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Area Under Curves — JEE Main & Advanced Mathematics PYQs

435 previous year questions from Area Under Curves with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

435 questionsMathematicsSolutions on every page
1

Passage: Consider the curve C₁ given by y = e^ -x for x [0, 10 ] , and the curve C₂ given by y = e^ -x ( x + x) for x [0, 10 ] . Let n be the total number of points of intersection

JEE Advanced 2026 Solution View → 2

Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If is the area of the common region that lies inside both the given ellipses, then the value o

JEE Advanced 2026 Solution View → 3

The area of the region (x, y) : x^2 - 8x y -x is :

JEE Main 2026 Solution View → 4

The area of the region (x, y) : 0 y 6 - x, y^2 4x - 3, x 0 is:

JEE Main 2026 Solution View → 5

The area of the region R = (x, y): xy 27, 1 y x^2 is equal to:

JEE Main 2026 Solution View → 6

The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to:

JEE Main 2026 Solution View → 7

The area of the region (x, y): y - |x|, y |x x|, y 0 is:

JEE Main 2026 Solution View → 8

If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A + 6 _e(3)) is equal to _______.

JEE Main 2026 Solution View → 9

Let P₁: y=4 x² and P₂: y=x²+27 be two parabolas. If the area of the bounded region enclosed between P₁ and P₂ is six times the area of the bounded region enclosed between the line

JEE Main 2026 Solution View → 10

The area of the region R = (x, y): x y 8,1 y x², x 0 is

JEE Main 2026 Solution View → 11

Let f( ) denote the area of the region in the first quadrant bounded by x=0, x=1, y²=x and y=| x-5|-|1- x|+ x² . Then (f(0)+f(1)) is equal to

JEE Main 2026 Solution View → 12

Let A ₁ be the bounded area enclosed by the curves y=x²+2, x+y=8 and y -axis that lies in the first quadrant. Let A ₂ be the bounded area enclosed by the curves y=x²+2, y²=x, x=2 ,

JEE Main 2026 Solution View → 13

The area of the region enclosed between the circles x²+y²=4 and x²+(y-2)²=4 is:

JEE Main 2026 Solution View → 14

Let the area of the region bounded by the curve y= x, x , lines x=0, x= 3 2 , and the x -axis be A. Then, A + A ² is equal to _ _ _ _ .

JEE Main 2026 Solution View → 15

The area of the region A = (x, y): 4 x²+y² 8 . and .y² 4 x is:

JEE Main 2026 Solution View → 16

Let the line x=-1 divide the area of the region (x, y): 1+x² y 3-x in the ratio m: n, gcd (m, n)=1 . Then m+n is equal to

JEE Main 2026 Solution View → 17

If the area of the region (x, y): 1-2 x y 4-x², x 0, y 0 is , , N , gcd ( , )=1 , then the value of ( + ) is :

JEE Main 2026 Solution View → 18

The area of the region, inside the ellipse x²+4 y²=4 and outside the region bounded by the curves y=|x|-1 and y=1-|x| , is :

JEE Main 2026 Solution View → 19

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 x+4 y-17 <0 is

JEE Advanced 2025 Solution View → 20

Let the area of the bounded region (x, y): 0 9 x y^2, y 3 x-6 be A. Then 6 A is equal to ________

JEE Main 2025 Solution View → 21

If the area of the region ( x , y ): 1+ x ^2 y x +7,11-3 x is A , then 3 A is equal to

JEE Main 2025 Solution View → 22

If the area of the region bounded by the curves (y=4- x^2 4 ) and (y= x-4 2 ) is equal to ( ), then (6 ) equals

JEE Main 2025 Solution View → 23

If the area of the region (x, y):|x-5| y 4 x is A , then 3 A is equal to _____ .

JEE Main 2025 Solution View → 24

The area of the region (x, y):|x-y| y 4 x is

JEE Main 2025 Solution View → 25

The area of the region bounded by the curve y= |x|, x|x-2| , then x -axis and the lines x=-2 and x=4 is equal to _______ .

JEE Main 2025 Solution View → 26

If the area of the region (x, y): |4-x^2 | y x^2, y 4, x 0 is ( 80 2 - ), , N , then + is equal to _______.

JEE Main 2025 Solution View → 27

Let the area enclosed between the curves |y|=1-x^2 and x^2+y^2=1 be . If 9 = + ; , are integers, then the value of | - | equals.

