1
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1

Let $$y = p(x)$$ be the parabola passing through the points $$( - 1,0),(0,1)$$ and $$(1,0)$$. If the area of the region $$\{ (x,y):{(x + 1)^2} + {(y - 1)^2} \le 1,y \le p(x)\}$$ is A, then $$12(\pi - 4A)$$ is equal to ___________.

2
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 _____________.

3
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 ___________.

4
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 ____________.