JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q77

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MathematicsSingle correct+4 / -1Question 77 of 90

If $(2+\sin x)\dfrac{dy}{dx}+(y+1)\cos x=0$ and $y(0)=1$ , then $y\left(\dfrac\pi2\right)$ is equal to :

-\dfrac23

-\dfrac13

\dfrac43

\dfrac13

Answer and worked solution

Official answer: D

The equation is $\dfrac d{dx}\left[(y+1)(2+\sin x)\right]=0$ , so $(y+1)(2+\sin x)=4$ (from $y(0)=1$ ). At $\frac\pi2$ : $3(y+1)=4$ , so $y=\frac13$ .

Topics:Variable separable

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 77