1
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
Let the latus ractum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radius 2$$\sqrt 5$$. Then, the distance between the centres of the circles C1 and C2 is :
A
8
B
12
C
$$8\sqrt 5$$
D
$$4\sqrt 5$$
2
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
Let e1 and e2 be the eccentricities of the ellipse,
$${{{x^2}} \over {25}} + {{{y^2}} \over {{b^2}}} = 1$$(b < 5) and the hyperbola,
$${{{x^2}} \over {16}} - {{{y^2}} \over {{b^2}}} = 1$$ respectively satisfying e1e2 = 1. If $$\alpha$$
and $$\beta$$ are the distances between the foci of the
ellipse and the foci of the hyperbola
respectively, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :
A
(8, 10)
B
(8, 12)
C
$$\left( {{{24} \over 5},10} \right)$$
D
$$\left( {{{20} \over 3},12} \right)$$
3
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
A hyperbola having the transverse axis of length $$\sqrt 2$$ has the same foci as that of the ellipse 3x2 + 4y2 = 12, then this hyperbola does not pass through which of the following points ?
A
$$\left( {1, - {1 \over {\sqrt 2 }}} \right)$$
B
$$\left( {\sqrt {{3 \over 2}} ,{1 \over {\sqrt 2 }}} \right)$$
C
$$\left( { - \sqrt {{3 \over 2}} ,1} \right)$$
D
$$\left( {{1 \over {\sqrt 2 }},0} \right)$$
4
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
Let P be a point on the parabola, y2 = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is $${4 \over 3}$$, then :
A
MQ = $${1 \over 3}$$
B
PN = 4
C
PN = 3
D
MQ = $${1 \over 4}$$
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