t_2} - {t_1}} \right)} \over 2}$$

2a(t₁ + t₂) + b

a(t₂ – t₁) + b

JEE Main 2020 (Online) 5th September Evening Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

Which of the following points lies on the tangent to the curve

x⁴e^y + 2$$\sqrt {y + 1} $$ = 3 at the point (1, 0)?

(2, 2)

(–2, 4)

(2, 6)