1
IIT-JEE 2006
MCQ (More than One Correct Answer)
+5
-1.25
In $$\Delta ABC$$, internal angle bisector of $$\angle A$$ meets side $$BC$$ in $$D$$. $$DE \bot AD$$ meets $$AC$$ in $$E$$ and $$AB$$ in $$F$$. Then
A
$$AE$$ is $$HM$$ of $$b$$ and $$c$$
B
$$AD$$ $$ = {{2bc} \over {b + c}}\cos {A \over 2}$$
C
$$EF$$ $$ = {{4bc} \over {b + c}}\sin {A \over 2}$$
D
$$\Delta AEF$$ is isosceles
2
IIT-JEE 1987
MCQ (More than One Correct Answer)
+2
-0.5
In a triangle, the lengths of the two larger sides are $$10$$ and $$9$$, respectively. If the angles are in $$AP$$. Then the length of the third side can be
A
$$5 - \sqrt 6 $$
B
$$3\sqrt 3 $$
C
$$5$$
D
$$5 + \sqrt 6 $$
3
IIT-JEE 1986
MCQ (More than One Correct Answer)
+2
-0.5
There exists a triangle $$ABC$$ satisfying the conditions
A
$$b\sin A = a,A < \pi /2$$
B
$$b\sin A > a,A > \pi /2$$
C
$$b\sin A > a,A < \pi /2$$
D
$$b\sin A < a,A < \pi /2,b > a$$
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