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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Area Under Curves

NDA 2024 · Mathematics · Area Under Curves

Paragraph: The area bounded by the parabola y^2=k x and the line...

Paragraph: The area bounded by the parabola y2=kxy^2=k x and the line x=kx=k, where k>0k > 0, is 43\frac{4}{3} square units.
Question: What is the value of kk ?

Options

  1. A12\frac{1}{2}
  2. B11
  3. C2\sqrt{2}
  4. D22

Correct answer

B. 11

Step-by-step solution

Given, Area bounded =43squar\frac{4}{3} squar0=2 \int_0^kydx{\mathrm{k}} \mathrm{ydx}43=2∫0kkxdx⇒43=2k23(k)32⇒1=k2⇒k=±1( since k>0)⇒k=1\begin{aligned} & \frac{4}{3}=2 \int_0^{\mathrm{k}} \sqrt{\mathrm{k}}\sqrt{\mathrm{x}}\mathrm{dx} \Rightarrow \frac{4}{3}=2 \sqrt{\mathrm{k}}\frac{2}{3}(\mathrm{k})^{\frac{3}{2}} \Rightarrow 1=\mathrm{k}^2 \\ & \Rightarrow \mathrm{k}=\pm 1 \quad(\text{ since } \mathrm{k} > 0) \\ & \Rightarrow \mathrm{k}=1\end{aligned}$
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