1
JEE Main 2023 (Online) 8th April Evening Shift
Numerical
+4
-1

Let the area enclosed by the lines $$x+y=2, \mathrm{y}=0, x=0$$ and the curve $$f(x)=\min \left\{x^{2}+\frac{3}{4}, 1+[x]\right\}$$ where $$[x]$$ denotes the greatest integer $$\leq x$$, be $$\mathrm{A}$$. Then the value of $$12 \mathrm{~A}$$ is _____________.

2
JEE Main 2023 (Online) 6th April Morning Shift
Numerical
+4
-1

If the area of the region $$S=\left\{(x, y): 2 y-y^{2} \leq x^{2} \leq 2 y, x \geq y\right\}$$ is equal to $$\frac{n+2}{n+1}-\frac{\pi}{n-1}$$, then the natural number $$n$$ is equal to ___________.

3
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

Let $$A$$ be the area bounded by the curve $$y=x|x-3|$$, the $$x$$-axis and the ordinates $$x=-1$$ and $$x=2$$. Then $$12 A$$ is equal to ____________.

4
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Let the area of the region

$\left\{(x, y):|2 x-1| \leq y \leq\left|x^{2}-x\right|, 0 \leq x \leq 1\right\}$ be $\mathrm{A}$.

Then $(6 \mathrm{~A}+11)^{2}$ is equal to
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