1
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x3 $$-$$ 3x2 $$-$$ 12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to ______________.
2
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
The area of the region $$S = \{ (x,y):3{x^2} \le 4y \le 6x + 24\}$$ is ____________.
3
JEE Main 2021 (Online) 22th July Evening Shift
Numerical
+4
-1
The area (in sq. units) of the region bounded by the curves x2 + 2y $$-$$ 1 = 0, y2 + 4x $$-$$ 4 = 0 and y2 $$-$$ 4x $$-$$ 4 = 0, in the upper half plane is _______________.
4
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
Let T be the tangent to the ellipse E : x2 + 4y2 = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = $$\sqrt 5$$ is $$\alpha$$$$\sqrt 5$$ + $$\beta$$ + $$\gamma$$ cos$$-$$1$$\left( {{1 \over {\sqrt 5 }}} \right)$$, then |$$\alpha$$ + $$\beta$$ + $$\gamma$$| is equal to ______________.