Question 1: Palette 1/124

JEE Mains 2026 MCQ

Let $P_1 : y = 4x^2$ and $P_2 : y = x^2 + 27$ be two parabolas. If the area of the bounded region enclosed between $P_1$ and $P_2$ is six times the area of the bounded region enclosed between the line $y = \alpha x$, $\alpha > 0$ and $P_1$, then $\alpha$ is equal to :

A

12

B

15

C

8

D

6

Question 2: Palette 2/124

JEE Mains 2026 MCQ

The area of the region $\mathrm{R}=\left\{(x, y): x y \leq 8,1 \leq y \leq x^2, x \geq 0\right\}$ is

A

$\frac{2}{3}\left(20 \log _e(2)+9\right)$

B

$\frac{1}{3}\left(40 \log _e(2)+27\right)$

C

$\frac{1}{3}\left(49 \log _e(2)-15\right)$

D

$\frac{2}{3}\left(24 \log _e(2)-7\right)$

Question 3: Palette 3/124

JEE Mains 2026 MCQ

Let $f(\alpha)$ denote the area of the region in the first quadrant bounded by $x=0, x=1, y^2=x$ and $y=|\alpha x-5|-|1-\alpha x|+\alpha x^2$. Then $(f(0)+f(1))$ is equal to

A

12

B

14

C

9

D

7

Question 4: Palette 4/124

JEE Mains 2026 MCQ

Let $\mathrm{A}_1$ 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 $\mathrm{A}_2$ be the bounded area enclosed by the curves $y=x^2+2, y^2=x, x=2$, and $y$-axis that lies in the first quadrant. Then $\mathrm{A}_1-\mathrm{A}_2$ is equal to

A

$\frac{2}{3}(2 \sqrt{2}+1)$

B

$\frac{2}{3}(3 \sqrt{2}+1)$

C

$\frac{2}{3}(\sqrt{2}+1)$

D

$\frac{2}{3}(4 \sqrt{2}+1)$

Question 5: Palette 5/124

JEE Mains 2026 MCQ

The area of the region enclosed between the circles $x^2+y^2=4$ and $x^2+(y-2)^2=4$ is:

A

$\frac{2}{3}(4 \pi-3 \sqrt{3})$

B

$\frac{4}{3}(2 \pi-\sqrt{3})$

C

$\frac{4}{3}(2 \pi-3 \sqrt{3})$

D

$\frac{2}{3}(2 \pi-3 \sqrt{3})$

Question 6: Palette 6/124

JEE Mains 2026 MCQ

The area of the region $\mathrm{A}=\left\{(x, y): 4 x^2+y^2 \leqslant 8\right.$ and $\left.y^2 \leqslant 4 x\right\}$ is:

A

$\pi+\frac{2}{3}$

B

$\frac{\pi}{2}+2$

C

$\pi+4$

D

$\frac{\pi}{2}+\frac{1}{3}$

Question 7: Palette 7/124

JEE Mains 2026 MCQ

Let the line $x=-1$ divide the area of the region $\left\{(x, y): 1+x^2 \leq y \leq 3-x\right\}$ in the ratio $m: n, \operatorname{gcd}(m, n)=1$. Then $m+n$ is equal to

A

27

B

28

C

25

D

26

Question 8: Palette 8/124

JEE Mains 2026 MCQ

If the area of the region $\{(x, y) : 1-2x \leq y \leq 4-x^2,\; x \geq 0,\; y \geq 0 \}$ is $\dfrac{\alpha}{\beta}$, $\alpha, \beta \in \mathbb{N}, \gcd(\alpha,\beta)=1$, then the value of $(\alpha+\beta)$ is:

A

73

B

85

C

67

D

91

Question 9: Palette 9/124

JEE Mains 2026 MCQ

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 :

A

$2 \pi-1$

B

$3(\pi-1)$

C

$2(\pi-1)$

D

$2 \pi-\frac{1}{2}$

Question 10: Palette 10/124

JEE Mains 2026 MCQ

Let $f:(1, \infty) \rightarrow \mathbf{R}$ be a function defined as $f(x)=\frac{x-1}{x+1}$. Let $f^{i+1}(x)=f\left(f^i(x)\right), i=1,2, \ldots, 25$, where $f^1(x)=f(x)$. If $g(x)+f^{26}(x)=0, x \in(1, \infty)$, then the area of the region bounded by the curves $y=g(x), 2 y=2 x-3, y=0$ and $x=4$ is :

A

$\frac{1}{8}+\log _{\mathrm{e}} 2$

B

$\frac{1}{4}+\log _{\mathrm{e}} 2$

C

$\frac{5}{6}+3 \log _e 2$

D

$\frac{5}{6}+\log _e 2$

Question 11: Palette 11/124

JEE Mains 2026 MCQ

The area of the region $\left\{(x, y): x^2-8 x \leq y \leq-x\right\}$ is :

A

$\frac{343}{6}$

B

$\frac{637}{6}$

C

$ \frac{437}{6}$

D

$\frac{523}{6}$

Question 12: Palette 12/124

JEE Mains 2026 MCQ

The area of the region $\left\{(x, y): 0 \leq y \leq 6-x, y^2 \geq 4 x-3, x \geq 0\right\}$ is :

A

8

B

9

C

12

D

15

Question 13: Palette 13/124

JEE Mains 2026 MCQ

Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\} \rightarrow\left\{1, e, e^2, e^3\right\}$ and $\mathrm{g}:\left\{1, e, e^2, e^3\right\} \rightarrow\left\{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$ be two bijective functions such that $f$ is strictly decreasing and $g$ is strictly increasing. If $\phi(x)=\left[f^{-1}\left\{g^{-1}\left(\frac{1}{2}\right)\right\}\right]^x$, then the area of the region $\mathrm{R}=\left\{(x, y): x^2 \leq y \leq \phi(x), 0 \leq x \leq 1\right\}$ is :

