1
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$y = y(x)$$ be the solution of the differential equation $$(x + 1)y' - y = {e^{3x}}{(x + 1)^2}$$, with $$y(0) = {1 \over 3}$$. Then, the point $$x = - {4 \over 3}$$ for the curve $$y = y(x)$$ is :

A
not a critical point
B
a point of local minima
C
a point of local maxima
D
a point of inflection
2
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the solution curve $$y = y(x)$$ of the differential equation $${y^2}dx + ({x^2} - xy + {y^2})dy = 0$$, which passes through the point (1, 1) and intersects the line $$y = \sqrt 3 x$$ at the point $$(\alpha ,\sqrt 3 \alpha )$$, then value of $${\log _e}(\sqrt 3 \alpha )$$ is equal to :

A
$${\pi \over 3}$$
B
$${\pi \over 2}$$
C
$${\pi \over 12}$$
D
$${\pi \over 6}$$
3
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$x = 2t$$, $$y = {{{t^2}} \over 3}$$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $$SA \bot BA$$, where A is any point on the conic. If k is the ordinate of the centroid of the $$\Delta$$SAB, then $$\mathop {\lim }\limits_{t \to 1} k$$ is equal to :

A
$${{17} \over {18}}$$
B
$${{19} \over {18}}$$
C
$${{11} \over {18}}$$
D
$${{13} \over {18}}$$
4
JEE Main 2022 (Online) 25th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a circle C in complex plane pass through the points $${z_1} = 3 + 4i$$, $${z_2} = 4 + 3i$$ and $${z_3} = 5i$$. If $$z( \ne {z_1})$$ is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then $$arg(z)$$ is equal to :

A
$${\tan ^{ - 1}}\left( {{2 \over {\sqrt 5 }}} \right) - \pi $$
B
$${\tan ^{ - 1}}\left( {{{24} \over 7}} \right) - \pi $$
C
$${\tan ^{ - 1}}\left( 3 \right) - \pi $$
D
$${\tan ^{ - 1}}\left( {{3 \over 4}} \right) - \pi $$
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