1
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1

Let for $$x \in \mathbb{R}$$,

$$f(x)=\frac{x+|x|}{2} \text { and } g(x)=\left\{\begin{array}{cc} x, & x<0 \\ x^{2}, & x \geq 0 \end{array}\right. \text {. }$$

Then area bounded by the curve $$y=(f \circ g)(x)$$ and the lines $$y=0,2 y-x=15$$ is equal to __________.

2
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
Let $A$ be the area of the region

$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$.

Then $540 \mathrm{~A}$ is equal to :
3
JEE Main 2023 (Online) 30th January Morning Shift
Numerical
+4
-1

Let $$\alpha$$ 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 $$3 \alpha$$ is equal to ___________.

4
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1

If the area enclosed by the parabolas $$\mathrm{P_1:2y=5x^2}$$ and $$\mathrm{P_2:x^2-y+6=0}$$ is equal to the area enclosed by $$\mathrm{P_1}$$ and $$\mathrm{y=\alpha x,\alpha > 0}$$, then $$\alpha^3$$ is equal to ____________.

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