JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q11

MathematicsSingle correct+4 / -1Question 11 of 90

If $\dfrac{dy}{dx}+2y\tan x=\sin x$ , $0<x<\dfrac\pi2$ and $y\left(\dfrac\pi3\right)=0$ , then the maximum value of $y(x)$ is :

\dfrac18

\dfrac34

\dfrac14

\dfrac38

Answer and worked solution

Official answer: A

Integrating factor $\sec^2x$ : $y\sec^2x=\sec x+C$ ; $y\left(\frac\pi3\right)=0$ gives $C=-2$ .

y $=\cos x-2\cos^2x$ , maximum $\frac18$ at $\cos x=\frac14$ .

(A)

Topics:Linear first-order equations Maxima and minima

JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 11