1
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1 If $$y = {m_1}x + {c_1}$$ and $$y = {m_2}x + {c_2}$$, $${m_1} \ne {m_2}$$ are two common tangents of circle $${x^2} + {y^2} = 2$$ and parabola y2 = x, then the value of $$8|{m_1}{m_2}|$$ is equal to :

A
$$3 + 4\sqrt 2$$
B
$$- 5 + 6\sqrt 2$$
C
$$- 4 + 3\sqrt 2$$
D
$$7 + 6\sqrt 2$$
2
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1 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
$${{13} \over {18}}$$
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1 A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with

A
length of latus rectum 3
B
length of latus rectum 6
C
focus $$\left( {{4 \over 3},0} \right)$$
D
focus $$\left( {0,{3 \over 4}} \right)$$
4
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1 Let the maximum area of the triangle that can be inscribed in the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over 4} = 1,\,a > 2$$, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $$6\sqrt 3$$. Then the eccentricity of the ellipse is :

A
$${{\sqrt 3 } \over 2}$$
B
$${1 \over 2}$$
C
$${1 \over {\sqrt 2 }}$$
D
$${{\sqrt 3 } \over 4}$$
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