1
IIT-JEE 2000 Screening
+2
-0.5
In a triangle $$ABC$$, $$2ac\,\sin {1 \over 2}\left( {A - B + C} \right) =$$
A
$${a^2} + {b^2} - {c^2}$$
B
$${c^2} + {a^2} - {b^2}$$
C
$${b^2} - {c^2} - {a^2}$$
D
$${c^2} - {a^2} - {b^2}$$
2
IIT-JEE 2000 Screening
+2
-0.5
In a triangle $$ABC$$, let $$\angle C = {\pi \over 2}$$. If $$r$$ is the inradius and $$R$$ is the circumradius of the triangle, then $$2(r+R)$$ is equal to
A
$$a+b$$
B
$$b+c$$
C
$$c+a$$
D
$$a+b+c$$
3
IIT-JEE 2000 Screening
+2
-0.5
A pole stands vertically inside a triangular park $$\Delta ABC$$. If the angle of elevation of the top of the pole from each corner of the park is same, then in $$\Delta ABC$$ the foot of the pole is at the
A
centroid
B
circumcentre
C
incentre
D
orthocentre
4
IIT-JEE 1998
+2
-0.5
If in a triangle $$PQR$$, $$\sin P,\sin Q,\sin R$$ are in $$A.P.,$$ then
A
the altitudes are in $$A.P.$$
B
the altitudes are in $$H.P.$$
C
the medians are in $$G.P.$$
D
the medians are in $$A.P$$
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