JEE Main 2025 Solution View → 28

Let the area of the region ( (x, y): 2 y x^2+3, y+|x| 3, y |x-1| ) be A. Then 6 A is equal to :

JEE Main 2025 Solution View → 29

The area of the region bounded by the curves x (1+y^2 )=1 and y^2=2 x is:

JEE Main 2025 Solution View → 30

The area (in sq. units) of the region (x, y): 0 y 2|x|+1,0 y x^2+1,|x| 3 is

JEE Main 2025 Solution View → 31

The area of the region enclosed by the curves y= e ^x, y= | e ^x-1 | and y -axis is:

JEE Main 2025 Solution View → 32

The area of the region (x, y): x^2+4 x+2 y |x+2| is equal to

JEE Main 2025 Solution View → 33

Consider the region R= (x, y): x y 9- 11 3 x^2, x 0 . The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:

JEE Main 2025 Solution View → 34

If the area of the region (x, y):-1 x 1,0 y a+ e ^ |x| - e ^ -x , a 0 is e ^2+8 e +1 e , then the value of a is :

JEE Main 2025 Solution View → 35

If the area of the larger portion bounded between the curves x^2+y^2=25 and y=|x-1| is 1 4 (b +c), b, c N , then b+c is equal to

JEE Main 2025 Solution View → 36

The area of the region enclosed by the curves y=x^2-4 x+4 and y^2=16-8 x is :

JEE Main 2025 Solution View → 37

Let f: R R be a twice differentiable function such that f(x+y)=f(x) f(y) for all x, y R . If f^ (0)=4 a and f satisfies f^ (x)-3 a f^ (x)-f(x)=0 , a 0 , then the area of the region

JEE Main 2025 Solution View → 38

The area of the region, inside the circle (x-2 3 )^2+y^2=12 and outside the parabola y^2=2 3 x is :

JEE Main 2025 Solution View → 39

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

JEE Advanced 2024 Solution View → 40

The area (in square units) of the region enclosed by the ellipse x^2+3 y^2=18 in the first quadrant below the line y=x is

JEE Main 2024 Solution View → 41

The parabola y^2=4 x divides the area of the circle x^2+y^2=5 in two parts. The area of the smaller part is equal to:

JEE Main 2024 Solution View → 42

The area of the region in the first quadrant inside the circle x^2+y^2=8 and outside the parabola y^2=2 x is equal to :

JEE Main 2024 Solution View → 43

Let f(x) be a positive function such that the area bounded by y=f(x), y=0 from x=0 to x=a>0 is e^ -a +4 a^2+a-1 . Then the differential equation, whose general solution is y=c₁ f(x

JEE Main 2024 Solution View → 44

Let the area of the region enclosed by the curve y= x, x and the x axis between x=- to x= be A . Then A^2 is equal to ___________

JEE Main 2024 Solution View → 45

If the area of the region (x, y): a x^2 y 1 x , 1 x 2,0 < a < 1 is ( _ e 2 )- 1 7 then the value of 7 a -3 is equal to:

JEE Main 2024 Solution View → 46

Let the area of the region enclosed by the curves y=3 x, 2 y=27-3 x and y=3 x-x x be A . Then 10 A is equal to

JEE Main 2024 Solution View → 47

The area enclosed between the curves y=x|x| and y=x-|x| is :

JEE Main 2024 Solution View → 48

The area of the region enclosed by the parabolas y=x^2-5 x and y=7 x-x^2 is

JEE Main 2024 Solution View → 49

The area (in sq. units) of the region described by (x, y): y^2 2 x . , and .y 4 x-1 is

JEE Main 2024 Solution View → 50

One of the points of intersection of the curves y=1+3 x-2 x^2 and y= 1 x is ( 1 2 , 2 ) . Let the area of the region enclosed by these curves be 1 24 (l 5 + m )- n _ e (1+ 5 ) , wh

JEE Main 2024 Solution View → 51

Three points O 0 , 0 , P a , a 2 , Q − b , b 2 , a > 0 , b > 0 , are on the parabola y = x 2 . Let S 1 be the area of the region bounded by the line P Q and the parabola, and S 2 b

JEE Main 2024 Solution View → 52

The sum of squares of all possible values of k , for which area of the region bounded by the parabolas 2 y 2 = k x and k y 2 = 2 y − x is maximum, is equal to:

JEE Main 2024 Solution View → 53

The area enclosed by the curves x y + 4 y = 16 and x + y = 6 is equal to:

JEE Main 2024 Solution View → 54

The area of the region enclosed by the parabola y = 4 x − x 2 and 3 y = x − 4 2 is equal to

JEE Main 2024 Solution View → 55

The area of the region x , y : y 2 ≤ 4 x , x < 4 , x y x - 1 x - 2 x - 3 x - 4 > 0 , x ≠ 3 is

JEE Main 2024 Solution View → 56

The area of the region enclosed by the parabola ( y - 2 ) 2 = x - 1 , the line x - 2 y + 4 = 0 and the positive coordinate axes is __________.

