JEE Main 2020 (Online) 6th September Evening Slot | Application of Derivatives Question 135 | Mathematics

The set of all real values of $$\lambda $$ for which the function

$$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$

has exactly one maxima and exactly one minima, is :

$$\left( { - {3 \over 2},{3 \over 2}} \right) - \left\{ 0 \right\}$$

$$\left( { - {3 \over 2},{3 \over 2}} \right)$$

$$\left( { - {1 \over 2},{1 \over 2}} \right) - \left\{ 0 \right\}$$

$$\left( { - {1 \over 2},{1 \over 2}} \right)$$

JEE Main 2020 (Online) 6th September Evening Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

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

If x = 1 is a critical point of the function
f(x) = (3x² + ax – 2 – a)e^x , then :

x = 1 is a local maxima and x = $$ - {2 \over 3}$$ is a local minima of f.

x = 1 and x = $$ - {2 \over 3}$$ are local maxima of f.

x = 1 and x = $$ - {2 \over 3}$$ are local minima of f.

x = 1 is a local minima and x = $$ - {2 \over 3}$$ is a local maxima of f.