EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 2 - 2018>Q 1

HARD

JEE Advanced

IMPORTANT

Earn 100

Consider two straight lines, each of which is tangent to both the circle $x^{2} + y^{2} = \frac{1}{2}$ and the parabola $y^{2} = 4 x$ . Let these lines intersect at the point $Q$ . Consider the ellipse whose center is at the origin $O (0, 0)$ and whose semi-major axis is $O Q$ . If the length of the minor axis of this ellipse is $\sqrt{2}$ , then which of the following statement(s) is (are) TRUE?

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Important Questions on Area Under Curves

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 2 - 2017>Q 2

If the line

x = α

divides the area of the region

R = {(x, y) \in R^{2} : x^{3} \leq y \leq x, 0 \leq x \leq 1}

into two equal parts, then

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 2 - 2016>Q 3

Area of the region

{(x, y) \in R^{2} : y \geq \sqrt{|x + 3|},

5 y \leq x + 9 \leq 15}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 1 - 2021>Q 4

The area of the region

\{(x, y) : 0 \leq x \leq \frac{9}{4}, 0 \leq y \leq 1, x \geq 3 y, x + y \geq 2\}

is

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 1 - 2020>Q 5

Let the functions

f : R \to R

and

g : R \to R

be defined by

f (x) = e^{x - 1} - e^{- |x - 1|}

and

g (x) = \frac{1}{2} (e^{x - 1} + e^{1 - x})

.
Then the area (in sq. units) of the region in the first quadrant bounded by the curves

y = f (x), y = g (x)

and

x = 0

is

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 1 - 2019>Q 6

The area of the region

\{(x, y) : x y \leq 8, 1 \leq y \leq x^{2}\}

is

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 1 - 2018>Q 7

A farmer

F_{1}

has a land in the shape of a triangle with vertices at

P (0, 0), Q (1, 1)

and

R (2, 0) .

From this land, a neighbouring farmer

F_{2}

takes away the region which lies between the side

P Q

and a curve of the form

y = x^{n}, n > 1

. If the area of the region taken away by the farmer

F_{2}

is exactly

30%

of the area of

∆ P Q R,

then the value of

n

is

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Area Under Curves>JEE Advanced Paper 1 - 2013>Q 9

The area enclosed by the curves

y = \sin x + \cos x

and

y = |\cos x - \sin x|

over the interval

[0, \frac{π}{2}]

is