1
JEE Main 2025 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $x+2 y=0$ is $\alpha x^2+\beta y^2-\gamma x y-30 x-60 y+225=0$, then $\alpha+\beta+\gamma$ is equal to :

A
6
B
8
C
7
D
9
2
JEE Main 2025 (Online) 23rd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the shortest distance from $(a, 0), a>0$, to the parabola $y^2=4 x$ be 4 . Then the equation of the circle passing through the point $(a, 0)$ and the focus of the parabola, and having its centre on the axis of the parabola is :

A
$x^2+y^2-8 x+7=0$
B
$x^2+y^2-6 x+5=0$
C
$x^2+y^2-4 x+3=0$
D
$x^2+y^2-10 x+9=0$
3
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the line $3 x-2 y+12=0$ intersects the parabola $4 y=3 x^2$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment AB subtends an angle equal to

A
$\frac{\pi}{2}-\tan ^{-1}\left(\frac{3}{2}\right)$
B
$\tan ^{-1}\left(\frac{9}{7}\right)$
C
$\tan ^{-1}\left(\frac{11}{9}\right)$
D
$\tan ^{-1}\left(\frac{4}{5}\right)$
4
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\mathrm{P}(4,4 \sqrt{3})$ be a point on the parabola $y^2=4 \mathrm{a} x$ and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :

A
$\frac{34 \sqrt{3}}{3}$
B
$\frac{343 \sqrt{3}}{8}$
C
$17 \sqrt{3}$
D
$\frac{263 \sqrt{3}}{8}$
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