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Area Under Curves — NDA Mathematics PYQs

54 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.

54 questionsMathematicsSolutions on every page
1

Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

NDA 2026 Solution View → 2

Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the area bounded by the curves, the lines x=0 and x=1 ?

NDA 2026 Solution View → 3

Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

NDA 2026 Solution View → 4

Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| . What is the area bounded by the curve f(x) and y = 3 ?

NDA 2025 Solution View → 5

Consider the following for the two (02) items that follow: Let the function f(x) = x^2 - 1 . What is the area bounded by the function f(x) and the x -axis?

NDA 2025 Solution View → 6

For the following three (03) items: Consider the function f(x) = x|x| . What is the area bounded by the curve f(x) , the x -axis and the lines x = -2 and x = 1 ?

NDA 2025 Solution View → 7

Consider the following for the two (02) items that follow: The slope of the tangent to the curve y = f(x) at (x, f(x)) is 4 for every real number x and the curve passes through the

NDA 2025 Solution View → 8

What is the area of the region bounded by |x| 2k and |y| k , where k is a positive real number?

NDA 2025 Solution View → 9

Consider the following for the two (02) items that follow: Let f(x) = [x^2] , where [ ] is the greatest integer function. What is _ 2 ^ 3 f(x) , dx equal to?

NDA 2025 Solution View → 10

Paragraph: The area bounded by the parabola y^2=k x and the line x=k , where k>0 , is 4 3 square units. Question: What is the value of k ?

NDA 2024 Solution View → 11

The circle x^2+y^2-2 x=0 is partitioned by line y=x in two segments. Let A ₁, ~A ₂ be the areas of major and minor segments respectively. What is the value of 2 (A₁+A₂ ) A₁-3 A₂ ?

NDA 2024 Solution View → 12

Paragraph: The area bounded by the parabola y^2=k x and the line x=k , where k>0 , is 4 3 square units. Question: What is the area of the parabola bounded by the latus rectum?

NDA 2024 Solution View → 13

The circle x^2+y^2-2 x=0 is partitioned by line y=x in two segments. Let A ₁, ~A ₂ be the areas of major and minor segments respectively. What is the value of A₁ ?

NDA 2024 Solution View → 14

What is the area between the curve f(x)=x|x| and x -axis for x [-1,1] ?

NDA 2023 Solution View → 15

For what value of m with m 0 , is the area bounded by the lines y=x, y=m x and x=2 equal to 3 ?

NDA 2023 Solution View → 16

What is the area of the region (in the first quadrant) bounded by y= 1-x^2 , y=x and y=0 ?

NDA 2022 Solution View → 17

What is the area of the region enclosed in the first quadrant by x^2+y^2= ^2, y= x and x=0 ?

NDA 2022 Solution View → 18

What is the area included in the first quadrant between the curves y=x and y=x^3 ?

NDA 2022 Solution View → 19

What is the area of the region bounded by x-|y|=0 and x-2=0 ?

NDA 2022 Solution View → 20

What is the area bounded by y=[x] , where [ ] is the greatest integer function, the x -axis and the lines x=-1.5 and x=-1.8 ?

NDA 2021 Solution View → 21

What is the area bounded by y= 16-x^2 , y 0 and the x -axis?

NDA 2021 Solution View → 22

What is the area of the region enclosed between the curve y^2=2 x and the straight line y=x ?

NDA 2020 Solution View → 23

What is the area of the region bounded by |x| 5, y=0 and y=8 ?

NDA 2019 Solution View → 24

What is the area of the region enclosed between the curve y^2=2 x and the straight line y=x ?

NDA 2019 Solution View → 25

What is the area of one of the loops between the curve y = c x and x -axis?

NDA 2019 Solution View → 26

What is the area of the region bounded by the parabolas y^2=6(x-1) and y^2=3 x ?

NDA 2018 Solution View → 27

The area bounded by the curve |x|+|y|=1 is

NDA 2017 Solution View → 28

What is the area bounded by the curves |y|=1-x^2 ?

