1
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
If x2 + 9y2 $$-$$ 4x + 3 = 0, x, y $$\in$$ R, then x and y respectively lie in the intervals :
A
$$\left[ { - {1 \over 3},{1 \over 3}} \right]$$ and $$\left[ { - {1 \over 3},{1 \over 3}} \right]$$
B
$$\left[ { - {1 \over 3},{1 \over 3}} \right]$$ and [1, 3]
C
[1, 3] and [1, 3]
D
[1, 3] and $$\left[ { - {1 \over 3},{1 \over 3}} \right]$$
2
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
On the ellipse $${{{x^2}} \over 8} + {{{y^2}} \over 4} = 1$$ let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S' be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS' then, the value of (5 $$-$$ e2). A is :
A
6
B
12
C
14
D
24
3
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity $${1 \over 3}$$ and the distance of the nearer focus from this directrix is $${8 \over {\sqrt {53} }}$$, then the equation of the other directrix can be :
A
11x + 7y + 8 = 0 or 11x + 7y $$-$$ 15 = 0
B
11x $$-$$ 7y $$-$$ 8 = 0 or 11x + 7y + 15 = 0
C
2x $$-$$ 7y + 29 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0
D
2x $$-$$ 7y $$-$$ 39 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0
4
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
If a tangent to the ellipse x2 + 4y2 = 4 meets the tangents at the extremities of it major axis at B and C, then the circle with BC as diameter passes through the point :
A
$$(\sqrt 3 ,0)$$
B
$$(\sqrt 2 ,0)$$
C
(1, 1)
D
($$-$$1, 1)
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