1
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^{2} x}+9^{\tan ^{2} x}=10\right\}$$ and $$\beta=\sum_\limits{x \in S} \tan ^{2}\left(\frac{x}{3}\right)$$, then $$\frac{1}{6}(\beta-14)^{2}$$ is equal to :

A
16
B
32
C
8
D
64
2
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let A be the point $$(1,2)$$ and B be any point on the curve $$x^{2}+y^{2}=16$$. If the centre of the locus of the point P, which divides the line segment $$\mathrm{AB}$$ in the ratio $$3: 2$$ is the point C$$(\alpha, \beta)$$, then the length of the line segment $$\mathrm{AC}$$ is :

A
$$\frac{3 \sqrt{5}}{5}$$
B
$$\frac{6 \sqrt{5}}{5}$$
C
$$\frac{2 \sqrt{5}}{5}$$
D
$$\frac{4 \sqrt{5}}{5}$$
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 Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{A}=\{2,3,4\}$$ and $$\mathrm{B}=\{8,9,12\}$$. Then the number of elements in the relation $$\mathrm{R}=\left\{\left(\left(a_{1}, \mathrm{~b}_{1}\right),\left(a_{2}, \mathrm{~b}_{2}\right)\right) \in(A \times B, A \times B): a_{1}\right.$$ divides $$\mathrm{b}_{2}$$ and $$\mathrm{a}_{2}$$ divides $$\left.\mathrm{b}_{1}\right\}$$ is :

A
18
B
24
C
36
D
12
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