Question 1: Palette 1/9

BITSAT 2025 MCQ

What is the area enclosed by the curves $y=x^4$ and $y=x^{\frac{1}{3}}$

A

$\frac{2}{5}$

B

$\frac{11}{20}$

C

$\frac{3}{4}$

D

$\frac{1}{5}$

Question 2: Palette 2/9

BITSAT 2024 MCQ

The line $ y=m x $ bisects the area unclosed by lines $ x=0, y=0 $ and $ x=\frac{3}{2} $ and the curve $ y=1+4 x-x^{2} $. Then, the value of $ m $ is

A

$ \frac{13}{6} $

B

$ \frac{13}{2} $

C

$ \frac{13}{5} $

D

$ \frac{13}{7} $

Question 3: Palette 3/9

BITSAT 2024 MCQ

The area enclosed by the curves $ y=x^{3} $ and $ y=\sqrt{x} $ is

A

$ \frac{5}{3} $ sq. units

B

$ \frac{5}{4} $ sq. units

C

$ \frac{5}{12} $ sq. unit

D

$ \frac{12}{5} $ sq. units then $ k $ is

Question 4: Palette 4/9

BITSAT 2023 MCQ

The area of the region bounded by the parabola $y=x^2+1$ and lines $y=x+1, y=0, x=\frac{1}{2}$ and $x=2$ is

A

$\frac{23}{6}$

B

$\frac{23}{16}$

C

$\frac{79}{24}$

D

$\frac{79}{16}$

Question 5: Palette 5/9

BITSAT 2023 MCQ

Let the functions $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by $f(x)=e^{x-1}-e^{-|x-1|}$ and $g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)$. Then, the area of the region in the first quadrant bounded by the curves $y=f(x), y=g(x)$ and $x=0$ is.

A

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

B

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

C

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

D

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

Question 6: Palette 6/9

BITSAT 2022 MCQ

What is the area enclosed by the parabola described by ${(y - 2)^2} = (x - 1)$, its tangent line at the point (2, 3), and the X-axis?

A

3

B

6

C

9

D

12

Question 7: Palette 7/9

BITSAT 2022 MCQ

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

A

$4(\sqrt 2 - 1)$

B

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

C

$2(\sqrt 2 + 1)$

D

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

Question 8: Palette 8/9

BITSAT 2021 MCQ

The area of one curvilinear triangle formed by curves y = sin x, y = cos x and X-axis, is

A

2 sq units

B

(2 + $\sqrt2$) sq units

C

(2 $-$ $\sqrt2$) sq units

D

None of these

Question 9: Palette 9/9

BITSAT 2020 MCQ

Circle centered at origin and having radius $\pi$ units is divided by the curve y = sin x in two parts. Then area of upper parts equals to

A

${{{\pi ^2}} \over 2}$

B

${{{\pi ^3}} \over 4}$

C

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

D

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