Q JEE Main 2024

The area (in sq. units) of the region described by $\left\{(x, y): y^2 \leq 2 x\right.$, and $...

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Q JEE MAIN 2024

The sum of squares of all possible values of $k$, for which area of the region bounded by the parabolas...

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Q JEE MAIN 2024

Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $S_1$ be the area of...

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Q JEE MAIN 2024

The area of the region enclosed by the parabola $(y-2)^2=x-1$, the line $x-2 y+4=0$ and the positive coordinate axes is

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Q JEE-Main 2024

If the area of the region $\left\{(x, y): 0 \leq y \leq \min \left\{2 x, 6 x-x^2\right\}\right\}$ is $A$, then...

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Q Jee Main 2024

\text { The area of the region enclosed by the parabola } y=4 x-x^2 \text { and } 3 y=(x-4)^2...

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Q JEE MAIN 2026

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....

JEE Main Mathematics Medium

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Q JEE MAIN_2026_

Let the area of the region bounded by the curve $y=\max \{\sin x, \cos x\}$, lines $x=0, x=\frac{3 \pi}{2}$, and...

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Q JEE MAIN 2026

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

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Q JEE MAIN_2026_

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...

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Q JEE MAIN 2026

If the area of the region $\left\{(x, y): 1-2 x \leq y \leq 4-x^2, x \geq 0, y \geq 0\right\}$...

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Q JEE MAIN 2026

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...

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Q JEE MAIN 2019

The area (in sq. units) of the region $A=\left\{(x, y): x^2 \leq y \leq x+2\right\}$ is :

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Q JEE MAIN 2020

The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^2=8 x$, with one of its vertices...

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Q JEE MAIN 2020

Consider a region $\mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^2 \cdot \mathrm{x}^2 \leq \mathrm{y} \leq 2 \mathrm{x}\right\}$. if a line $\mathrm{y}=\alpha$ divides the...

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Q JEE Main 2020

Area (in sq. units) of the region outside $\frac{|x|}{2}+\frac{|y|}{3}=1$ and inside the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is :

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Q JEE MAIN 2019

JEE Main Mathematics Medium

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Q JEE-MAIN 2019

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

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Q JEE MAIN 2019

The area of the region A = {(x, y) : 0 ≤ y ≤ x|x| + 1 and –1 ≤...

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Q JEE MAIN 2020

The area (in sq. units) of the region enclosed by the curves $y=x^2-1$ and $y=1-x^2$ is equal to :

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Q JEE MAIN 2019

The area of the region $A=\{(x, y): 0 \leq y \leq x|x|+1$ and $-1 \leq x \leq 1\}$ in sq....

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Q JEE MAIN 2020

For $a>0$, let the curves $C_1: y^2=a x$ and $C_2: x^2=$ ay intersect at origin $O$ and a point $P$....

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Q JEE MAIN 2019

The area (in sq. units) of the region bounded by the curve $x^2=4 y$ and the straight line $x=4 y-2$...

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Q JEE MAIN 2019

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

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Q JEE MAIN_2021_

The area of the region bounded by the parabola $(y-2)^2=(x-1)$, the tangent to it at the point whose ordinate is...

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Q JEE Main 2019

If the area enclosed between the curves $y=k x^2$ and $x=k y^2,(k>0)$, is 1 square unit. Then $k$ is :

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Q JEE MAIN 2020

Let $f(\mathrm{x})=|\mathrm{x}-2|$ and $\mathrm{g}(\mathrm{x})=f(f(\mathrm{x})), \mathrm{x} \in[0,4]$. Then $\int^3(g(x)-f(x)) d x$ is equal to:

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Q JEE MAIN 2019

The area (in sq. units) in the first quadrant bounded by the parabola, $y=x^2+1$, the tangent to it at the...

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Q JEE MAIN 2020

JEE Main Mathematics Medium

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Q JEE MAIN 2020

The area (in sq. units) of the region $\left\{(x, y) \in \mathbb{R}^2: x^2 \leq y \leq 3-2 x\right\}$, is

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Q JEE Main 2021

If the line $y=m x$ bisects the area enclosed by the lines $x=0, y=0, x=3 / 2$ and the curve...

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Q JEE MAIN 2020

The area of the region, enclosed by the circle $x^2+ y^2=2$ which is not common to the region bounded by...

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Q JEE Main 2021

The area of the region $S=\left\{(x, y): 3 x^2 \leq 4 y \leq 6 x+24\right\}$ is $\_\_\_\_$ .