A

$\frac{3-\log _e(2)}{3 \log _e(2)}$

B

$ \frac{1}{3 \log _e(2)} $

C

$ 3+\log _e(2) $

D

$ \frac{3+\log _e(2)}{2+\log _e(3)} $

Question 14: Palette 14/124

JEE Mains 2026 MCQ

The area of the region $\mathrm{R}=\left\{(x, y): x y \leq 27,1 \leq y \leq x^2\right\}$ is equal to :

A

$ 78 \log _e 3-\frac{52}{3} $

B

$ 54 \log _e 3-\frac{52}{3} $

C

$ 54 \log _e 3-\frac{26}{3} $

D

$ 54 \log _e 3+\frac{26}{3} $

Question 15: Palette 15/124

JEE Mains 2026 MCQ

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

A

$\frac{1}{3}$

B

$\frac{2}{3}$

C

$\frac{4}{3}$

D

$\frac{5}{3}$

Question 16: Palette 16/124

JEE Mains 2026 MCQ

The area of the region $\{(x, y): y \leq \pi-|x|, y \leq|x \sin x|, y \geq 0\}$ is:

A

$1+\frac{\pi^2}{8}$

B

$ 2+\frac{\pi^2}{4} $

C

$ \frac{\pi^2}{8}-1 $

D

$ 4+\frac{\pi^2}{2} $

Question 17: Palette 17/124

JEE Mains 2025 MCQ

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

A

50

B

46

C

49

D

47

Question 18: Palette 18/124

JEE Mains 2025 MCQ

If the area of the region bounded by the curves $y=4-\frac{x^2}{4}$ and $y=\frac{x-4}{2}$ is equal to $\alpha$, then $6 \alpha$. equals

A

210

B

250

C

240

D

220

Question 19: Palette 19/124

JEE Mains 2025 MCQ

Let $f:[0, \infty) \rightarrow \mathbb{R}$ be a differentiable function such that

$f(x)=1-2 x+\int_0^x e^{x-t} f(t) d t$ for all $x \in[0, \infty)$.

Then the area of the region bounded by $y=f(x)$ and the coordinate axes is

A

$\sqrt5$

B

2

C

$\sqrt2$

D

$\frac{1}{2}$

Question 20: Palette 20/124

JEE Mains 2025 MCQ

The area of the region $\{(x, y):|x-y| \leq y \leq 4 \sqrt{x}\}$ is

A

$\frac{512}{3}$

B

$\frac{2048}{3}$

C

512

D

$\frac{1024}{3}$

Question 21: Palette 21/124

JEE Mains 2025 MCQ

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

A

15

B

18

C

33

D

27

Question 22: Palette 22/124

JEE Mains 2025 MCQ

Let the area of the region

$ (x, y) : 2y \leq x^2 + 3,\ y + |x| \leq 3, \ y \geq |x - 1| $ be $ A $. Then $ 6A $ is equal to :

A

14

B

18

C

16

D

12

Question 23: Palette 23/124

JEE Mains 2025 MCQ

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

A

$\frac{\pi}{4} - \frac{1}{3}$

B

$\frac{\pi}{2} - \frac{1}{3}$

C

$2\left(\frac{\pi}{2} - \frac{1}{3}\right)$

D

$\frac{1}{2}\left(\frac{\pi}{2} - \frac{1}{3}\right)$

Question 24: Palette 24/124

JEE Mains 2025 MCQ

The area (in sq. units) of the region $\left\{(x, \mathrm{y}): 0 \leq \mathrm{y} \leq 2|x|+1,0 \leq \mathrm{y} \leq x^2+1,|x| \leq 3\right\}$ is

A

$\frac{32}{3}$

B

$\frac{64}{3}$

C

$\frac{17}{3}$

D

$\frac{80}{3}$

Question 25: Palette 25/124

JEE Mains 2025 MCQ

The area of the region enclosed by the curves $y=\mathrm{e}^x, y=\left|\mathrm{e}^x-1\right|$ and $y$-axis is :

A

$1+\log _{\mathrm{e}} 2$

B

$\log _{\mathrm{e}} 2$

C

$1-\log _{\mathrm{e}} 2$

D

$2 \log _{\mathrm{e}} 2-1$

Question 26: Palette 26/124

JEE Mains 2025 MCQ

The area of the region $\left\{(x, y): x^2+4 x+2 \leq y \leq|x+2|\right\}$ is equal to

A

7

B

24/5

C

20/3

D

5

Question 27: Palette 27/124

JEE Mains 2025 MCQ

If the area of the region $\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq \mathrm{a}+\mathrm{e}^{|x|}-\mathrm{e}^{-x}, \mathrm{a}>0\right\}$ is $\frac{\mathrm{e}^2+8 \mathrm{e}+1}{\mathrm{e}}$, then the value of $a$ is :

A

7

B

5

C

6

D

8

Question 28: Palette 28/124

JEE Mains 2025 MCQ

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

A

$\frac{8}{3}$

B

$5$

C

$8$

D

$\frac{4}{3}$

Question 29: Palette 29/124

JEE Mains 2025 MCQ

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

A

$3 \pi-8$

B

 $6 \pi-8$

C

$3 \pi+8$

D

$6 \pi-16$

Question 30: Palette 30/124

JEE Mains 2024 MCQ

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

A

$\sqrt{3} \pi+1$

B

$\sqrt{3} \pi$

C

$\sqrt{3} \pi-\frac{3}{4}$

D

$\sqrt{3} \pi+\frac{3}{4}$

Question 31: Palette 31/124

JEE Mains 2024 MCQ

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 :

A

$\frac{2}{3}+5 \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)$

B

$\frac{2}{3}+\sqrt{5} \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)$

C

$\frac{1}{3}+5 \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)$

D

$\frac{1}{3}+\sqrt{5} \sin ^{-1}\left(\frac{2}{\sqrt{5}}\right)$

Question 32: Palette 32/124

JEE Mains 2024 MCQ

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 :

A

$\frac{\pi}{2}-\frac{1}{3}$

B

$\pi-\frac{1}{3}$

C

$\pi-\frac{2}{3}$

D

$\frac{\pi}{2}-\frac{2}{3}$

Question 33: Palette 33/124

JEE Mains 2024 MCQ

If the area of the region $\left\{(x, y): \frac{\mathrm{a}}{x^2} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2,0<\mathrm{a}<1\right\}$ is $\left(\log _{\mathrm{e}} 2\right)-\frac{1}{7}$ then the value of $7 \mathrm{a}-3$ is equal to :

A

1

B

0

C

2

D

$-$1

Question 34: Palette 34/124

JEE Mains 2024 MCQ

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

A

172

B

154

C

162

D

184

Question 35: Palette 35/124

JEE Mains 2024 MCQ

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

A

$\frac{8}{3}$

B

$\frac{2}{3}$

C

$\frac{4}{3}$

D

1

Question 36: Palette 36/124

JEE Mains 2024 MCQ

The area (in sq. units) of the region described by $ \left\{(x, y): y^2 \leq 2 x \text {, and } y \geq 4 x-1\right\} $ is

A

$\frac{9}{32}$

B

$\frac{11}{12}$

C

$\frac{8}{9}$

D

$\frac{11}{32}$

Question 37: Palette 37/124

JEE Mains 2024 MCQ

One of the points of intersection of the curves $y=1+3 x-2 x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$. Let the area of the region enclosed by these curves be $\frac{1}{24}(l \sqrt{5}+\mathrm{m})-\mathrm{n} \log _{\mathrm{e}}(1+\sqrt{5})$, where $l, \mathrm{~m}, \mathrm{n} \in \mathbf{N}$. Then $l+\mathrm{m}+\mathrm{n}$ is equal to

A

30

B

29

C

31

D

32

Question 38: Palette 38/124

JEE Mains 2024 MCQ

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

A

$28-30 \log _{\mathrm{e}} 2$

B

$30-28 \log _{\mathrm{e}} 2$

C

$30-32 \log _{\mathrm{e}} 2$

D

$32-30 \log _{\mathrm{e}} 2$

Question 39: Palette 39/124

JEE Mains 2024 MCQ

The area of the region enclosed by the parabolas $y=4 x-x^2$ and $3 y=(x-4)^2$ is equal to :

A

$\frac{32}{9}$

B

$\frac{14}{3}$

C

4

D

6

Question 40: Palette 40/124

JEE Mains 2024 MCQ

The area of the region $\left\{(x, y): y^2 \leq 4 x, x<4, \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0, x \neq 3\right\}$ is

A

$\frac{32}{3}$

B

$\frac{16}{3}$

C

$\frac{8}{3}$

D

$\frac{64}{3}$

Question 41: Palette 41/124

JEE Mains 2024 MCQ

The area (in square units) of the region bounded by the parabola $y^2=4(x-2)$ and the line $y=2 x-8$, is :

A

7

B

8

C

9

D

6

Question 42: Palette 42/124

JEE Mains 2023 MCQ

The area of the region $\left\{(x, y): x^{2} \leq y \leq\left|x^{2}-4\right|, y \geq 1\right\}$ is

A

$\frac{4}{3}(4 \sqrt{2}+1)$

B

$\frac{3}{4}(4 \sqrt{2}+1)$

C

$\frac{4}{3}(4 \sqrt{2}-1)$

D

$\frac{3}{4}(4 \sqrt{2}-1)$

Question 43: Palette 43/124

JEE Mains 2023 MCQ

The area of the region enclosed by the curve $f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi$ and the $x$-axis is

A

$2 \sqrt{2}(\sqrt{2}+1)$

B

4

C

$2(\sqrt{2}+1)$

D

$4(\sqrt{2})$

Question 44: Palette 44/124

JEE Mains 2023 MCQ

The area of the region enclosed by the curve $y=x^{3}$ and its tangent at the point $(-1,-1)$ is :

A

$\frac{23}{4}$

B

$\frac{19}{4}$

C

$\frac{27}{4}$

D

$\frac{31}{4}$

Question 45: Palette 45/124

JEE Mains 2023 MCQ

Area of the region $\left\{(x, y): x^{2}+(y-2)^{2} \leq 4, x^{2} \geq 2 y\right\}$ is

A

$2 \pi+\frac{16}{3}$

B

$\pi-\frac{8}{3}$

C

$\pi+\frac{8}{3}$

D

$2 \pi-\frac{16}{3}$

Question 46: Palette 46/124

JEE Mains 2023 MCQ

The area of the region $\left\{(x, y): x^{2} \leq y \leq 8-x^{2}, y \leq 7\right\}$ is :

A

18

B

24

C

20

D

21

Question 47: Palette 47/124

JEE Mains 2023 MCQ

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

A

5

B

4

C

6

D

3

Question 48: Palette 48/124

JEE Mains 2023 MCQ

The area of the region given by $\{ (x,y):xy \le 8,1 \le y \le {x^2}\} $ is :

A

$16{\log _e}2 - {{14} \over 3}$

B

$8{\log _e}2 - {{13} \over 3}$

C

$16{\log _e}2 + {7 \over 3}$

D

$8{\log _e}2 + {7 \over 6}$

Question 49: Palette 49/124

JEE Mains 2023 MCQ

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 $\left\{(x, y): 0 \leq y \leq(x-q)^2, 0 \leq x \leq q\right\}$ is :

A

$\frac{125}{3}$

B

243

C

164

D

25

Question 50: Palette 50/124

JEE Mains 2023 MCQ

The area of the region $A = \left\{ {(x,y):\left| {\cos x - \sin x} \right| \le y \le \sin x,0 \le x \le {\pi \over 2}} \right\}$ is

A

$\sqrt 5 + 2\sqrt 2 - 4.5$

B

$1 - {3 \over {\sqrt 2 }} + {4 \over {\sqrt 5 }}$

C

$\sqrt 5 - 2\sqrt 2 + 1$

D

${3 \over {\sqrt 5 }} - {3 \over {\sqrt 2 }} + 1$

Question 51: Palette 51/124

JEE Mains 2023 MCQ

Let $\Delta$ be the area of the region $\left\{ {(x,y) \in {R^2}:{x^2} + {y^2} \le 21,{y^2} \le 4x,x \ge 1} \right\}$. Then ${1 \over 2}\left( {\Delta - 21{{\sin }^{ - 1}}{2 \over {\sqrt 7 }}} \right)$ is equal to

A

$2\sqrt 3 - {1 \over 3}$

B

$2\sqrt 3 - {2 \over 3}$

C

$\sqrt 3 - {4 \over 3}$

D

$\sqrt 3 - {2 \over 3}$

Question 52: Palette 52/124

JEE Mains 2023 MCQ

Let $[x]$ denote the greatest integer $\le x$. Consider the function $f(x) = \max \left\{ {{x^2},1 + [x]} \right\}$. Then the value of the integral $\int\limits_0^2 {f(x)dx} $ is

A

${{5 + 4\sqrt 2 } \over 3}$

B

${{4 + 5\sqrt 2 } \over 3}$

C

${{8 + 4\sqrt 2 } \over 3}$

D

${{1 + 5\sqrt 2 } \over 3}$

Question 53: Palette 53/124

JEE Mains 2023 MCQ

Let $A=\left\{(x, y) \in \mathbb{R}^{2}: y \geq 0,2 x \leq y \leq \sqrt{4-(x-1)^{2}}\right\}$ and

$ B=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: 0 \leq y \leq \min \left\{2 x, \sqrt{4-(x-1)^{2}}\right\}\right\} \text {. } $.

Then the ratio of the area of A to the area of B is

A

$\frac{\pi}{\pi+1}$

B

$\frac{\pi-1}{\pi+1}$

C

$\frac{\pi}{\pi-1}$

D

$\frac{\pi+1}{\pi-1}$

Question 54: Palette 54/124

JEE Mains 2023 MCQ

The area enclosed by the curves ${y^2} + 4x = 4$ and $y - 2x = 2$ is :

A

${{22} \over 3}$

B

9

C

${{23} \over 3}$

D

${{25} \over 3}$

Question 55: Palette 55/124

JEE Mains 2022 MCQ

The area of the region

$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

A

$\frac{5}{2} \sin ^{-1}\left(\frac{3}{5}\right)-\frac{1}{2}$

B

$\frac{5 \pi}{4}-\frac{3}{2}$

C

$\frac{3 \pi}{4}+\frac{3}{2}$

D

$\frac{5 \pi}{4}-\frac{1}{2}$

Question 56: Palette 56/124

JEE Mains 2022 MCQ

The area enclosed by the curves $y=\log _{e}\left(x+\mathrm{e}^{2}\right), x=\log _{e}\left(\frac{2}{y}\right)$ and $x=\log _{\mathrm{e}} 2$, above the line $y=1$ is:

A

$2+\mathrm{e}-\log _{\mathrm{e}} 2$

B

$1+e-\log _{e} 2$

C

$e-\log _{e} 2$

D

$1+\log _{e} 2$

Question 57: Palette 57/124

JEE Mains 2022 MCQ

The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$, is equal to :

A

$\frac{40}{3}$

B

$\frac{56}{3}$

C

$\frac{112}{3}$

D

$\frac{80}{3}$

Question 58: Palette 58/124

JEE Mains 2022 MCQ

Consider a curve $y=y(x)$ in the first quadrant as shown in the figure. Let the area $\mathrm{A}_{1}$ is twice the area $\mathrm{A}_{2}$. Then the normal to the curve perpendicular to the line $2 x-12 y=15$ does NOT pass through the point.

A

(6, 21)

B

(8, 9)

C

(10, $-$4)

D

(12, $-$15)

Question 59: Palette 59/124

JEE Mains 2022 MCQ

The area of the smaller region enclosed by the curves $y^{2}=8 x+4$ and $x^{2}+y^{2}+4 \sqrt{3} x-4=0$ is equal to

A

$\frac{1}{3}(2-12 \sqrt{3}+8 \pi)$

B

$\frac{1}{3}(2-12 \sqrt{3}+6 \pi)$

C

$\frac{1}{3}(4-12 \sqrt{3}+8 \pi)$

D

$\frac{1}{3}(4-12 \sqrt{3}+6 \pi)$

Question 60: Palette 60/124

JEE Mains 2022 MCQ

The area bounded by the curves $y=\left|x^{2}-1\right|$ and $y=1$ is

A

$\frac{2}{3}(\sqrt{2}+1)$

B

$\frac{4}{3}(\sqrt{2}-1)$

C

$2(\sqrt{2}-1)$

D

$\frac{8}{3}(\sqrt{2}-1)$

Question 61: Palette 61/124

JEE Mains 2022 MCQ

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

A

3

B

5

C

7

D

9

Question 62: Palette 62/124

JEE Mains 2022 MCQ

The area of the region given by

$A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\}$ is :

A

$\frac{31}{8}$

B

$\frac{17}{6}$

C

$\frac{19}{6}$

D

$\frac{27}{8}$

Question 63: Palette 63/124

JEE Mains 2022 MCQ

Let the locus of the centre $(\alpha, \beta), \beta>0$, of the circle which touches the circle $x^{2}+(y-1)^{2}=1$ externally and also touches the $x$-axis be $\mathrm{L}$. Then the area bounded by $\mathrm{L}$ and the line $y=4$ is:

A

$ \frac{32 \sqrt{2}}{3} $

B

$ \frac{40 \sqrt{2}}{3} $

C

$\frac{64}{3}$

D

$ \frac{32}{3} $

Question 64: Palette 64/124

JEE Mains 2022 MCQ

The area enclosed by y² = 8x and y = $\sqrt2$ x that lies outside the triangle formed by y = $\sqrt2$ x, x = 1, y = 2$\sqrt2$, is equal to:

A

${{16\sqrt 2 } \over 6}$

B

${{11\sqrt 2 } \over 6}$

C

${{13\sqrt 2 } \over 6}$

D

${{5\sqrt 2 } \over 6}$

Question 65: Palette 65/124

JEE Mains 2022 MCQ

The area of the bounded region enclosed by the curve

$y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$ and the x-axis is :

A

${9 \over 4}$

B

${45 \over 16}$

C

${27 \over 8}$

D

${63 \over 16}$

Question 66: Palette 66/124

JEE Mains 2022 MCQ

The area of the region S = {(x, y) : y² $\le$ 8x, y $\ge$ $\sqrt2$x, x $\ge$ 1} is

A

${{13\sqrt 2 } \over 6}$

B

${{11\sqrt 2 } \over 6}$

C

${{5\sqrt 2 } \over 6}$

D

${{19\sqrt 2 } \over 6}$

Question 67: Palette 67/124

JEE Mains 2022 MCQ

The area of the region bounded by y² = 8x and y² = 16(3 $-$ x) is equal to:

A

${{32} \over 3}$

B

${{40} \over 3}$

C

16

D

19

Question 68: Palette 68/124

JEE Mains 2022 MCQ

The area bounded by the curve y = |x² $-$ 9| and the line y = 3 is :

A

$4(2\sqrt 3 + \sqrt 6 - 4)$

B

$4(4\sqrt 3 + \sqrt 6 - 4)$

C

$8(4\sqrt 3 + 3\sqrt 6 - 9)$

D

$8(4\sqrt 3 + 2\sqrt 6 - 9)$

Question 69: Palette 69/124

JEE Mains 2022 MCQ

The area of the region enclosed between the parabolas y² = 2x $-$ 1 and y² = 4x $-$ 3 is

A

${1 \over {3}}$

B

${1 \over {6}}$

C

${2 \over {3}}$

D

${3 \over {4}}$

Question 70: Palette 70/124

JEE Mains 2021 MCQ

The area, enclosed by the curves $y = \sin x + \cos x$ and $y = \left| {\cos x - \sin x} \right|$ and the lines $x = 0,x = {\pi \over 2}$, is :

A

$2\sqrt 2 (\sqrt 2 - 1)$

B

$2(\sqrt 2 + 1)$

C

$4(\sqrt 2 - 1)$

D

$2\sqrt 2 (\sqrt 2 + 1)$

Question 71: Palette 71/124

JEE Mains 2021 MCQ

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 :

A

9

B

10

C

4

D

6

Question 72: Palette 72/124

JEE Mains 2021 MCQ

The area of the region bounded by y $-$ x = 2 and x² = y is equal to :

A

${{16} \over 3}$

B

${{2} \over 3}$

C

${{9} \over 2}$

D

${{4} \over 3}$

Question 73: Palette 73/124

JEE Mains 2021 MCQ

If the area of the bounded region
$R = \left\{ {(x,y):\max \{ 0,{{\log }_e}x\} \le y \le {2^x},{1 \over 2} \le x \le 2} \right\}$ is ,
$\alpha {({\log _e}2)^{ - 1}} + \beta ({\log _e}2) + \gamma $, then the value of ${(\alpha + \beta - 2\lambda )^2}$ is equal to :

A

8

B

2

C

4

D

1

Question 74: Palette 74/124

JEE Mains 2021 MCQ

The area (in sq. units) of the region, given by the set $\{ (x,y) \in R \times R|x \ge 0,2{x^2} \le y \le 4 - 2x\} $ is :

A

${8 \over 3}$

B

${{17} \over 3}$

C

${{13} \over 3}$

D

${7 \over 3}$

Question 75: Palette 75/124

JEE Mains 2021 MCQ

The area bounded by the curve 4y² = x²(4 $-$ x)(x $-$ 2) is equal to :

A

${\pi \over {16}}$

B

${\pi \over {8}}$

C

${3\pi \over {2}}$

D

${3\pi \over {8}}$

Question 76: Palette 76/124

JEE Mains 2021 MCQ

Let A₁ be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant. Also, let A₂ be the area of the region bounded by the curves y = sinx, y = cosx, x-axis and x = ${\pi \over 2}$ in the first quadrant. Then,

A

${A_1}:{A_2} = 1:\sqrt 2 $ and ${A_1} + {A_2} = 1$

B

${A_1} = {A_2}$ and ${A_1} + {A_2} = \sqrt 2 $

C

$2{A_1} = {A_2}$ and ${A_1} + {A_2} = 1 + \sqrt 2 $

D

${A_1}:{A_2} = 1:2$ and ${A_1} + {A_2} = 1$

Question 77: Palette 77/124

JEE Mains 2021 MCQ

The area of the region : $R = \{ (x,y):5{x^2} \le y \le 2{x^2} + 9\} $ is :

A

$6\sqrt 3 $ square units

B

$12\sqrt 3 $ square units

C

$11\sqrt 3 $ square units

D

$9\sqrt 3 $ square units

Question 78: Palette 78/124

JEE Mains 2021 MCQ

The area (in sq. units) of the part of the circle x² + y² = 36, which is outside the parabola y² = 9x, is :

A

$12\pi - 3\sqrt 3 $

B

$24\pi + 3\sqrt 3 $

C

$24\pi - 3\sqrt 3 $

D

$12\pi + 3\sqrt 3 $

Question 79: Palette 79/124

JEE Mains 2020 MCQ

The area (in sq. units) of the region enclosed
by the curves y = x² – 1 and y = 1 – x² is equal to :

A

${8 \over 3}$

B

${4 \over 3}$

C

${7 \over 2}$

D

${{16} \over 3}$

Question 80: Palette 80/124

JEE Mains 2020 MCQ

The area (in sq. units) of the region
A = {(x, y) : |x| + |y| $ \le $ 1, 2y² $ \ge $ |x|}

