Let S=(0,2 \pi)-\{\frac{\pi}{2}, \frac{3 \pi}{4}, \frac{3 \pi}{2}, \frac{7 \pi}{4}\}. Let y=y(x), {\x} \in {\S}, be the solution curve of the differential equation \frac{d y}{d x}=\frac{1}{1+\sin 2 x}, y(\frac{\pi}{4})=\frac{1}{2}. If the sum of abscissas of all the points of intersection of the curve {\y}= {\y}( {\x}) with the curve y=\sqrt{2} \sin x is \frac{k \pi}{12}, then {\k} is equal to____ [26-Jun-2022-Shift-1]

JEE Main 26 June 2022 Shift 1 Solved Paper

Section: Mathematics

Question : 30 of 90

Marks: +1, -0

Let S=(0,2π)−{‌

,‌

3π

,‌

3π

,‌

7π

}. Let y=y(x),x∈S, be the solution curve of the differential equation ‌

=‌

1+sin‌2‌x

,y(‌

)=‌

. If the sum of abscissas of all the points of intersection of the curve y=y(x) with the curve y=√2‌sin‌x is ‌

kπ

, then k is equal to____

[26-Jun-2022-Shift-1]

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