1
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$\frac{3}{2}\sqrt5$$
2
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$4{y^2} - 18y - 3x + 18 = 0$$
3
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let T and C respectively be the transverse and conjugate axes of the hyperbola $$16{x^2} - {y^2} + 64x + 4y + 44 = 0$$. Then the area of the region above the parabola $${x^2} = y + 4$$, below the transverse axis T and on the right of the conjugate axis C is :

A
$$4\sqrt 6 - {{28} \over 3}$$
B
$$4\sqrt 6 - {{44} \over 3}$$
C
$$4\sqrt 6 + {{28} \over 3}$$
D
$$4\sqrt 6 + {{44} \over 3}$$
4
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The distance of the point $$(6,-2\sqrt2)$$ from the common tangent $$\mathrm{y=mx+c,m > 0}$$, of the curves $$x=2y^2$$ and $$x=1+y^2$$ is :

A
$$\frac{1}{3}$$
B
5
C
$$\frac{14}{3}$$
D
5$$\sqrt3$$
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