1
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\alpha = \mathop {\lim }\limits_{x \to {\pi \over 4}} {{{{\tan }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}$$ and $$\beta = \mathop {\lim }\limits_{x \to 0 } {(\cos x)^{\cot x}}$$ are the roots of the equation, ax2 + bx $$-$$ 4 = 0, then the ordered pair (a, b) is :
A
(1, $$-$$3)
B
($$-$$1, 3)
C
($$-$$1, $$-$$3)
D
(1, 3)
2
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The locus of mid-points of the line segments joining ($$-$$3, $$-$$5) and the points on the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$$ is :
A
$$9{x^2} + 4{y^2} + 18x + 8y + 145 = 0$$
B
$$36{x^2} + 16{y^2} + 90x + 56y + 145 = 0$$
C
$$36{x^2} + 16{y^2} + 108x + 80y + 145 = 0$$
D
$$36{x^2} + 16{y^2} + 72x + 32y + 145 = 0$$
3
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $${{dy} \over {dx}} = {{{2^x}y + {2^y}{{.2}^x}} \over {{2^x} + {2^{x + y}}{{\log }_e}2}}$$, y(0) = 0, then for y = 1, the value of x lies in the interval :
A
(1, 2)
B
$$\left( {{1 \over 2},1} \right]$$
C
(2, 3)
D
$$\left( {0,{1 \over 2}} \right]$$
4
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
An angle of intersection of the curves, $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and x2 + y2 = ab, a > b, is :
A
$${\tan ^{ - 1}}\left( {{{a + b} \over {\sqrt {ab} }}} \right)$$
B
$${\tan ^{ - 1}}\left( {{{a - b} \over {2\sqrt {ab} }}} \right)$$
C
$${\tan ^{ - 1}}\left( {{{a - b} \over {\sqrt {ab} }}} \right)$$
D
$${\tan ^{ - 1}}\left( {2\sqrt {ab} } \right)$$
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