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NDA 2019 Maths · Mathematics · Derivatives · easy

For the cycloid x=a(θ-sin θ), y=a(1-cos θ), the value of dy/dx at θ=(π)/(2) is

Single correct option

For the cycloid x=a(θ−sin⁡θ)x=a(\theta-\sin\theta), y=a(1−cos⁡θ)y=a(1-\cos\theta), the value of dydx\dfrac{dy}{dx} at θ=π2\theta=\dfrac\pi2 is
  1. A. 00
  2. B. π2\frac{\pi}{2}
  3. C. 11
  4. D. −1-1
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Answer: (C) 11

dxdθ=a(1−cos⁡θ)\frac{dx}{d\theta}=a(1-\cos\theta) and dydθ=asin⁡θ\frac{dy}{d\theta}=a\sin\theta, so dydx=sin⁡θ1−cos⁡θ=cot⁡θ2\frac{dy}{dx}=\frac{\sin\theta}{1-\cos\theta}=\cot\frac\theta2. At θ=π2\theta=\frac\pi2 this is cot⁡π4=1\cot\frac\pi4=1. The value 00 results from dropping the 11 in the denominator and putting cos⁡π2=0\cos\frac\pi2=0 in the numerator.
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Original question written in the NDA 2019 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