1

### JEE Advanced 2016 Paper 1 Offline

MCQ (More than One Correct Answer)
In a triangle $$\Delta$$$$XYZ$$, let $$x, y, z$$ be the lengths of sides opposite to the angles $$X, Y, Z$$ respectively, and $$2s = x + y + z$$.
If $${{s - x} \over 4} = {{s - y} \over 3} = {{s - z} \over 2}$$ and area of incircle of the triangle $$XYZ$$ is $${{8\pi } \over 3}$$, then
A
area of the triangle $$XYZ$$ is $$6\sqrt 6$$
B
the radius of circumcircle of the triangle $$XYZ$$ is $${{35} \over 6}\sqrt 6$$
C
$$\sin {X \over 2}\sin {Y \over 2}\sin {Z \over 2} = {4 \over {35}}$$
D
$${\sin ^2}\left( {{{X + Y} \over 2}} \right) = {3 \over 5}$$
2

### JEE Advanced 2013 Paper 2 Offline

MCQ (More than One Correct Answer)
In a triangle $$PQR$$, $$P$$ is the largest angle and $$\cos P = {1 \over 3}$$. Further the incircle of the triangle touches the sides $$PQ$$, $$QR$$ and $$RP$$ at $$N,L$$ and $$M$$ respectively, such that the lengths of $$PN, QL$$ and $$RM$$ are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)
A
$$16$$
B
$$18$$
C
$$24$$
D
$$22$$
3

### IIT-JEE 2006

MCQ (More than One Correct Answer)
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
4

### IIT-JEE 1987

MCQ (More than One Correct Answer)
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
$$5 + \sqrt 6$$

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