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NDA 2023 Maths · Mathematics · Application of Derivatives · hard

A ladder 5 m long leans against a vertical wall. Its foot is pulled away at 2 m/s. When the foot is 3 m from the wall, the top of the ladder slides…

Single correct option

A ladder 55 m long leans against a vertical wall. Its foot is pulled away at 22 m/s. When the foot is 33 m from the wall, the top of the ladder slides down at the rate of
  1. A. 32\dfrac32 m/s
  2. B. 43\dfrac43 m/s
  3. C. 22 m/s
  4. D. 83\dfrac83 m/s
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Answer: (A) 32\dfrac32 m/s

With x2+y2=25x^2+y^2=25, xdxdt+ydydt=0x\dfrac{dx}{dt}+y\dfrac{dy}{dt}=0. When x=3x=3, y=4y=4, so dydt=−34⋅2=−32\dfrac{dy}{dt}=-\dfrac34\cdot2=-\dfrac32; the top slides down at 32\dfrac32 m/s. The value 83\dfrac83 uses y/xy/x instead of x/yx/y.
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Original question written in the NDA 2023 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