Area Under Curves: JEE Main Mathematics Previous Year Questions

201 previous year questions from Area Under Curves. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $Let A_{1} be the bounded area enclosed by the curves y = x^{2} + 2, x + y = 8 and y -axis that lies in the first quadrant. Let A_{2} be the bounded area en\dots$
2. $The curve y = a x^{2} + bx passes through the point (1, 2) and lies above the X -axis for 0 \leq x \leq 8 . If the area enclosed by this cur\dots$
3. $If the area of the region bounded by the curves y = x^{2} and x = y^{2} is k, then the area of the region bounded by the curves\dots$
4. $The area (in sq. units) of the region bounded by the curves y = 4 | cos x | and y = - | cos x | from\dots$
5. $The area of the region bounded by the lines y = mx, x = 1, x = 2, and x axis is 6 sq. units, then ' m' is$
6. $The area enclosed by the closed curve C given by the differential equation \frac{dy}{dx} + \frac{x - 1}{y - 2} = 0, y (1) = 0 is 4 π . Let P and Q\dots$
7. $The area bounded by the curve y = sin (\frac{x}{3}), x -axis and lines x = 0 and x = 3 π is$
8. $The area of the region enclosed between the circles x^{2} + y^{2} = 4 and x^{2} + (y - 2)^{2} = 4 is:$
9. $Area of the region bounded by the curve y = tan x, the x -axis and the line x = \frac{π}{3} is$
10. $Let f (α) denote the area of the region in the first quadrant bounded by x = 0, x = 1, y^{2} = x and\dots$
11. $The area of the region, inside the ellipse x^{2} + 4 y^{2} = 4 and outside the region bounded by the curves y = | x | - 1 and y = 1 - | x |, is :$
12. $Let f (x) be a positive function such that the area bounded by y = f (x), y = 0 from x = 0 to x = a > 0 is e^{- a} + 4 a^{2} + a - 1 . The\dots$
13. $If the area of the ellipse is \frac{x ^{2}}{25} + \frac{y ^{2}}{λ ^{2}} = 1 is 20 π square units, then λ is$
14. $Let the area of the region {(x, y) : ∣2 x - 1∣ \leq y \leq ∣ x^{2} - x ∣, 0 \leq x \leq 1} be A . Then (6 A + 11)^{2} is equal to ________$
15. $Let f : [0, \infty) \to R be a differentiable function such that\dots$
16. $Let y = y (x) be the solution of the differentialequation xdy - ydx = (x^{2} - y^{2}) dx, x \geq 1, with\dots$
17. $The area of the triangle formed by the tangent and the normal drawn to the curve y^{2} = 4 x at (1, 2) with Y -axis is (in square units)$
18. $For a > 0, let the curves C_{1} : y^{2} = ax and C_{2} : x^{2} = ay intersect at origin O and a point P . Let the line\dots$
19. $Let A be the area bounded by the curve y = x (x - 3), the x -axis and the ordinates x = - 1 and x = 2. Then 12 A is equal to _______ .$
20. $The sum of squares of all possible values of k, for which area of the region bounded by the parabolas 2 y^{2} = kx and ky^{2} = 2 (y - x) \dots$
21. $The area included between the parabola y = \frac{x ^{2}}{4 a} and the curve y = \frac{8 a ^{3}}{( x ^{2} + 4 a ^{2} )} is$
22. $The area of the region R = ((x, y) : xy \leq 8, 1 \leq y \leq x^{2}, x \geq 0) is$
23. $The area enclosed between the parabola y = x^{2} - x + 2 and the line y = x + 2 in sq. units equals$
24. $The parabola y^{2} = 4 x divides the area of the circle x^{2} + y^{2} = 5 in two parts. The area of the smaller part is equal to:$
25. $The area (in sq. units) of the region bounded by the curve x^{2} = 4 y and the straight line x = 4 y - 2 is :$

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Area Under Curves: JEE Main Mathematics Previous Year Questions

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