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1

### IIT-JEE 1994

Subjective
Let $${A_1},{A_2},........,{A_n}$$ be the vertices of an $$n$$-sided regular polygon such that $${1 \over {{A_1}{A_2}}} = {1 \over {{A_1}{A_3}}} + {1 \over {{A_1}{A_4}}}$$, Find the value of $$n$$.

$$7$$
2

### IIT-JEE 1994

Subjective
A tower $$AB$$ leans towards west making an angle $$\alpha$$ with the vertical. The angular elevation of $$B$$, the topmost point of the tower is $$\beta$$ as observed from a point $$C$$ due west of $$A$$ at a distance $$d$$ from $$A$$. If the angular elevation of $$B$$ from a point $$D$$ due east of $$C$$ at a distance $$2d$$ from $$C$$ is $$\gamma$$, then prove that $$2$$ tan $$\alpha = - \cot \beta + \cot \gamma$$.

Solve it.
3

### IIT-JEE 1993

Subjective
An observer at $$O$$ notices that the angle of elevation of the top of a tower is $${30^ \circ }$$. The line joining $$O$$ to the base of the tower makes an angle of $${\tan ^{ - 1}}\left( {1/\sqrt 2 } \right)$$ with the North and is inclined Eastwards. The observer travels a distance of $$300$$ meters towards the North to a point A and finds the tower to his East. The angle of elevation of the top of the tower at $$A$$ is $$\phi$$, Find $$\phi$$ and the height of the tower.

$${45^ \circ }$$, $${150\sqrt 2 }$$ $$m$$
4

### IIT-JEE 1992

Subjective
Three circles touch the one another externally. The tangent at their point of contact meet at a point whose distance from a point of contact is $$4$$. Find the ratio of the product of the radii to the sum of the radii of the circles.

$$16:1$$

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