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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 5 · Set 1 · Q34
Sketch the curve {( x, y ): 100 x^2+25 y^2=2500} and find the area of the region enclosed by it, using integration.
Sketch the curve $\displaystyle \left\{(\mathrm{x}, \mathrm{y}): 100 \mathrm{x}^{2}+25 \mathrm{y}^{2}=2500\right\}$ and find the area of the region enclosed by it, using integration.
Marking-scheme solution
Required area $\displaystyle =4 \int_{0}^{5} \dfrac{10}{5} \sqrt{25-x^{2}}\, d x$
$\displaystyle =8\left[\dfrac{x}{2} \sqrt{25-x^{2}}+\dfrac{25}{2} \sin^{-1} \dfrac{x}{5}\right]_{0}^{5}$
$\displaystyle =50 \pi$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.