1
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let the circle S : 36x2 + 36y2 $$-$$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x $$-$$ 2y = 4 and 2x $$-$$ y = 5 lies inside the circle S, then :
A
$${{25} \over 9} < C < {{13} \over 3}$$
B
100 < C < 165
C
81 < C < 156
D
100 < C < 156
2
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let n denote the number of solutions of the equation z2 + 3$$\overline z $$ = 0, where z is a complex number. Then the value of $$\sum\limits_{k = 0}^\infty {{1 \over {{n^k}}}} $$ is equal to :
A
1
B
$${4 \over 3}$$
C
$${3 \over 2}$$
D
2
3
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the domain of the function $$f(x) = {{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} } \over {\sqrt {{{\sin }^{ - 1}}\left( {{{2x - 1} \over 2}} \right)} }}$$ is the interval ($$\alpha$$, $$\beta$$], then $$\alpha$$ + $$\beta$$ is equal to :
A
$${3 \over 2}$$
B
2
C
$${1 \over 2}$$
D
1
4
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$\to$$ R be defined as $$f(x) = \left\{ {\matrix{ {{{{x^3}} \over {{{(1 - \cos 2x)}^2}}}{{\log }_e}\left( {{{1 + 2x{e^{ - 2x}}} \over {{{(1 - x{e^{ - x}})}^2}}}} \right),} & {x \ne 0} \cr {\alpha ,} & {x = 0} \cr } } \right.$$

If f is continuous at x = 0, then $$\alpha$$ is equal to :
A
1
B
3
C
0
D
2
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