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JEE Main 202621 JanuaryEvening Shift

Exam: JEE Main
Year: 2026
Date: 21 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2026 · 21 January · Evening Shift · Mathematics · Area Under Curves

If the area of the region \ (x, y): 1-2 x ≤ y ≤ 4-x^ 2 , x ≥ 0, y ≥...

If the area of the region

\left\{(x, y): 1-2 x \leqslant y \leqslant 4-x^{2}, x \geqslant 0, y \geqslant 0\right\}

is

\frac{\alpha}{\beta}, \alpha, \beta \in \mathbf{N}, \operatorname{gcd}(\alpha, \beta)=1

, then the value of

(\alpha+\beta)

is : $If the area of the region \ (x, y): 1-2 x ≤ y ≤ 4-x^ 2 , x ≥ 0, y ≥ 0\ is (α)/(β), α, β ∈ N, gcd(α, β)=1 , then the$

Options

A $67$
B $91$
C73
D85

Correct answer

C. 73

Step-by-step solution

$If the area of the region \ (x, y): 1-2 x ≤ y ≤ 4-x^ 2 , x ≥ 0, y ≥ 0\ is (α)/(β), α, β ∈ N, gcd(α, β)=1 , then the$
Required area

= \dfrac{2}{3} \times 8 - \dfrac{1}{2} \times \dfrac{1}{2} \times 1

= \dfrac{16}{3} - \dfrac{1}{4} = \dfrac{61}{12} = \dfrac{\alpha}{\beta}

\Rightarrow \alpha + \beta = 73

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