1
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1

Let R be a rectangle given by the lines $$x=0, x=2, y=0$$ and $$y=5$$. Let A$$(\alpha,0)$$ and B$$(0,\beta),\alpha\in[0,2]$$ and $$\beta\in[0,5]$$, be such that the line segment AB divides the area of the rectangle R in the ratio 4 : 1. Then, the mid-point of AB lies on a :

A
hyperbola
B
straight line
C
parabola
D
circle
2
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1
Out of Syllabus

Let $$\mathrm{P}\left(x_{0}, y_{0}\right)$$ be the point on the hyperbola $$3 x^{2}-4 y^{2}=36$$, which is nearest to the line $$3 x+2 y=1$$. Then $$\sqrt{2}\left(y_{0}-x_{0}\right)$$ is equal to :

A
3
B
$$-$$9
C
$$-$$3
D
9
3
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
Let $\mathrm{H}$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is :
A
$\frac{5}{2}$
B
3
C
2
D
$\frac{3}{2}$
4
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

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
$$4\sqrt 6 + {{44} \over 3}$$
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