1
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is $$k{\left( {{3 \over 4}} \right)^9}$$ then k lies in the set :
A
{x $$\in$$ R : |x $$-$$ 3| < 1}
B
{x $$\in$$ R : |x $$-$$ 2| $$\le$$ 1}
C
{x $$\in$$ R : |x $$-$$ 1| < 1}
D
{x $$\in$$ R : |x $$-$$ 5| $$\le$$ 1}
2
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The number of real roots of the equation $${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$$ is :
A
2
B
4
C
6
D
1
3
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let an ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, $${a^2} > {b^2}$$, passes through $$\left( {\sqrt {{3 \over 2}} ,1} \right)$$ and has eccentricity $${1 \over {\sqrt 3 }}$$. If a circle, centered at focus F($$\alpha$$, 0), $$\alpha$$ > 0, of E and radius $${2 \over {\sqrt 3 }}$$, intersects E at two points P and Q, then PQ2 is equal to :
A
$${8 \over 3}$$
B
$${4 \over 3}$$
C
$${{16} \over 3}$$
D
3
4
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
Change Language
Let y = y(x) be solution of the following differential equation $${e^y}{{dy} \over {dx}} - 2{e^y}\sin x + \sin x{\cos ^2}x = 0,y\left( {{\pi \over 2}} \right) = 0$$ If $$y(0) = {\log _e}(\alpha + \beta {e^{ - 2}})$$, then $$4(\alpha + \beta )$$ is equal to ______________.
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