1
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1

If the area of the region bounded by the curves $$y^2-2y=-x,x+y=0$$ is A, then 8 A is equal to __________

2
JEE Main 2022 (Online) 25th July Evening Shift
Numerical
+4
-1

Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve $$4{x^3} - 3x{y^2} + 6{x^2} - 5xy - 8{y^2} + 9x + 14 = 0$$ at the point ($$-$$2, 3) be A. Then 8A is equal to ______________.

3
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1

If for some $$\alpha$$ > 0, the area of the region $$\{ (x,y):|x + \alpha | \le y \le 2 - |x|\}$$ is equal to $${3 \over 2}$$, then the area of the region $$\{ (x,y):0 \le y \le x + 2\alpha ,\,|x| \le 1\}$$ is equal to ____________.

4
JEE Main 2022 (Online) 29th June Evening Shift
Numerical
+4
-1

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

Area $$\left\{ {(x,y):{x^2} + {y^2} \le {a^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} \ge 1} \right\} = 30\pi$$

and

Area $$\left\{ {(x,y):{x^2} + {y^2} \le {b^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} \le 1} \right\} = 18\pi$$

Then, the value of (a $$-$$ b)2 is equal to ___________.