right angled with A = 90°, B = 60°, C = 30°

JEE Questions for Maths Properties Of Triangle Quiz 4

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. An incorrect statement among the following is

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there is a regular polygon with r/R = 1/2
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there is a regular polygon with r/R = 1/√2
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there is a regular polygon with r/R = 2/3
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there is a regular polygon with r/R = √3/2

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2)
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sin 2C
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sin B + sin C
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sin C
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sin A + sin B

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2)
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cos B sin A
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cos A cos C
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cos A sin B
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sin B sin C

If in a triangle ABC, the line joining the circumcentre O and the incentre I is parallel to BC, then

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r = R cos A
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r = R sin A
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R = r cos A
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R = r sin A

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2)
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30°
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60°
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45°
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75°

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2)
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In a triangle ABC, the median AD is perpendicular to AC. If b = 5 and c = 11, then a is equal to

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10
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12
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14
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60°
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90°
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120°
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135°

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2)
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none of these

If α β, are the acute angles of an obtuse angled triangle, then tan α tan β is

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< 1
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> 1
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= 1
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none of these

If R and r are the radii of the circumcircle and incircle of a regular polygon of n sides, each side being of length a, then a is equal to

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2)
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none of these

In a triangle ABC, if c = (a - b) sec θ, then tan θ is equal to

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2)
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If the angles of a triangle are in the ratio 1 : 3 : 5 and θ denotes the smallest angle, then the ratio of the largest side to the smallest side of the triangle is

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2)
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In a cyclic quadrilateral ABCD; a, b, c, d denote the length of the sides AB, BC,CD and DA respectively. Then cos A is equal to

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2)
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The angles of a triangle ABC are in A.P. The largest is twice the smallest and the median to the largest side divides the angle at the vertex in the ratio 2 : 3. If the length of the median is 2√3 cm, then the length of the largest side is