Question 1: Palette 1/14

AP-EAPCET 2025 MCQ

The area (in sq units) of the region given by $R=\left\{(x, y) ; \frac{y^2}{2} \leq x \leq y+4\right\}$ is

A

16

B

18

C

24

D

30

Question 2: Palette 2/14

AP-EAPCET 2025 MCQ

The area of the region (in sq units) bounded by the curves $x^2+y^2=16$ and $y^2=6 x$ is

A

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

B

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

C

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

D

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

Question 3: Palette 3/14

AP-EAPCET 2025 MCQ

The area (in sq. units) of the region bounded by the curves $y=x^2$ and $y=8-x^2$ is

A

$\frac{32}{3}$

B

$\frac{16}{3}$

C

$\frac{64}{3}$

D

$\frac{128}{3}$

Question 4: Palette 4/14

AP-EAPCET 2025 MCQ

Area of the region (in sq. units) bounded by the curve $y=x^2-5 x+4, x=0, x=2$ and the $X$-axis is

A

$\frac{8}{3}$

B

3

C

5

D

$\frac{5}{2}$

Question 5: Palette 5/14

AP-EAPCET 2025 MCQ

The area (in sq. units) of the region bounded by the lines $x=0, x=\frac{\pi}{2}$ and $f(x)=\sin x, g(x)=\cos x$ is

A

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

B

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

C

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

D

$3 \sqrt{2}+1$

Question 6: Palette 6/14

AP-EAPCET 2025 MCQ

The area of the region lying between the curves $y=\sqrt{4-x^2}, y^2=3 x$ and the $Y$-axis is

A

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

B

$\frac{\pi}{6}+\frac{1}{2 \sqrt{3}}$

C

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

D

$\frac{\pi}{6}-\frac{1}{2 \sqrt{3}}$

Question 7: Palette 7/14

AP-EAPCET 2025 MCQ

The area of the region (in sq. units) enclosed between the curves $y=|x|, y=[x]$ and the ordinates $x=-1$, $x=0, x=1$ is

A

2

B

$3 / 2$

C

3

D

$5 / 2$

Question 8: Palette 8/14

AP-EAPCET 2024 MCQ

If $(a, \beta)$ is the stationary point of the curve $y=2 x-x^2$, then the area bounded by the curves $y=2^x, y=2 x-x^2, x=0$ and $x=\alpha$ is

A

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

B

$\frac{3+\log 4}{6}$

C

$\frac{3-\log 4}{3 \log 2}$

D

$\frac{1}{\log 2}+\frac{3}{4}$

Question 9: Palette 9/14

AP-EAPCET 2024 MCQ

The area (in sq units) bounded by the curves $x=y^2$ and $x=3-2 y^2$ is

A

8

B

$8 / 3$

C

4

D

6

Question 10: Palette 10/14

AP-EAPCET 2024 MCQ

Area of the region enclosed by the curves $3 x^2-y^2-2 x y+4 x+1=0$ and $3 x^2-y^2-2 x y+6 x+2 y=0$ is

A

$\frac{3}{4}$

B

$\frac{1}{4}$

C

1

D

$\frac{1}{2}$

Question 11: Palette 11/14

AP-EAPCET 2024 MCQ

The area of the region under the curve $y=|\sin -\cos x|$, $0 \leq x \leq \frac{n}{2}$ and above $X$-axis, is (in sq units)

A

$2 \sqrt{2}$

B

$2 \sqrt{2}-1$

C

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

D

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

Question 12: Palette 12/14

AP-EAPCET 2024 MCQ

Area of the region (in sq units) enclosed by the curves $y^2=8(x+2), y^2=4(1-x)$ and the $Y$-axis is

A

$\frac{8}{3}(5-3 \sqrt{2})$

B

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

C

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

D

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

Question 13: Palette 13/14

AP-EAPCET 2024 MCQ

The area (in sq units) of the smaller region lying above the $X$-axis and bounded between the circle $x^2+y^2=2 a x$ and the parabola $y^2=a x$ is

A

$2 a^2\left(\frac{\pi}{4}-\frac{2}{3}\right)$

B

$a^2\left(\frac{\pi}{4}-\frac{2}{3}\right)$

C

$a^2\left(\frac{\pi}{4}+\frac{2}{3}\right)$

D

$a^2\left(\frac{\pi^2}{4}-\frac{1}{3}\right)$

Question 14: Palette 14/14

AP-EAPCET 2024 MCQ

The area of the region ( in sq units) enclosed by the curve $y=x^3-19 x+30$ and the $X$-axis, is

A

$\frac{167}{2}$

B

$\frac{517}{2}$

C

36

D

72