1

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
$$a+b+c$$
2

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
$${c^2} - {a^2} - {b^2}$$
3

IIT-JEE 1998

MCQ (Single Correct Answer)
Let $${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments $${A_0}{A_1},{A_0}{A_2}$$ and $${A_0}{A_4}$$ is
A
$${3 \over 4}$$
B
$$3\sqrt 3 $$
C
$$3$$
D
$${{3\sqrt 3 } \over 2}$$
4

IIT-JEE 1998

MCQ (Single Correct Answer)
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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