IIT-JEE 2006 | Properties of Triangle Question 17 | Mathematics

IIT-JEE 2006

MCQ (More than One Correct Answer)

-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

$$AE$$ is $$HM$$ of $$b$$ and $$c$$

$$AD$$ $$ = {{2bc} \over {b + c}}\cos {A \over 2}$$

$$EF$$ $$ = {{4bc} \over {b + c}}\sin {A \over 2}$$

$$\Delta AEF$$ is isosceles

IIT-JEE 1987

MCQ (More than One Correct Answer)

-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

$$5 - \sqrt 6 $$

$$3\sqrt 3 $$

$$5$$

$$5 + \sqrt 6 $$

IIT-JEE 1986

MCQ (More than One Correct Answer)

-0.5

There exists a triangle $$ABC$$ satisfying the conditions

$$b\sin A = a,A < \pi /2$$

$$b\sin A > a,A > \pi /2$$

$$b\sin A > a,A < \pi /2$$

$$b\sin A < a,A < \pi /2,b > a$$

JEE Advanced Subjects