EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 30 January 2023 Shift 1>Q 83

HARD

JEE Main

IMPORTANT

Earn 100

Let $α$ 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 $3 α$ is equal to

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Important Questions on Area under Curves

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 30 January 2023 Shift 2>Q 84

Let

q

be the maximum integral value of

p

in

[0, 10]

for which the roots of the equation

x^{2} - p x + \frac{5}{4} p = 0

are rational. Then the area of the region

\{(x, y) : 0 \leq y \leq (x - q)^{2}, 0 \leq x \leq q\}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 30 January 2023 Shift 2>Q 85

Let $A$ be the area of the region $\{(x, y) : y \geq x^{2}, y \geq (1 - x)^{2}, y \leq 2 x (1 - x)\}$ . Then $540 A$ is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 31 January 2023 Shift 1>Q 86

Let for

x \in R

,

f (x) = \frac{x + |x|}{2}

and

g (x) = \{\begin{array}{l} x, \\ x^{2}, \end{array} \begin{matrix} x < 0 \\ x \geq 0 \end{matrix}

. Then area bounded by the curve

y = (f o g) (x)

and the lines

y = 0, 2 y - x = 15

is equal to _____sq. units.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 31 January 2023 Shift 2>Q 87

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 _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 1 February 2023 Shift 1>Q 88

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 _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 1 February 2023 Shift 2>Q 89

The area of the region given by

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

is :