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JEE Advanced 2025Paper 2

Exam: JEE Advanced
Year: 2025
Paper: Paper 2
Subject: Mathematics
Chapter: Area Under Curves

JEE Advanced 2025 · Paper 2 · Mathematics · Area Under Curves

Let ℝ denote the set of all real numbers. Then the area of the...

Let

\mathbb{R}

denote the set of all real numbers. Then the area of the region \left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x>0, y>\frac{1}{x}, 5 x-4 y-1>0,4 x+4 y-17 <0\right\}$ is $Let ℝ denote the set of all real numbers. Then the area of the region \ (x, y) ∈ ℝ × ℝ: x>0, y>(1)/(x), 5 x-4 y-1>0,4$ $Let ℝ denote the set of all real numbers. Then the area of the region \ (x, y) ∈ ℝ × ℝ: x>0, y>(1)/(x), 5 x-4 y-1>0,4$

Options

A $\frac{17}{16}-\log _e 4$
B $\frac{33}{8}-\log _e 4$
C $\frac{57}{8}-\log _e 4$
D $\frac{17}{2}-\log _e 4$

Correct answer

B. $\frac{33}{8}-\log _e 4$

Step-by-step solution

$Let ℝ denote the set of all real numbers. Then the area of the region \ (x, y) ∈ ℝ × ℝ: x>0, y>(1)/(x), 5 x-4 y-1>0,4$
$Let ℝ denote the set of all real numbers. Then the area of the region \ (x, y) ∈ ℝ × ℝ: x>0, y>(1)/(x), 5 x-4 y-1>0,4$
Area =\frac{13}{8}+\frac{20}{8}-\log _e 4=\left(\frac{33}{8}-\log _e 4\right)

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