JEE Main 2024 Solution View → 57

Let Y = Y ( X ) be a curve lying in the first quadrant such that the area enclosed by the line Y - y = Y ' ( x ) ( X - x ) and the co-ordinate axes, where ( x , y ) is any point on

JEE Main 2024 Solution View → 58

The area (in square units) of the region bounded by the parabola y 2 = 4 ( x - 2 ) and the line y = 2 x - 8 .

JEE Main 2024 Solution View → 59

Let the area of the region ( x , y ) : 0 ≤ x ≤ 3 , 0 ≤ y ≤ min x 2 + 2 , 2 x + 2 be A . Then 12 A is equal to ______.

JEE Main 2024 Solution View → 60

The area (in sq. units) of the part of circle x 2 + y 2 = 169 which is below the line 5 x - y = 13 is π α 2 β - 65 2 + α β sin - 1 12 13 where α , β are coprime numbers. Then α + β

JEE Main 2024 Solution View → 61

If the area of the region ( x , y ) : 0 ≤ y ≤ min 2 x , 6 x - x 2 is A , then 12 A is equal to _______.

JEE Main 2024 Solution View → 62

Let the area of the region ( x , y ) : x - 2 y + 4 ≥ 0 , x + 2 y 2 ≥ 0 , x + 4 y 2 ≤ 8 , y ≥ 0 be m n , where m and n are coprime numbers. Then m + n is equal to ______.

JEE Main 2024 Solution View → 63

Let f : 0 , 1 &#8594; 0 , 1 be the function defined by f x = x 3 3 - x 2 + 5 9 x + 17 36 . Consider the square region S = 0 , 1 &#215; 0 , 1 . Let G = x , y &#8712; S : y &#62; f x

JEE Advanced 2023 Solution View → 64

Let n &#8805; 2 be a natural number and f : 0 , &#160; 1 &#8594; &#8477; be the function defined by f x = n 1 - 2 n x if 0 &#8804; x &#8804; 1 2 n 2 n 2 n x - 1 if 1 2 n &#8804; x

JEE Advanced 2023 Solution View → 65

If the area bounded by the curve 2 y 2 = 3 x , lines x + y = 3 , y = 0 and outside the circle x - 3 2 + y 2 = 2 is A, then 4 &#960; + 4 A is equal to __________.

JEE Main 2023 Solution View → 66

The area of the region x , y : x 2 &#8804; y &#8804; x 2 - 4 , y &#8805; 1 is

JEE Main 2023 Solution View → 67

The area of the region enclosed by the curve f x = max sin x , cos x , - &#960; &#8804; x &#8804; &#960; and the x - axis is

JEE Main 2023 Solution View → 68

The area of the region enclosed by the curve y = x 3 and its tangent at the point ( &#8211; 1 , &#8211; 1 ) is

JEE Main 2023 Solution View → 69

If A is the area in the first quadrant enclosed by the curve C : 2 x 2 - y + 1 = 0 , the tangent to C at the point 1 , 3 and the line x + y = 1 , then the value of 60 A is.........

JEE Main 2023 Solution View → 70

Area of the region x , y : x 2 + y - 2 2 &#8804; 4 , x 2 &#8805; 2 y is

JEE Main 2023 Solution View → 71

If the area of the region x , y : x 2 - 2 &#8804; y &#8804; x is A , then 6 A + 16 2 is equal to ______________

JEE Main 2023 Solution View → 72

Let y = p x be the parabola passing through the points &#8211; 1 , 0 , 0 , 1 and 1 , 0 . If the area of the region x , y : x + 1 2 + y - 1 2 &#8804; 1 , y &#8804; p x is A , then 1

JEE Main 2023 Solution View → 73

Let the area enclosed by the lines x + y = 2 , y = 0 , x = 0 and the curve f ( x ) = min x 2 + 3 4 , 1 + [ x ] where [ x ] denotes the greatest integer &#8804; x , be A . Then the

JEE Main 2023 Solution View → 74

The area of the region x , y : x 2 &#8804; y &#8804; 8 - x 2 , y &#8804; 7 is

JEE Main 2023 Solution View → 75

The area bounded by the curves y = x - 1 + x - 2 and y = 3 is equal to

JEE Main 2023 Solution View → 76

If the area of the region S = ( x , y ) : 2 y - y 2 &#8804; x 2 &#8804; 2 y , x &#8805; y is equal to n + 2 n + 1 - &#960; n - 1 , then the natural number n is equal to _ _ _ _ _ _

JEE Main 2023 Solution View → 77

The area of the region given by x , y : x y &#8804; 8 , 1 &#8804; y &#8804; x 2 is :

JEE Main 2023 Solution View → 78

The area enclosed by the closed curve C given by the differential equation d y d x + x + a y - 2 = 0 , y 1 = 0 is 4 &#960; . Let P and Q be the points of intersection of the curve

JEE Main 2023 Solution View → 79

Let A be the area bounded by the curve y = x x - 3 , the x -axis and the ordinates x = - 1 and x = 2 . Then 12 A is equal to _____ .