A

${1 \over 6}$

B

${5 \over 6}$

C

${1 \over 3}$

D

${7 \over 6}$

Question 81: Palette 81/124

JEE Mains 2020 MCQ

The area (in sq. units) of the region

A = {(x, y) : (x – 1)[x] $ \le $ y $ \le $ 2$\sqrt x $, 0 $ \le $ x $ \le $ 2}, where [t]

denotes the greatest integer function, is :

A

${8 \over 3}\sqrt 2 - 1$

B

${4 \over 3}\sqrt 2 + 1$

C

${8 \over 3}\sqrt 2 - {1 \over 2}$

D

${4 \over 3}\sqrt 2 - {1 \over 2}$

Question 82: Palette 82/124

JEE Mains 2020 MCQ

The area (in sq. units) of the region

{ (x, y) : 0 $ \le $ y $ \le $ x² + 1, 0 $ \le $ y $ \le $ x + 1,

${1 \over 2}$ $ \le $ x $ \le $ 2 } is :

A

${{79} \over {16}}$

B

${{79} \over {24}}$

C

${{23} \over {6}}$

D

${{23} \over {16}}$

Question 83: Palette 83/124

JEE Mains 2020 MCQ

Consider a region R = {(x, y) $ \in $ R : x² $ \le $ y $ \le $ 2x}. if a line y = $\alpha $ divides the area of region R into two equal parts, then which of the following is true?

A

3$\alpha $² - 8$\alpha $ + 8 = 0

B

$\alpha $³ - 6$\alpha $^3/2 - 16 = 0

C

3$\alpha $² - 8$\alpha $^3/2 + 8 = 0

D

$\alpha $³ - 6$\alpha $² + 16 = 0

Question 84: Palette 84/124

JEE Mains 2020 MCQ

Area (in sq. units) of the region outside

${{\left| x \right|} \over 2} + {{\left| y \right|} \over 3} = 1$ and inside the ellipse ${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$ is :

A

$6\left( {4 - \pi } \right)$

B

$3\left( {4 - \pi } \right)$

C

$6\left( {\pi - 2} \right)$

D

$3\left( {\pi - 2} \right)$

Question 85: Palette 85/124

JEE Mains 2020 MCQ

Given : $f(x) = \left\{ {\matrix{ {x\,\,\,\,\,,} & {0 \le x < {1 \over 2}} \cr {{1 \over 2}\,\,\,\,,} & {x = {1 \over 2}} \cr {1 - x\,\,\,,} & {{1 \over 2} < x \le 1} \cr } } \right.$

and $g(x) = \left( {x - {1 \over 2}} \right)^2,x \in R$

Then the area (in sq. units) of the region bounded by the curves, y = ƒ(x) and y = g(x) between the lines, 2x = 1 and 2x = $\sqrt 3 $, is :

A

${1 \over 2} + {{\sqrt 3 } \over 4}$

B

${1 \over 2} - {{\sqrt 3 } \over 4}$

C

${1 \over 3} + {{\sqrt 3 } \over 4}$

D

${{\sqrt 3 } \over 4} - {1 \over 3}$

Question 86: Palette 86/124

JEE Mains 2020 MCQ

The area (in sq. units) of the region

{(x,y) $ \in $ R² : x² $ \le $ y $ \le $ 3 – 2x}, is :

A

${{34} \over 3}$

B

${{29} \over 3}$

C

${{31} \over 3}$

D

${{32} \over 3}$

Question 87: Palette 87/124

JEE Mains 2020 MCQ

For a > 0, let the curves C₁ : y² = ax and C₂ : x² = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C₁ and C₂, and the area of
$\Delta $OQR = ${1 \over 2}$, then 'a' satisfies the equation :

A

x⁶ – 12x³ + 4 = 0

B

x⁶ – 12x³ – 4 = 0

C

x⁶ + 6x³ – 4 = 0

D

x⁶ – 6x³ + 4 = 0

Question 88: Palette 88/124

JEE Mains 2020 MCQ

The area (in sq. units) of the region
{(x, y) $ \in $ R² | 4x² $ \le $ y $ \le $ 8x + 12} is :

A

${{125} \over 3}$

B

${{128} \over 3}$

C

${{127} \over 3}$

D

${{124} \over 3}$

Question 89: Palette 89/124

JEE Mains 2020 MCQ

The area of the region, enclosed by the circle x² + y² = 2 which is not common to the region bounded by the parabola y² = x and the straight line y = x, is:

A

${1 \over 6}\left( {24\pi - 1} \right)$

B

${1 \over 3}\left( {12\pi - 1} \right)$

C

${1 \over 3}\left( {6\pi - 1} \right)$

D

${1 \over 6}\left( {12\pi - 1} \right)$

Question 90: Palette 90/124

JEE Mains 2019 MCQ

If the area (in sq. units) bounded by the parabola y² = 4$\lambda $x and the line y = $\lambda $x, $\lambda $ > 0, is ${1 \over 9}$ , then $\lambda $ is equal to :

A

$4\sqrt 3 $

B

2$\sqrt 6 $

C

48

D

24

Question 91: Palette 91/124

JEE Mains 2019 MCQ

If the area (in sq. units) of the region {(x, y) : y² $ \le $ 4x, x + y $ \le $ 1, x $ \ge $ 0, y $ \ge $ 0} is a $\sqrt 2 $ + b, then a – b is equal to :

A

${8 \over 3}$

B

$ - {2 \over 3}$

C

6

D

${{10} \over 3}$

Question 92: Palette 92/124

JEE Mains 2019 MCQ

The area (in sq.units) of the region bounded by the curves y = 2^x and y = |x + 1|, in the first quadrant is :

A

${1 \over 2}$

B

${3 \over 2}$

C

${3 \over 2} - {1 \over {\log _e^2}}$

D

$\log _e^2 + {3 \over 2}$

Question 93: Palette 93/124

JEE Mains 2019 MCQ

The area (in sq. units) of the region
A = {(x, y) : ${{y{}^2} \over 2}$ $ \le $ x $ \le $ y + 4} is :-

