1
JEE Main 2023 (Online) 11th April Evening Shift
Numerical
+4
-1

If A is the area in the first quadrant enclosed by the curve $$\mathrm{C: 2 x^{2}-y+1=0}$$, the tangent to $$\mathrm{C}$$ at the point $$(1,3)$$ and the line $$\mathrm{x}+\mathrm{y}=1$$, then the value of $$60 \mathrm{~A}$$ is _________.

2
JEE Main 2023 (Online) 10th April Evening Shift
Numerical
+4
-1

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

3
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 ___________.

4
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 _____________.