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Q JEE MAIN 2021

Let $a$ and $b$ respectively be the points of local maximum and local minimum of the function $...

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Q JEE MAIN 2019

The area (in sq. units) of the region $...

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Q JEE Main 2019

The area (in sq. units) bounded by the parabola $y=x^2-1$, the tangent at the point $(2,3)$ to it and the...

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Q JEE MAIN 2021

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

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Q JEE MAIN_2021_

The area (in sq. units) of the region, given by the set $...

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Q JEE MAIN 2021 S2

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

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Q JEE MAIN 2021

Let A_1 be the area of the region bounded by the curves $y=\sin x, y=\cos x$ and $y$-axis in the...

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Q JEE MAIN 2021

Let $T$ be the tangent to the ellipse $E: x^2+4 y^2=5$ at the point $P(1,1)$. If the area of the...

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Q JEE MAIN 2021

If the area of the bounded region $...

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Q JEE-MAIN 2021

Let $f:[-3,1] \rightarrow R$ given as $$ f(x)=\left\{\begin{array}{cc} \min \left\{(x+6), x^2\right\}, & -3 \leq x \leq 0 \\ \max \left\{\sqrt{x},...

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Q JEE MAIN 2021

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

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Q JEE MAIN 2021

The area (in sq. units) of the part of the circle $x^2+y^2=36$, which is outside the parabola $y^2=9 x$, is...

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Q JEE MAIN 2021

The area of the region : $$ R=\left\{(x, y): 5 \times 2 \leq y \leq 2 x^2+9\right\} \text { is...

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Q JEE MAIN 2021

The area bounded by the lines y = ||x – 1| – 2| is

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Q JEE MAIN 2021

Let $\mathrm{A}_1, \mathrm{~A}_2, \mathrm{~A}_3$, $\_\_\_\_$ be squares such that for each $n \geq 1$, the length of the side of...

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Q JEE MAIN 2021

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points...

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Q JEE MAIN_2022

The odd natural number $a$, such that the area of the region bounded by $y=1, y=3, x \mid=0, x=y^a$ is...

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Q JEE MAIN 2022

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...

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Q JEE MAIN 2022

The area of the region given by $A=\left\{(x, y): x^2 \leq y \leq \min \{x+2,4-3 x\}\right\}$ is i.

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Q JEE MAIN 2022

If the area of the region $\left\{(x, y): x^{\frac{2}{3}}+y^{\frac{2}{3}} \leq 1, x+y \leq 0, y \geq 0\right\}$ is $A$, then...

JEE Main Mathematics Hard

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Q JEE MAIN 2022

For real numbers a, b (a > b > 0), let

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Q JEE MAIN 2022

The area (in sq. units) of the region enclosed between the parabola $y^2$ = 2x and the line x +...

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Q JEE MAIN 2022

The area of the bounded region enclosed by the curve $y=3-\left|x-\frac{1}{2}\right|-|x+1|$ and the $x$-axis is

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Q JEE MAIN 2022

The area of the region bounded by $y^2=8 x$ and $y^2=16(3-x)$ is equal to:-

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

Let $A_1=\left\{(x, y):|x| \leq y^2,|x|+2 y \leq 8\right\}$ and $A_2=\{(x, y):|x|+|y| \leq k\}$. If $27\left(\operatorname{Area} A_1\right)=5\left(\operatorname{Area} A_2\right)$, then $k$ is...

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Q JEE MAIN 2022

The area enclosed by $y^2=8 x$ and $y=\sqrt{2} x$ that lies outside the triangle formed by $...

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

Let $[t]$ denote the greatest integer less than or equal to $t$. Then, the value of the integral $...

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Q JEE-MAIN 2022

The area bounded by the curve $y=\left|x^2-9\right|$ and the line $y=3$ is :

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Q JEE MAIN 2022

Let $S$ be the region bounded by the curves $y=x^3$ and $y^2=x$. The curve $y=2|x|$ divides $S$ into two regions...

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Q

Let the area enclosed by the lines $x+y=2, y=0, x=0$ and the curve $f(x)=\min \left\{x^2+\frac{3}{4}, 1+[x]\right\}$ where $[x]$ denotes the...

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Q JEE MAIN 2023

If the area of the region $\left\{(x, y):\left|x^2-2\right| \leq y \leq x\right\}$ is $A$, then $6 A+16 \sqrt{2}$ is equal...