A

30

B

18

C

${{53} \over 3}$

D

16

Question 94: Palette 94/124

JEE Mains 2019 MCQ

The area (in sq. units) of the region

A = {(x, y) : x² $ \le $ y $ \le $ x + 2} is

A

${{31 \over 6}}$

B

${{10 \over 3}}$

C

${{13 \over 6}}$

D

${{9 \over 2}}$

Question 95: Palette 95/124

JEE Mains 2019 MCQ

Let S($\alpha $) = {(x, y) : y² $ \le $ x, 0 $ \le $ x $ \le $ $\alpha $} and A($\alpha $) is area of the region S($\alpha $). If for a $\lambda $, 0 < $\lambda $ < 4, A($\lambda $) : A(4) = 2 : 5, then $\lambda $ equals

A

$2{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$

B

$2{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$

C

$4{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$

D

$4{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$

Question 96: Palette 96/124

JEE Mains 2019 MCQ

The area (in sq. units) of the region
A = { (x, y) $ \in $ R × R|  0 $ \le $ x $ \le $ 3, 0 $ \le $ y $ \le $ 4, y $ \le $ x² + 3x} is :

A

${{59} \over 6}$

B

${{26} \over 3}$

C

8

D

${{53} \over 6}$

Question 97: Palette 97/124

JEE Mains 2019 MCQ

The area (in sq. units) of the region bounded by the parabola, y = x² + 2 and the lines, y = x + 1, x = 0 and x = 3, is

A

${{15} \over 4}$

B

${{15} \over 2}$

C

${{21} \over 2}$

D

${{17} \over 4}$

Question 98: Palette 98/124

JEE Mains 2019 MCQ

The area (in sq. units) in the first quadrant bounded by the parabola, y = x² + 1, the tangent to it at the point (2, 5) and the coordinate axes is :

A

${8 \over 3}$

B

${{14} \over 3}$

C

${{187} \over {24}}$

D

${{37} \over {24}}$

Question 99: Palette 99/124

JEE Mains 2019 MCQ

The area (in sq. units) of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is :

A

${3 \over 4}$

B

${5 \over 4}$

C

${7 \over 8}$

D

${9 \over 8}$

Question 100: Palette 100/124

JEE Mains 2019 MCQ

If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is -

A

$\sqrt 3 $

B

${{\sqrt 3 } \over 2}$

C

${2 \over {\sqrt 3 }}$

D

${1 \over {\sqrt 3 }}$

Question 101: Palette 101/124

JEE Mains 2019 MCQ

The area of the region

A = {(x, y) : 0 $ \le $ y $ \le $x |x| + 1  and  $-$1 $ \le $ x $ \le $1} in sq. units, is :

A

${2 \over 3}$

B

2

C

${4 \over 3}$

D

${1 \over 3}$

Question 102: Palette 102/124

JEE Mains 2019 MCQ

The area (in sq. units) bounded by the parabolae y = x² – 1, the tangent at the point (2, 3) to it and the y-axis is :

A

$56\over3$

B

$32\over3$

C

$8\over3$

D

$14\over3$

Question 103: Palette 103/124

JEE Mains 2018 MCQ

If the area of the region bounded by the curves, $y = {x^2},y = {1 \over x}$ and the lines y = 0 and x= t (t >1) is 1 sq. unit, then t is equal to :

A

${e^{{3 \over 2}}}$

B

${4 \over 3}$

C

${3 \over 2}$

D

${e^{{2 \over 3}}}$

Question 104: Palette 104/124

JEE Mains 2018 MCQ

Let g(x) = cosx², f(x) = $\sqrt x $ and $\alpha ,\beta \left( {\alpha < \beta } \right)$ be the roots of the quadratic equation 18x² - 9$\pi $x + ${\pi ^2}$ = 0. Then the area (in sq. units) bounded by the curve
y = (gof)(x) and the lines $x = \alpha $, $x = \beta $ and y = 0 is :

A

${1 \over 2}\left( {\sqrt 2 - 1} \right)$

B

${1 \over 2}\left( {\sqrt 3 - 1} \right)$

C

${1 \over 2}\left( {\sqrt 3 + 1} \right)$

D

${1 \over 2}\left( {\sqrt 3 - \sqrt 2 } \right)$

Question 105: Palette 105/124

JEE Mains 2018 MCQ

The area (in sq. units) of the region

{x $ \in $ R : x $ \ge $ 0, y $ \ge $ 0, y $ \ge $ x $-$ 2  and y $ \le $ $\sqrt x $}, is :

A

${{13} \over 3}$

B

${{8} \over 3}$

C

${{10} \over 3}$

D

${{5} \over 3}$

Question 106: Palette 106/124

JEE Mains 2017 MCQ

The area (in sq. units) of the smaller portion enclosed between the curves, x² + y² = 4 and y² = 3x, is :

A

${1 \over {2\sqrt 3 }} + {\pi \over 3}$

B

${1 \over {\sqrt 3 }} + {{2\pi } \over 3}$

C

${1 \over {2\sqrt 3 }} + {{2\pi } \over 3}$

D

${1 \over {\sqrt 3 }} + {{4\pi } \over 3}$

Question 107: Palette 107/124

JEE Mains 2017 MCQ

The area (in sq. units) of the region

$\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \sqrt x } \right\}$ is

A

${3 \over 2}$

B

${7 \over 3}$

C

${5 \over 2}$

D

${59 \over 12}$

Question 108: Palette 108/124

JEE Mains 2016 MCQ

The area (in sq. units) of the region described by

A= {(x, y) $\left| {} \right.$y$ \ge $ x² $-$ 5x + 4, x + y $ \ge $ 1, y $ \le $ 0} is :

A

${7 \over 2}$

B

${{19} \over 6}$

C

${{13} \over 6}$

D

${{17} \over 6}$

Question 109: Palette 109/124

JEE Mains 2016 MCQ

The area (in sq. units) of the region $\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\}$ is :

