1
IIT-JEE 1982
Subjective
+3
-0
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.
2
IIT-JEE 1981
Subjective
+2
-0
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 $$A$$.
3
IIT-JEE 1980
Subjective
+3
-0
$$ABC$$ is a triangle. $$D$$ is the middle point of $$BC$$. If $$AD$$ is perpendicular to $$AC$$, then prove that $$\cos A\,\cos C = {{2\left( {{c^2} - {a^2}} \right)} \over {3ac}}$$$4 IIT-JEE 1980 Subjective +3 -0 $$ABC$$ is a triangle with $$AB=AC$$. $$D$$ is any point on the side $$BC$$. $$E$$ and $$F$$ are points on the side $$AB$$ and $$AC$$, respectively, such that $$DE$$ is parallel to $$AC$$, and $$DF$$ is parallel to $$AB$$. Prove that $$DF + FA + AE + ED = AB + AC$$$
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