1
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 $$\left( {0,{3 \over 4}} \right)$$
2
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$${{\sqrt 3 } \over 4}$$
3
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the area of the triangle with vertices A(1, $$\alpha$$), B($$\alpha$$, 0) and C(0, $$\alpha$$) be 4 sq. units. If the points ($$\alpha$$, $$-$$$$\alpha$$), ($$-$$$$\alpha$$, $$\alpha$$) and ($$\alpha$$2, $$\beta$$) are collinear, then $$\beta$$ is equal to :

A
64
B
$$-$$8
C
$$-$$64
D
512
4
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of distinct real roots of the equation

x7 $$-$$ 7x $$-$$ 2 = 0 is

A
5
B
7
C
1
D
3
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