1
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
$${{32} \over 3}$$
2
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
If $$I = \int\limits_1^2 {{{dx} \over {\sqrt {2{x^3} - 9{x^2} + 12x + 4} }}}$$, then :
A
$${1 \over 16} < {I^2} < {1 \over 9}$$
B
$${1 \over 8} < {I^2} < {1 \over 4}$$
C
$${1 \over 9} < {I^2} < {1 \over 8}$$
D
$${1 \over 6} < {I^2} < {1 \over 2}$$
3
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Let ƒ(x) = (sin(tan–1x) + sin(cot–1x))2 – 1, |x| > 1.
If $${{dy} \over {dx}} = {1 \over 2}{d \over {dx}}\left( {{{\sin }^{ - 1}}\left( {f\left( x \right)} \right)} \right)$$ and $$y\left( {\sqrt 3 } \right) = {\pi \over 6}$$, then y($${ - \sqrt 3 }$$) is equal to
A
$${{5\pi } \over 6}$$
B
$$- {\pi \over 6}$$
C
$${\pi \over 3}$$
D
$${{2\pi } \over 3}$$
4
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
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