Let S denote the locus of the mid-points of those chords of the parabola y^2=x, such that the area of the region enclosed between the parabola and the chord is \frac{4}{3}. Let R denote the region lying in the first quadrant, enclosed by the parabola y^2=x, the curve S, and the lines x=1 and x=4. Then which of the following statements is (are) TRUE? [JEE Adv 2025 P2]

Area of R is \frac{14}{3}-2 \sqrt{3}

Area of R is \frac{14}{3}-\sqrt{3}

JEE Advanced 2025 Paper 2

Section: Mathematics

Question : 6 of 48

Marks: +1, -0

Let S denote the locus of the mid-points of those chords of the parabola y2=x, such that the area of the region enclosed between the parabola and the chord is ‌

. Let R denote the region lying in the first quadrant, enclosed by the parabola y2=x, the curve S, and the lines x=1 and x=4.
Then which of the following statements is (are) TRUE?

[JEE Adv 2025 P2]

(4,√3)∈S
(5,√2)∈S
Area of R is ‌
14
3
−2√3
Area of R is ‌
14
3
−√3

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