1
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
2
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 ______________.
Your input ____
3
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
Change Language
Consider the following frequency distribution :

Class : 10-20 20-30 30-40 40-50 50-60
Frequency : $$\alpha $$ 110 54 30 $$\beta $$


If the sum of all frequencies is 584 and median is 45, then | $$\alpha$$ $$-$$ $$\beta$$ | is equal to _______________.
Your input ____
4
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
Change Language
Let $$\overrightarrow p = 2\widehat i + 3\widehat j + \widehat k$$ and $$\overrightarrow q = \widehat i + 2\widehat j + \widehat k$$ be two vectors. If a vector $$\overrightarrow r = (\alpha \widehat i + \beta \widehat j + \gamma \widehat k)$$ is perpendicular to each of the vectors ($$(\overrightarrow p + \overrightarrow q )$$ and $$(\overrightarrow p - \overrightarrow q )$$, and $$\left| {\overrightarrow r } \right| = \sqrt 3 $$, then $$\left| \alpha \right| + \left| \beta \right| + \left| \gamma \right|$$ is equal to _______________.
Your input ____
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