1

### IIT-JEE 1984

Subjective
For a triangle $$ABC$$ it is given that $$\cos A + \cos B + \cos C = {3 \over 2}$$. Prove that the triangle is equilateral.

Solve it.
2

### IIT-JEE 1983

Subjective
The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta$$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.

Solve it.
3

### IIT-JEE 1982

Subjective
A vertical pole stands at a point $$Q$$ on a horizontal ground. $$A$$ and $$B$$ are points on the ground, $$d$$ meters apart. The pole subtends angles $$\alpha$$ and $$\beta$$ at $$A$$ and $$B$$ respectively. $$AB$$ subtends an angle $$\gamma$$ and $$Q$$. Find the height of the pole.

$${d \over {\sqrt {{{\cot }^2}\alpha + {{\cot }^2}\beta - \cot \alpha \cot \beta \cot \gamma } }}$$
4

### IIT-JEE 1981

Subjective
Let the angles $$A, B, C$$ of a triangle $$ABC$$ be in A.P. and let $$b:c = \sqrt 3 :\sqrt 2$$. Find the angle $$A$$.

$${75^ \circ }$$

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