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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Differentiation

NDA 2012 · Mathematics · Differentiation

If x^m+y^m=1 such that (d y)/(d x)=-(x)/(y) , then what should be...

If xm+ym=1x^m+y^m=1 such that dydx=−xy\frac{d y}{d x}=-\frac{x}{y}, then what should be the value of mm ?

Options

  1. A0
  2. B1
  3. C2
  4. DNone of the above

Correct answer

C. 2

Step-by-step solution

xm+ym=1mxm−1+mym−1⋅dydx=0\begin{aligned} & x^m+y^m=1 \\ & m x^{m-1}+m y^{m-1} \cdot \frac{d y}{d x}=0\end{aligned}\frac{d y}{d x}=\left(-\frac{x}{y}\right)^{m-1}(−xy)1=(−xy)m−1⇒m−1=1∴m=2.\begin{aligned} & \quad\left(-\frac{x}{y}\right)^1=\left(-\frac{x}{y}\right)^{m-1} \\ & \Rightarrow m-1=1 \quad \therefore m=2.\end{aligned}$
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