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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Area Under Curves

NDA 2023 · Mathematics · Area Under Curves

For what value of m with m < 0 , is the area bounded by the lines...

For what value of mm with m<0m < 0, is the area bounded by the lines y=x,y=mxy=x, y=m x and x=2x=2 equal to 3 ?

Options

  1. A−12-\frac{1}{2}
  2. B−1-1
  3. C−32-\frac{3}{2}
  4. D−2-2

Correct answer

A. −12-\frac{1}{2}

Step-by-step solution

O(0,0)O(0,0) is the origin A=A(2,2),B=B(2,2m)Area⁡(△OAB)=3A=\mathrm{A}(2,2), B=\mathrm{B}(2,2 m)\operatorname{Area}(\triangle O A B)=3
\frac{1}{2}\left|00122122m1\begin{array}{ccc}0 & 0 & 1 \\ 2 & 2 & 1 \\ 2 & 2 m & 1\end{array}\right|=3\Rightarrow|4 m-4|=6 \Rightarrow 4 m-4= \pm 64 m=10,-2 \Rightarrow \therefore m=\frac{10}{4}, \frac{-2}{4}\because \quad m < 0 so, m=−12m=-\frac{1}{2}
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