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

Let x2 + y2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x2 at (2, 4). Then A + C is equal to ___________.

A
16
B
88/5
C
72
D
$$-$$8
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Consider the parabola with vertex $$\left( {{1 \over 2},{3 \over 4}} \right)$$ and the directrix $$y = {1 \over 2}$$. Let P be the point where the parabola meets the line $$x = - {1 \over 2}$$. If the normal to the parabola at P intersects the parabola again at the point Q, then (PQ)2 is equal to :
A
$${{75} \over 8}$$
B
$${{125} \over {16}}$$
C
$${{25} \over 2}$$
D
$${{15} \over 2}$$
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Modern Physics
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