1
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Given : $$f(x) = \left\{ {\matrix{ {x\,\,\,\,\,,} & {0 \le x < {1 \over 2}} \cr {{1 \over 2}\,\,\,\,,} & {x = {1 \over 2}} \cr {1 - x\,\,\,,} & {{1 \over 2} < x \le 1} \cr } } \right.$$

and $$g(x) = \left( {x - {1 \over 2}} \right)^2,x \in R$$

Then the area (in sq. units) of the region bounded by the curves, y = ƒ(x) and y = g(x) between the lines, 2x = 1 and 2x = $$\sqrt 3$$, is :
A
$${1 \over 2} + {{\sqrt 3 } \over 4}$$
B
$${1 \over 2} - {{\sqrt 3 } \over 4}$$
C
$${1 \over 3} + {{\sqrt 3 } \over 4}$$
D
$${{\sqrt 3 } \over 4} - {1 \over 3}$$
2
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
The area (in sq. units) of the region

{(x,y) $$\in$$ R2 : x2 $$\le$$ y $$\le$$ 3 – 2x}, is :
A
$${{34} \over 3}$$
B
$${{29} \over 3}$$
C
$${{31} \over 3}$$
D
$${{32} \over 3}$$
3
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of
$$\Delta$$OQR = $${1 \over 2}$$, then 'a' satisfies the equation :
A
x6 – 12x3 + 4 = 0
B
x6 – 12x3 – 4 = 0
C
x6 + 6x3 – 4 = 0
D
x6 – 6x3 + 4 = 0
4
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
The area (in sq. units) of the region
{(x, y) $$\in$$ R2 | 4x2 $$\le$$ y $$\le$$ 8x + 12} is :
A
$${{125} \over 3}$$
B
$${{128} \over 3}$$
C
$${{127} \over 3}$$
D
$${{124} \over 3}$$
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