1
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the radius of the largest circle with centre (2,0) inscribed in the ellipse $$x^2+4y^2=36$$ is r, then 12r$$^2$$ is equal to :

A
72
B
92
C
115
D
69
2
JEE Main 2023 (Online) 11th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Consider ellipses $$\mathrm{E}_{k}: k x^{2}+k^{2} y^{2}=1, k=1,2, \ldots, 20$$. Let $$\mathrm{C}_{k}$$ be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse $$\mathrm{E}_{k}$$. If $$r_{k}$$ is the radius of the circle $$\mathrm{C}_{k}$$, then the value of $$\sum_\limits{k=1}^{20} \frac{1}{r_{k}^{2}}$$ is :

A
2870
B
3210
C
3320
D
3080
3
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let a circle of radius 4 be concentric to the ellipse $$15 x^{2}+19 y^{2}=285$$. Then the common tangents are inclined to the minor axis of the ellipse at the angle :

A
$$\frac{\pi}{4}$$
B
$$\frac{\pi}{3}$$
C
$$\frac{\pi}{6}$$
D
$$\frac{\pi}{12}$$
4
JEE Main 2023 (Online) 10th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the ellipse $$E:{x^2} + 9{y^2} = 9$$ intersect the positive x and y-axes at the points A and B respectively. Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If the area of the triangle with vertices A, P and the origin O is $${m \over n}$$, where m and n are coprime, then $$m - n$$ is equal to :

A
15
B
16
C
17
D
18
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