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NDA 2021 Maths · Mathematics · Differential Equations · medium

The curve passing through ((π)/(2),3) whose slope at every point (x,y) equals cos x is

Single correct option

The curve passing through (π2,3)\left(\dfrac\pi2,3\right) whose slope at every point (x,y)(x,y) equals cos⁡x\cos x is
  1. A. y=sin⁡x+3y=\sin x+3
  2. B. y=−sin⁡x+4y=-\sin x+4
  3. C. y=sin⁡x+2y=\sin x+2
  4. D. y=cos⁡x+3y=\cos x+3
Show answer and solution

Answer: (C) y=sin⁡x+2y=\sin x+2

The slope condition is dydx=cos⁡x\dfrac{dy}{dx}=\cos x, so y=sin⁡x+Cy=\sin x+C. Using the point: 3=sin⁡π2+C=1+C3=\sin\dfrac\pi2+C=1+C, so C=2C=2. The option sin⁡x+3\sin x+3 ignores the value of sin⁡x\sin x at the given point.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake