QJEEAdv24Mab426: JEE Advanced 2024 Mathematics - Class 12 JEEAdv24Mab426 Solution: Let and . If the area of the region is , then is equal to

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QJEEAdv24Mab426: JEE Advanced 2024 Mathematics - Class 12 JEEAdv24Mab426 Solution: Let and . If the area of the region is , then is equal to

Let

S=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0, y \geq 0, y^2 \leq 4 x, y^2 \leq 12-2 x\right.

and

\left.3 y+\sqrt{8} x \leq 5 \sqrt{8}\right\}

. If the area of the region

S

is

\alpha \sqrt{2}

, then

\alpha

is equal to

Multiple Choice Options

A $\frac{17}{2}$
B $\frac{17}{3}$
C $\frac{17}{4}$
D $\frac{17}{5}$

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Accepted Answer

JEE Advanced 2024 Paper 2 Online Mathematics - Application of Integration Question 2 English Explanation

Point of intersection of all curves is $(2, 2 \sqrt{2})$

$\begin{aligned} Area = A_{1} + A_{2} \\ α \sqrt{2} = \int_{0}^{2} 2 \sqrt{x} dx + \frac{1}{2} \times 3 \times 2 \sqrt{2} \\ α \sqrt{2} = 2 {[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]}_{0}^{2} + 3 \sqrt{2} \\ α \sqrt{2} = \frac{17 \sqrt{2}}{3} \\ α = \frac{17}{3} \end{aligned}$

QJEEAdv24Mab426: JEE Advanced 2024 Mathematics - Class 12 JEEAdv24Mab426 Solution: Let and . If the area of the region is , then is equal to

Multiple Choice Options

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