1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a1, a2, ..........., a21 be an AP such that $$\sum\limits_{n = 1}^{20} {{1 \over {{a_n}{a_{n + 1}}}} = {4 \over 9}} $$. If the sum of this AP is 189, then a6a16 is equal to :
A
57
B
72
C
48
D
36
2
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The function f(x), that satisfies the condition
$$f(x) = x + \int\limits_0^{\pi /2} {\sin x.\cos y\,f(y)\,dy} $$, is :
A
$$x + {2 \over 3}(\pi - 2)\sin x$$
B
$$x + (\pi + 2)\sin x$$
C
$$x + {\pi \over 2}\sin x$$
D
$$x + (\pi - 2)\sin x$$
3
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let $$\theta$$ be the acute angle between the tangents to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 1} = 1$$ and the circle $${x^2} + {y^2} = 3$$ at their point of intersection in the first quadrant. Then tan$$\theta$$ is equal to :
A
$${5 \over {2\sqrt 3 }}$$
B
$${2 \over {\sqrt 3 }}$$
C
$${4 \over {\sqrt 3 }}$$
D
2
4
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
Change Language
Let X be a random variable with distribution.

x $$ - $$2 $$ - $$1 3 4 6
P(X = x) $${1 \over 5}$$ a $${1 \over 3}$$ $${1 \over 5}$$ b


If the mean of X is 2.3 and variance of X is $$\sigma$$2, then 100 $$\sigma$$2 is equal to :
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