1
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let N be the set of natural numbers and a relation R on N be defined by $$R = \{ (x,y) \in N \times N:{x^3} - 3{x^2}y - x{y^2} + 3{y^3} = 0\} $$. Then the relation R is :
A
symmetric but neither reflexive nor transitive
B
reflexive but neither symmetric nor transitive
C
reflexive and symmetric, but not transitive
D
an equivalence relation
2
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $$6\sqrt 5 $$ on the x-axis. Then the radius of the circle C is equal to :
A
$$\sqrt {53} $$
B
9
C
8
D
$$\sqrt {82} $$
3
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : (a, b) $$\to$$ R be twice differentiable function such that $$f(x) = \int_a^x {g(t)dt} $$ for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least :
A
twelve roots in (a, b)
B
five roots in (a, b)
C
seven roots in (a, b)
D
three roots in (a, b)
4
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Change Language
If the real part of the complex number $$z = {{3 + 2i\cos \theta } \over {1 - 3i\cos \theta }},\theta \in \left( {0,{\pi \over 2}} \right)$$ is zero, then the value of sin23$$\theta$$ + cos2$$\theta$$ is equal to _______________.
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