1
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 ___________.

2
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 ____________.

3
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 __________

4
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 ______________.

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