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Q JEE MAIN 2023

In the figure, $\theta_1+\theta_2=\frac{\pi}{2}$ and $\sqrt{3}(B E)=4(A B)$. If the area of $\triangle C A B$ is $2 \sqrt{3}-3$ unit...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

Let the area of the bounded region $\left\{(x, y): 0 \leq 9 x \leq y^2, y \geq 3 x-6\right\}$ be...

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

The area bounded by the curves y = |x – 1| + |x – 2| and y = 3 is...

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Q JEE MAIN_2025

If the area of the region $\left\{(x, y): 1+x^2 \leqslant y \leqslant \min \{x+7.11-3 x\}\right\}$ is A , then 3...

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Q JEE MAIN 2025

A line passing through the point $\mathrm{A}(-2,0)$, touches the parabola $\mathrm{P}: y^2=x-2$ at the point $B$ in the first quadrant....

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Q JEE MAIN 2025

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

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Q JEE MAIN 2023

If the area bounded by the curve $2 y^2=3 x$, lines $x+y=3, y=0$ and outside the circle $(x-3)^2+y^2=2$ is $A$,...

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

Let $y=p(x)$ be the parabola passing through the points $(-1,0),(0,1)$ and $(1,0)$. If the area of the region $...

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Q JEE MAIN 2023

Let R be a rectangle given by the lines $x=0, x=2, y=0$ and $y=5$. Let $A(\alpha, 0)$ and $...

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Q JEE-Main

Let the point $(p, p+1)$ lie inside the region $...

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Q JEE-Main 2023

If the area of the region $\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) ; 2 \mathrm{y}-\mathrm{y}^2 \leq \mathrm{x}^2 \leq 2 \mathrm{y}, \mathrm{x} \geq \mathrm{y}\right\}$ is...

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Q JEE MAIN 2024

Let the area of the region enclosed by the curve $y=\min \{\sin x, \cos x\}$ and the $x$-axis between $x=-\pi$...

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Q JEE-Main 2024

Let the area of the region enclosed by the curves y=3x,2y=27-3x and y=3x-x√x be A. Then 10" " A is...

JEE Main Mathematics Hard

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Q JEE MAIN 2024

The area of the region enclosed by the parabolas $y=x^2-5 x$ and $y=7 x-x^2$ is

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Q JEE MAIN

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...

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Q JEE MAIN 2024

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...

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Q JEE MAIN

The area (in sq. units) of the part of circle $x^2+y^2=169$ which is below the line 5x-y=13 is $...

JEE Main Mathematics Medium

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Q JEE-Main 2024

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

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Q JEE MAIN 2024

The area of the region $\left\{(x, y): y^2 \leq 4 x, x0, x \neq 3\right\}$ is

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Q JEE MAIN 2024

Let the area of the region $...

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Q JEE MAIN 2025

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...

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Q JEE MAIN 2025

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

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Q JEE MAIN 2025

If the area of the region bounded by the curves $y = 4 - \frac{{{x^2}}}{4}$ and $...

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Q JEE MAIN 2025

If the area of the region $\{ (x,y):|x - 5| \le y \le 4\sqrt x \} $ is A ,...

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Q JEE MAIN 2025

The area of the region bounded by the curve $y = \max \{ |x|,x|x - 2|\} $, the x-axis and...

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Q JEE MAIN 2025

If the area of the region $...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $(2,3)$ be the largest open interval in which the function $f(x)=2 \log _{\mathrm{e}}(x-2)-x^{2}+a x+1$ is strictly increasing and $...

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Q JEE MAIN 2025

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

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Q JEE MAIN 2025

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 $\frac{\mathrm{e}^{2}+8 \mathrm{e}+1}{\mathrm{e}}$,...

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Q JEE MAIN 2025

Let the area of the region $...

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Q JEE MAIN 2025

The area (in sq. units) of the region $...

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Q JEE MAIN 2025

Consider the region $R = \left\{ {(x,y):x \le y \le 9 - \frac{{11}}{3}{x^2},x \ge 0} \right\}$. The area, of the...

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Q JEE MAIN 2025

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

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Q JEE MAIN 2025

If the area of the larger portion bounded between the curves ${x^2} + {y^2} = 25$ and $...

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Q JEE MAIN 2025

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f(x+y)=f(x) f(y)$ for all $x, y \in \mathbf{R}$....

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Q JEE MAIN 2025

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

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Q JEE MAIN 2025

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

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