A

$\pi - {{4\sqrt 2 } \over 3}$

B

${\pi \over 2} - {{2\sqrt 2 } \over 3}$

C

$\pi - {4 \over 3}$

D

$\pi - {8 \over 3}$

Question 110: Palette 110/124

JEE Mains 2015 MCQ

The area (in sq. units) of the region described by

$\left\{ {\left( {x,y} \right):{y^2} \le 2x} \right.$ and $\left. {y \ge 4x - 1} \right\}$ is :

A

${{15} \over {64}}$

B

${{9} \over {32}}$

C

${{7} \over {32}}$

D

${{5} \over {64}}$

Question 111: Palette 111/124

JEE Mains 2014 MCQ

The area of the region described by
$A = \left\{ {\left( {x,y} \right):{x^2} + {y^2} \le 1} \right.$ and $\left. {{y^2} \le 1 - x} \right\}$ is :

A

${\pi \over 2} - {2 \over 3}$

B

${\pi \over 2} + {2 \over 3}$

C

${\pi \over 2} + {4 \over 3}$

D

${\pi \over 2} - {4 \over 3}$

Question 112: Palette 112/124

JEE Mains 2013 MCQ

The area (in square units) bounded by the curves $y = \sqrt {x,} $ $2y - x + 3 = 0,$ $x$-axis, and lying in the first quadrant is :

A

$9$

B

$36$

C

$18$

D

${{27} \over 4}$

Question 113: Palette 113/124

JEE Mains 2012 MCQ

The area between the parabolas ${x^2} = {y \over 4}$ and ${x^2} = 9y$ and the straight line $y=2$ is :

A

$20\sqrt 2 $

B

${{10\sqrt 2 } \over 3}$

C

${{20\sqrt 2 } \over 3}$

D

$10\sqrt 2 $

Question 114: Palette 114/124

JEE Mains 2011 MCQ

The area of the region enclosed by the curves $y = x,x = e,y = {1 \over x}$ and the positive $x$-axis is :

A

$1$ square unit

B

${3 \over 2}$ square units

C

${5 \over 2}$ square units

D

${1 \over 2}$ square unit

Question 115: Palette 115/124

JEE Mains 2010 MCQ

The area bounded by the curves $y = \cos x$ and $y = \sin x$ between the ordinates $x=0$ and $x = {{3\pi } \over 2}$ is

A

$4\sqrt 2 + 2$

B

$4\sqrt 2 - 1$

C

$4\sqrt 2 + 1$

D

$4\sqrt 2 - 2$

Question 116: Palette 116/124

JEE Mains 2009 MCQ

The area of the region bounded by the parabola ${\left( {y - 2} \right)^2} = x - 1,$ the tangent of the parabola at the point $(2, 3)$ and the $x$-axis is :

A

$6$

B

$9$

C

$12$

D

$3$

Question 117: Palette 117/124

JEE Mains 2008 MCQ

The area of the plane region bounded by the curves $x + 2{y^2} = 0$ and $\,x + 3{y^2} = 1$ is equal to :

A

${5 \over 3}$

B

${1 \over 3}$

C

${2 \over 3}$

D

${4 \over 3}$

Question 118: Palette 118/124

JEE Mains 2007 MCQ

The area enclosed between the curves ${y^2} = x$ and $y = \left| x \right|$ is :

A

$1/6$

B

$1/3$

C

$2/3$

D

$1$

Question 119: Palette 119/124

JEE Mains 2005 MCQ

The parabolas ${y^2} = 4x$ and ${x^2} = 4y$ divide the square region bounded by the lines $x=4,$ $y=4$ and the coordinate axes. If ${S_1},{S_2},{S_3}$ are respectively the areas of these parts numbered from top to bottom ; then ${S_1},{S_2},{S_3}$ is :

A

$1:2:1$

B

$1:2:3$

C

$2:1:2$

D

$1:1:1$

Question 120: Palette 120/124

JEE Mains 2005 MCQ

The area enclosed between the curve $y = {\log _e}\left( {x + e} \right)$ and the coordinate axes is :

A

$1$

B

$2$

C

$3$

D

$4$

Question 121: Palette 121/124

JEE Mains 2005 MCQ

Let $f(x)$ be a non - negative continuous function such that the area bounded by the curve $y=f(x),$ $x$-axis and the ordinates $x = {\pi \over 4}$ and $x = \beta > {\pi \over 4}$ is $\left( {\beta \sin \beta + {\pi \over 4}\cos \beta + \sqrt 2 \beta } \right).$ Then $f\left( {{\pi \over 2}} \right)$ is

A

$\left( {{\pi \over 4} + \sqrt 2 - 1} \right)$

B

$\left( {{\pi \over 4} - \sqrt 2 + 1} \right)$

C

$\left( {1 - {\pi \over 4} - \sqrt 2 } \right)$

D

$\left( {1 - {\pi \over 4} + \sqrt 2 } \right)$

Question 122: Palette 122/124

JEE Mains 2004 MCQ

The area of the region bounded by the curves
$y = \left| {x - 2} \right|,x = 1,x = 3$ and the $x$-axis is :

A

$4$

B

$2$

C

$3$

D

$1$

Question 123: Palette 123/124

JEE Mains 2003 MCQ

The area of the region bounded by the curves $y = \left| {x - 1} \right|$ and $y = 3 - \left| x \right|$ is :

A

$6$ sq. units

B

$2$ sq. units

C

$3$ sq. units

D

$4$ sq. units

Question 124: Palette 124/124

JEE Mains 2002 MCQ

The area bounded by the curves $y = \ln x,y = \ln \left| x \right|,y = \left| {\ln {\mkern 1mu} x} \right|$ and $y = \left| {\ln \left| x \right|} \right|$ is :

A

$4$sq. units

B

$6$sq. units

C

$10$sq. units

D

none of these