JEE Main 2020 (Online) 8th January Evening Slot | Definite Integrals and Applications of Integrals Question 205 | Mathematics

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JEE Main 2020 (Online) 8th January Evening Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region
{(x,y) $$ \in $$ R² : x² $$ \le $$ y $$ \le $$ 3 – 2x}, is

$${{34} \over 3}$$

$${{29} \over 3}$$

$${{31} \over 3}$$

$${{32} \over 3}$$

JEE Main 2020 (Online) 8th January Evening Slot

MCQ (Single Correct Answer)

-1

If $$I = \int\limits_1^2 {{{dx} \over {\sqrt {2{x^3} - 9{x^2} + 12x + 4} }}} $$, then :

$${1 \over 16} < {I^2} < {1 \over 9}$$

$${1 \over 8} < {I^2} < {1 \over 4}$$

$${1 \over 9} < {I^2} < {1 \over 8}$$

$${1 \over 6} < {I^2} < {1 \over 2}$$

JEE Main 2020 (Online) 8th January Morning Slot

MCQ (Single Correct Answer)

-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

$${{5\pi } \over 6}$$

$$ - {\pi \over 6}$$

$${\pi \over 3}$$

$${{2\pi } \over 3}$$

JEE Main 2020 (Online) 8th January Morning Slot

MCQ (Single Correct Answer)

-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

x⁶ – 12x³ + 4 = 0

x⁶ – 12x³ – 4 = 0

x⁶ + 6x³ – 4 = 0

x⁶ – 6x³ + 4 = 0

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