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1

### 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.

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

### 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.

$$16:1$$
3

### IIT-JEE 1991

Subjective
In a triangle of base a the ratio of the other two sides is $$r\left( { < 1} \right)$$. Show that the altitude of the triangle is less than of equal to $${{ar} \over {1 - {r^2}}}$$

Solve it.
4

### IIT-JEE 1991

Subjective
A man notices two objects in a straight line due west. After walking a distance $$c$$ due north he observes that the objects subtend an angle $$\alpha$$ at his eye; and, after walking a further distance $$2c$$ due north, an angle $$\beta$$. Show that the distance between the objects is $${{8c} \over {3\cot \beta - \cot \alpha }}$$; the height of the man is being ignored.

Solve it.

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