1
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a, b c $$ \in $$ R be such that a2 + b2 + c2 = 1. If
$$a\cos \theta = b\cos \left( {\theta + {{2\pi } \over 3}} \right) = c\cos \left( {\theta + {{4\pi } \over 3}} \right)$$,
where $${\theta = {\pi \over 9}}$$, then the angle between the vectors $$a\widehat i + b\widehat j + c\widehat k$$ and $$b\widehat i + c\widehat j + a\widehat k$$ is :
A
0
B
$${{\pi \over 9}}$$
C
$${{{2\pi } \over 3}}$$
D
$${{\pi \over 2}}$$
2
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let the latus ractum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radius 2$$\sqrt 5 $$. Then, the distance between the centres of the circles C1 and C2 is :
A
8
B
12
C
$$8\sqrt 5 $$
D
$$4\sqrt 5 $$
3
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let R1 and R2 be two relation defined as follows :
R1 = {(a, b) $$ \in $$ R2 : a2 + b2 $$ \in $$ Q} and
R2 = {(a, b) $$ \in $$ R2 : a2 + b2 $$ \notin $$ Q},
where Q is the set of all rational numbers. Then :
A
Neither R1 nor R2 is transitive.
B
R2 is transitive but R1 is not transitive.
C
R1 and R2 are both transitive.
D
R1 is transitive but R2 is not transitive.
4
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the value of the integral
$$\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$$

is $${k \over 6}$$, then k is equal to :
A
$$2\sqrt 3 + \pi $$
B
$$3\sqrt 2 - \pi $$
C
$$3\sqrt 2 + \pi $$
D
$$2\sqrt 3 - \pi $$
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