This chapter is currently out of syllabus
1
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1
Out of Syllabus

The angle of elevation of the top of a tower from a point A due north of it is $$\alpha$$ and from a point B at a distance of 9 units due west of A is $$\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)$$. If the distance of the point B from the tower is 15 units, then $$\cot \alpha$$ is equal to :

A
$$\frac{6}{5}$$
B
$$\frac{9}{5}$$
C
$$\frac{4}{3}$$
D
$$\frac{7}{3}$$
2
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1
Out of Syllabus

A horizontal park is in the shape of a triangle $$\mathrm{OAB}$$ with $$\mathrm{AB}=16$$. A vertical lamp post $$\mathrm{OP}$$ is erected at the point $$\mathrm{O}$$ such that $$\angle \mathrm{PAO}=\angle \mathrm{PBO}=15^{\circ}$$ and $$\angle \mathrm{PCO}=45^{\circ}$$, where $$\mathrm{C}$$ is the midpoint of $$\mathrm{AB}$$. Then $$(\mathrm{OP})^{2}$$ is equal to :

A
$$\frac{32}{\sqrt{3}}(\sqrt{3}-1)$$
B
$$\frac{32}{\sqrt{3}}(2-\sqrt{3})$$
C
$$\frac{16}{\sqrt{3}}(\sqrt{3}-1)$$
D
$$\frac{16}{\sqrt{3}}(2-\sqrt{3})$$
3
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1
Out of Syllabus

The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is $$45^{\circ}$$. Let R be a point on AQ and from a point B, vertically above $$\mathrm{R}$$, the angle of elevation of $$\mathrm{P}$$ is $$60^{\circ}$$. If $$\angle \mathrm{BAQ}=30^{\circ}, \mathrm{AB}=\mathrm{d}$$ and the area of the trapezium $$\mathrm{PQRB}$$ is $$\alpha$$, then the ordered pair $$(\mathrm{d}, \alpha)$$ is :

A
$$(10(\sqrt{3}-1), 25)$$
B
$$\left(10(\sqrt{3}-1), \frac{25}{2}\right)$$
C
$$(10(\sqrt{3}+1), 25)$$
D
$$\left(10(\sqrt{3}+1), \frac{25}{2}\right)$$
4
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1
Out of Syllabus

Let a vertical tower $$A B$$ of height $$2 h$$ stands on a horizontal ground. Let from a point $$P%$$ on the ground a man can see upto height $$h$$ of the tower with an angle of elevation $$2 \alpha$$. When from $$P$$, he moves a distance $$d$$ in the direction of $$\overrightarrow{A P}$$, he can see the top $$B$$ of the tower with an angle of elevation $$\alpha$$. If $$d=\sqrt{7} h$$, then $$\tan \alpha$$ is equal to

A
$$\sqrt{5}-2$$
B
$$\sqrt{3}-1$$
C
$$\sqrt{7}-2$$
D
$$\sqrt{7}-\sqrt{3}$$
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