1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x2 $$-$$ y2 = 3. If L is also a tangent to the parabola y2 = $$\alpha$$x, then $$\alpha$$ is equal to :
A
12
B
$$-$$12
C
24
D
$$-$$24
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let $${E_1}:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,a > b$$. Let E2 be another ellipse such that it touches the end points of major axis of E1 and the foci of E2 are the end points of minor axis of E1. If E1 and E2 have same eccentricities, then its value is :
A
$${{ - 1 + \sqrt 5 } \over 2}$$
B
$${{ - 1 + \sqrt 8 } \over 2}$$
C
$${{ - 1 + \sqrt 3 } \over 2}$$
D
$${{ - 1 + \sqrt 6 } \over 2}$$
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Let P be a variable point on the parabola $$y = 4{x^2} + 1$$. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :
A
$${(3x - y)^2} + (x - 3y) + 2 = 0$$
B
$$2{(3x - y)^2} + (x - 3y) + 2 = 0$$
C
$${(3x - y)^2} + 2(x - 3y) + 2 = 0$$
D
$$2{(x - 3y)^2} + (3x - y) + 2 = 0$$
4
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Let the tangent to the parabola S : y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :
A
$${{25} \over 2}$$
B
$${{35} \over 2}$$
C
$${{15} \over 2}$$
D
25
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