1
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is $$\alpha$$ and the number of persons who speak only Hindi is $$\beta$$, then the eccentricity of the ellipse $$25\left(\beta^{2} x^{2}+\alpha^{2} y^{2}\right)=\alpha^{2} \beta^{2}$$ is :

A
$$\frac{\sqrt{129}}{12}$$
B
$$\frac{3 \sqrt{15}}{12}$$
C
$$\frac{\sqrt{119}}{12}$$
D
$$\frac{\sqrt{117}}{12}$$
2
JEE Main 2023 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the maximum distance of normal to the ellipse $$\frac{x^{2}}{4}+\frac{y^{2}}{b^{2}}=1, b < 2$$, from the origin is 1, then the eccentricity of the ellipse is :

A
$$\frac{\sqrt{3}}{4}$$
B
$$\frac{1}{2}$$
C
$$\frac{1}{\sqrt{2}}$$
D
$$\frac{\sqrt{3}}{2}$$
3
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a line L pass through the point of intersection of the lines $$b x+10 y-8=0$$ and $$2 x-3 y=0, \mathrm{~b} \in \mathbf{R}-\left\{\frac{4}{3}\right\}$$. If the line $$\mathrm{L}$$ also passes through the point $$(1,1)$$ and touches the circle $$17\left(x^{2}+y^{2}\right)=16$$, then the eccentricity of the ellipse $$\frac{x^{2}}{5}+\frac{y^{2}}{\mathrm{~b}^{2}}=1$$ is :

A
$$ \frac{2}{\sqrt{5}} $$
B
$$\sqrt{\frac{3}{5}}$$
C
$$\frac{1}{\sqrt{5}}$$
D
$$\sqrt{\frac{2}{5}}$$
4
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The acute angle between the pair of tangents drawn to the ellipse $$2 x^{2}+3 y^{2}=5$$ from the point $$(1,3)$$ is :

A
$$\tan ^{-1}\left(\frac{16}{7 \sqrt{5}}\right)$$
B
$$\tan ^{-1}\left(\frac{24}{7 \sqrt{5}}\right)$$
C
$$\tan ^{-1}\left(\frac{32}{7 \sqrt{5}}\right)$$
D
$$\tan ^{-1}\left(\frac{3+8 \sqrt{5}}{35}\right)$$
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