JEE Main 2023 Solution View → 80

Let the area of the region x , y : 2 x - 1 &#8804; y &#8804; x 2 - x , 0 &#8804; x &#8804; 1 be A . Then 6 A + 11 2 is equal to _____ .

JEE Main 2023 Solution View → 81

Let for x &#8712; R , f x = x + x 2 and g x = x , x 2 , x &#60; 0 x &#8805; 0 . Then area bounded by the curve y = f o g x and the lines y = 0 , 2 y - x = 15 is equal to _____ .

JEE Main 2023 Solution View → 82

Let q be the maximum integral value of p in 0 , 10 for which the roots of the equation x 2 - p x + 5 4 p = 0 are rational. Then the area of the region x , y : 0 &#8804; y &#8804; (

JEE Main 2023 Solution View → 83

Let A be the area of the region ( x , y ) : y &#8805; x 2 , y &#8805; ( 1 - x ) 2 , y &#8804; 2 x ( 1 - x ) . Then 540 A is equal to

JEE Main 2023 Solution View → 84

Let &#945; be the area of the larger region bounded by the curve y 2 = 8 x and the lines y = x and x = 2 , which lies in the first quadrant. Then the value of 3 &#945; is equal to

JEE Main 2023 Solution View → 85

The area of the region A = x , y : cos x - sin x &#8804; y &#8804; sin x , 0 &#8804; x &#8804; &#960; 2

JEE Main 2023 Solution View → 86

Let A = x , y &#8712; &#8477; 2 : y &#8805; 0 , 2 x &#8804; y &#8804; 4 - x - 1 2 and B = x , y &#8712; &#8477; &#215; &#8477; : 0 &#8804; y &#8804; min 2 x , 4 - x - 1 2 . Then th

JEE Main 2023 Solution View → 87

Let &#916; be the area of the region x , y &#8712; &#8477; 2 : x 2 + y 2 &#8804; 21 , y 2 &#8804; 4 x , x &#8805; 1 . Then 1 2 &#916; - 21 sin - 1 2 7 is equal to

JEE Main 2023 Solution View → 88

Let T and C respectively, be the transverse and conjugate axes of the hyperbola 16 x 2 - y 2 + 64 x + 4 y + 44 = 0 . Then the area of the region above the parabola x 2 = y + 4 , be

JEE Main 2023 Solution View → 89

If the area enclosed by the parabolas P 1 : 2 y = 5 x 2 and P 2 : x 2 - y + 6 = 0 is equal to the area enclosed by P 1 and y = &#945; x , &#945; &#62; 0 , then &#945; 3 is equal to

JEE Main 2023 Solution View → 90

If the area of the region bounded by the curves y 2 - 2 y = - x and x + y = 0 is A , then 8 A =

JEE Main 2023 Solution View → 91

The area enclosed between the curves y 2 + 4 x = 4 and y - 2 x = 2 is

JEE Main 2023 Solution View → 92

Consider the functions f , g : &#8477; &#8594; &#8477; defined by f x = x 2 + 5 12 and g x = 2 1 - 4 x 3 , x &#8804; 3 4 , 0 , x &#62; 3 4 If &#945; is the area of the region x , y

JEE Advanced 2022 Solution View → 93

The area of the region x , y : x - 1 &#8804; y &#8804; 5 - x 2 is equal to

JEE Main 2022 Solution View → 94

The area enclosed by the curves y = log e x + e 2 , x = log e 2 y and x = log e 2 , above the line y = 1 is

JEE Main 2022 Solution View → 95

The area of the region enclosed by y &#8804; 4 x 2 , x 2 &#8804; 9 y and y &#8804; 4 , is equal to

JEE Main 2022 Solution View → 96

Consider a curve y = y x in the first quadrant as shown in the figure. Let the area A 1 is twice the area A 2 . Then the normal to the curve perpendicular to the line 2 x - 12 y =