NDA 2016 Solution View → 29

Consider the function f ( x )=| x -1|+ x ^2 , where x R . What is the area of the region bounded by x -axis, the curve y=f(x) and the two ordinates x=1 and x= 3 2 ?

NDA 2016 Solution View → 30

Consider the function f ( x )=| x -1|+ x ^2 , where x R . What is the area of the region bounded by x -axis, the curve y=f(x) and the two ordinates x= 1 2 and x=1 ?

NDA 2016 Solution View → 31

Consider the curves y=|x-1| and |x|=2 What is the area of the region bounded by the curves and x-axis?

NDA 2016 Solution View → 32

Consider the curves f(x)=x|x|-1 and g(x)= cases 3 x 2 , & x 0 2 x, & x 0 cases What is the area bounded by the curves?

NDA 2016 Solution View → 33

The area bounded by the coordinate axes and the curve x + y =1 , is

NDA 2015 Solution View → 34

Consider the curves y= x and y= x . What is the area of the region bounded by the above two curves and the lines x= 4 and x= 2 ?

NDA 2015 Solution View → 35

Consider the curves y= x and y= x . What is the area of the region bounded by the above two curves and the lines x =0 and x= 4 ?

NDA 2015 Solution View → 36

Consider the line x= 3 y and the circle x^2+y^2=4 . What is the area of the region in the first quadrant enclosed by the x -axis, the line x= 3 and the circle?

NDA 2015 Solution View → 37

Consider the line x= 3 y and the circle x^2+y^2=4 . What is the area of the region in the first quadrant enclosed by the x -axis, the line x= 3 y and the circle?

NDA 2015 Solution View → 38

The line 2 y=3 x+12 cuts the parabola 4 y=3 x^2 . What is the area enclosed by the parabola, the line and the y -axis in the first quadrant?

NDA 2014 Solution View → 39

The line 2 y=3 x+12 cuts the parabola 4 y=3 x^2 . What is the area enclosed by the parabola and line?

NDA 2014 Solution View → 40

What is the area of the parabola x^2=y bounded by the line y=1 ?

NDA 2013 Solution View → 41

What is the area bounded by y= x, y=0 and x= 4 ?

NDA 2013 Solution View → 42

What is the area of the triangle bounded by the sides x=0, y=0 and x+y=2 ?

NDA 2013 Solution View → 43

What is the area bounded by the lines x=0 , y=0 and x+y+2=0 ?

NDA 2013 Solution View → 44

What is the area of the region enclosed by y=2|x| and y=4 ?

NDA 2013 Solution View → 45

The area bounded by the curve x=f(y) , the y -axis and the two lines y=a and y=b is equal to:

NDA 2012 Solution View → 46

What is the area of the portion of the curve y= x , lying between x=0, y=0 and x=2 ?

NDA 2012 Solution View → 47

What is the area of the region bounded by the lines y=x, y=0 and x=4 ?

NDA 2012 Solution View → 48

What is the area between the curve y= 3 x, 0 x 6 and the co-ordinate axes?

NDA 2011 Solution View → 49

What is the area bounded by the curves y=e^x , y=e^ -x and the straight line x=1 ?

NDA 2011 Solution View → 50

What is the area bounded by the curve x + y = a (x, y 0) and the coordinate axes?

NDA 2011 Solution View → 51

What is the area under the curve f(x)=x e^x above the x axis and between the lines x=0 and x=1 ?

NDA 2010 Solution View → 52

What is the area bounded by the curve y=x^2 and the line y=16 ?

NDA 2010 Solution View → 53

What is the area of the region bounded by the curve f(x)=1- x^2 4 , x [-2,2] and the x -axis)?

NDA 2010 Solution View → 54

What is the area enclosed between the curves y^2=12 x and the lines x=0 and y=6 ?

NDA 2010 Solution View →
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