1
IIT-JEE 2003 Screening
+2
-0.5
If the angles of a triangle are in the ratio $$4:1:1$$, then the ratio of the longest side to the perimeter is
A
$$\sqrt 3 :\left( {2 + \sqrt 3 } \right)$$
B
$$1:6$$
C
$$1:2 + \sqrt 3$$
D
$$2:3$$
2
IIT-JEE 2002 Screening
+2
-0.5
Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $$ABC$$ ($$R$$ being the radius of the circumcircle)?
A
$$a,\,\sin \,A,sin\,B$$
B
$$a,b,c$$
C
$$a,\,\sin \,B,R$$
D
$$a,\,\sin \,A,R$$
3
IIT-JEE 2001 Screening
+2
-0.5
A man from the top of a $$100$$ metres high tower sees a car moving towards the tower at an angle of depression of $${30^ \circ }$$. After some time,the angle of depression becomes $${60^ \circ }$$. The distance (in metres) travelled by the car during this time is
A
$$100\sqrt 3$$
B
$$200\sqrt 3 /3$$
C
$$100\sqrt 3 /3$$
D
$$200\sqrt 3$$
4
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
$${c^2} - {a^2} - {b^2}$$
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