JEE Main 2022 Solution View → 97

The area of the smaller region enclosed by the curves y 2 = 8 x + 4 and x 2 + y 2 + 4 3 x - 4 = 0 is equal to

JEE Main 2022 Solution View → 98

The area bounded by the curves y = x 2 - 1 and y = 1 is

JEE Main 2022 Solution View → 99

The odd natural number a, such that the area of the region bounded by y = 1 , y = 3 , x = 0 , x = y a is 364 3 , equal to:

JEE Main 2022 Solution View → 100

Let a curve y = y x pass through the point 3 , 3 and the area of the region under this curve, above the x -axis and between the abscissae 3 and x &#62; 3 be y x 3 . If this curve a

JEE Main 2022 Solution View → 101

The area of the region given by A = x , y : x 2 &#8804; y &#8804; min x + 2 , 4 - 3 x is

JEE Main 2022 Solution View → 102

For real numbers a , b a &#62; b &#62; 0 , let Area x , y : x 2 + y 2 &#8804; a 2 and x 2 a 2 + y 2 b 2 &#8805; 1 = 30 &#960; and Area x , y : x 2 + y 2 &#8805; b 2 and x 2 a 2 + y

JEE Main 2022 Solution View → 103

The area enclosed by y 2 = 8 x and y = 2 x that lies outside the triangle formed by y = 2 x , x = 1 , y = 2 2 , is equal to

JEE Main 2022 Solution View → 104

The area of the bounded region enclosed by the curve y = 3 - x - 1 2 - x + 1 and the x -axis is

JEE Main 2022 Solution View → 105

The area of the region S = x , y : y 2 &#8804; 8 x , y &#8805; 2 x , x &#8805; 1 is

JEE Main 2022 Solution View → 106

If the area of the region x , y : x 2 3 + y 2 3 &#8804; 1 , x + y &#8805; 0 , y &#8805; 0 is A , then 256 A &#960; is

JEE Main 2022 Solution View → 107

Let A 1 = x , y : x &#8804; y 2 , x + 2 y &#8804; 8 and A 2 = x , y : x + y &#8804; k . If 27 (Area A 1 ) = 5 (Area A 2 ), then k is equal to

JEE Main 2022 Solution View → 108

The area of the region bounded by y 2 = 8 x and y 2 = 16 3 - x is equal to

JEE Main 2022 Solution View → 109

The area bounded by the curve y = x 2 - 9 and the line y = 3 is

JEE Main 2022 Solution View → 110

The area of the region enclosed between the parabolas y 2 = 2 x - 1 and y 2 = 4 x - 3 is.

JEE Main 2022 Solution View → 111

The area (in sq. units) of the region enclosed between the parabola y 2 = 2 x and the line x + y = 4 is ______.

JEE Main 2022 Solution View → 112

Let S be the region bounded by the curves y = x 3 and y 2 = x . The curve y = 2 x divides S into two regions of areas R 1 and R 2 . If max R 1 , R 2 = R 2 , then R 2 R 1 is equal t

JEE Main 2022 Solution View → 113

The area of the region ( x , y ) : 0 &#8804; x &#8804; 9 4 , 0 &#8804; y &#8804; 1 , x &#8805; 3 y , x + y &#8805; 2 is

JEE Advanced 2021 Solution View → 114

The area, enclosed by the curves y = sin x + cos x and y = | cos x - sin x | and the lines x = 0 , x = &#960; 2 , is :

JEE Main 2021 Solution View → 115

If the line y = m x bisects the area enclosed by the lines x = 0 , y = 0 , x = 3 2 and the curve y = 1 + 4 x - x 2 , then 12 m is equal to .

JEE Main 2021 Solution View → 116

The area of the region bounded by the parabola ( y - 2 ) 2 = ( x - 1 ) , the tangent to it at the point whose ordinate is 3 and the x -axis, is:

JEE Main 2021 Solution View → 117

Let a and b respectively be the points of local maximum and local minimum of the function f ( x ) = 2 x 3 - 3 x 2 - 12 x . If A is the total area of the region bounded by y = f ( x

JEE Main 2021 Solution View → 118

The area of the region S = ( x , y ) : 3 x 2 &#8804; 4 y &#8804; 6 x + 24 is______.

JEE Main 2021 Solution View → 119

The area of the region bounded by y - x = 2 and x 2 = y is equal to :-

JEE Main 2021 Solution View → 120

If the area of the bounded region R = x , y : max 0 , log e x &#8804; y &#8804; 2 x , 1 2 &#8804; x &#8804; 2 is, &#945; log e 2 - 1 + &#946; log e 2 + &#947; then the value of &#9

JEE Main 2021 Solution View →
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