Application of Integrals · Question 3

JEE Advanced 2025 Paper 2MCQMedium📈 Topic in 33% papers+4−1

Let R denote the set of all real numbers. Then the area of the region \(x,y) R R:x>0, y> 1x, 5x-4y-1>0, 4x+4y-17<0 \ is

1716- e 4
338- e 4
578- e 4
172- e 4

Answer

(2) 338- e 4

Solution

Region: above y= 1x, below both lines y= 5x-14 and y= 17-4x4.

Lines meet at (2, 94); y= 5x-14 meets xy=1 at x=1; y= 17-4x4 meets xy=1 at x=4 (and x= 14, not relevant).

Area = 12 5x-14dx+ 24 17-4x4dx- 14 dxx

= 138+ 52- e 4= 338- e 4

Answer: (B)

JEE Advanced 2025 Paper 2

Keep practising — Application of Integrals

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 43. 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?

(4, 3) S
(5, 2) S
Area of R is 143-2 3
Area of R is 143- 3

JEE Advanced 2025 Paper 2

Let S= \(x,y) R R: x 0, y 0, y2 4x, y2 12-2x and 3y+ 8 x 5 8 \. If the area of the region S is 2, then is equal to

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