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NDA 2025 Maths · Mathematics · Application of Derivatives · medium

The slope of the normal to the curve y=x^2 at the point (1,1) is

Single correct option

The slope of the normal to the curve y=x2y=x^2 at the point (1,1)(1,1) is
  1. A. 12\dfrac12
  2. B. 22
  3. C. −12-\dfrac12
  4. D. −2-2
Show answer and solution

Answer: (C) −12-\dfrac12

The slope of the tangent is dydx=2x=2\frac{dy}{dx}=2x=2 at x=1x=1. The normal is perpendicular to it, so its slope is −12-\frac1 2. The value 22 is the tangent slope, −2-2 has the sign but not the reciprocal, and 12\frac12 has the reciprocal but not the sign. Both operations are needed.
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Original question written in the NDA 2025 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