IIT-JEE 2003 Screening | Properties of Triangle Question 22 | Mathematics

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IIT-JEE 2003 Screening

MCQ (Single Correct Answer)

-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

$$\sqrt 3 :\left( {2 + \sqrt 3 } \right)$$

$$1:6$$

$$1:2 + \sqrt 3 $$

$$2:3$$

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)

-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)?

$$a,\,\sin \,A,sin\,B$$

$$a,b,c$$

$$a,\,\sin \,B,R$$

$$a,\,\sin \,A,R$$

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)

-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

$$100\sqrt 3 $$

$$200\sqrt 3 /3$$

$$100\sqrt 3 /3$$

$$200\sqrt 3 $$

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)

-0.5

In a triangle $$ABC$$, $$2ac\,\sin {1 \over 2}\left( {A - B + C} \right) = $$

$${a^2} + {b^2} - {c^2}$$

$${c^2} + {a^2} - {b^2}$$

$${b^2} - {c^2} - {a^2}$$

$${c^2} - {a^2} - {b^2}$$