1
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
The parabolas : $a x^2+2 b x+c y=0$ and $d x^2+2 e x+f y=0$ intersect on the line $y=1$. If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in G.P., then :
A
$\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in A.P.
B
$\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in G.P.
C
$d, e, f$ are in A.P.
D
$d, e, f$ are in G.P.
2
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1
Out of Syllabus

If $$\mathrm{P}(\mathrm{h}, \mathrm{k})$$ be a point on the parabola $$x=4 y^{2}$$, which is nearest to the point $$\mathrm{Q}(0,33)$$, then the distance of $$\mathrm{P}$$ from the directrix of the parabola $$\quad y^{2}=4(x+y)$$ is equal to :

A
8
B
2
C
6
D
4
3
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1
Out of Syllabus

If the tangent at a point P on the parabola $$y^2=3x$$ is parallel to the line $$x+2y=1$$ and the tangents at the points Q and R on the ellipse $$\frac{x^2}{4}+\frac{y^2}{1}=1$$ are perpendicular to the line $$x-y=2$$, then the area of the triangle PQR is :

A
$$\frac{9}{\sqrt5}$$
B
$$3\sqrt5$$
C
$$5\sqrt3$$
D
$$\frac{3}{2}\sqrt5$$
4
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

The equations of two sides of a variable triangle are $$x=0$$ and $$y=3$$, and its third side is a tangent to the parabola $$y^2=6x$$. The locus of its circumcentre is :

A
$$4{y^2} - 18y - 3x - 18 = 0$$
B
$$4{y^2} + 18y + 3x + 18 = 0$$
C
$$4{y^2} - 18y + 3x + 18 = 0$$
D
$$4{y^2} - 18y - 3x + 18 = 0$$
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