IIT-JEE 2005 Screening | Properties of Triangle Question 19 | Mathematics

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.5

In a triangle $$ABC$$, $$a,b,c$$ are the lengths of its sides and $$A,B,C$$ are the angles of triangle $$ABC$$. The correct relation is given by

$$\left( {b - c} \right)\sin \left( {{{B - C} \over 2}} \right) = a\cos {A \over 2}$$

$$\left( {b - c} \right)cos\left( {{A \over 2}} \right) = a\,sin{{B - C} \over 2}$$

$$\left( {b + c} \right)\sin \left( {{{B + C} \over 2}} \right) = a\cos {A \over 2}$$

$$\left( {b - c} \right)cos\left( {{A \over 2}} \right) = 2a\,sin{{B + C} \over 2}$$

IIT-JEE 2005

MCQ (Single Correct Answer)

-0.5

In an equilateral triangle, $$3$$ coins of radii $$1$$ unit each are kept so that they touch each other and also the sides of the triangle. Area of the triangle is IIT-JEE 2005 Mathematics - Properties of Triangle Question 8 English

IIT-JEE 2005 Mathematics - Properties of Triangle Question 8 English

$$4 + 2\sqrt 3 $$

$$6 + 4\sqrt 3 $$

$$12 + {{7\sqrt 3 } \over 4}$$

$$3 + {{7\sqrt 3 } \over 4}$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

The sides of a triangle are in the ratio $$1:\sqrt 3 :2$$, then the angles of the triangle are in the ratio

$$1:3:5$$

$$2:3:4$$

$$3:2:1$$

$$1:2:3$$

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

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

$$1:6$$

$$1:2 + \sqrt 3 $$

$$2:3$$

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