TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 25

EASY

Mathematics

IMPORTANT

Earn 100

The sum of the squares of the sides of a triangle $ABC$ is two times the square of the diameter of the circumcircle, then

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Important Questions on Properties of Triangles

EASY

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 26

In a triangle

ABC

if

a^{4} + b^{4} + c^{4} = 2 c^{2} (a^{2} + b^{2})

, then angle

C

is equal to

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 1

In a triangle

A B C

, the sides

b

and

c

are the roots of the equation

x^{2} - 61 x + 820 = 0

and

A = \tan^{- 1} (\frac{4}{3})

, then

a^{2} + 3

is equal to...

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 2

A B C D

is a trapezium such that

A B

and

C D

are parallel and

C B

is perpendicular to them. If

∠ A D B = θ, B C = 45, C D = 30

and

\tan θ = \frac{1}{5}

, then

51 A B + 15

is equal to...

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 3

In a triangle

A B C; A = \frac{π}{3}, b = 50, c = 30, A D

is a median through

A

, then

A D^{2}

is equal to...

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 4

If in a triangle

A B C, \frac{s - a}{11} = \frac{s - b}{12} = \frac{s - c}{13}

. Then

429 \cot^{2} \frac{A}{2}

is equal to...

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 5

If in a triangle

A B C, R r (\sin A + \sin B + \sin C) = 96

, then the area of the triangle

A B C

is...

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 6

If in a triangle

A B C, a

is the arithmetic mean and

b, c

are the geometric means between any two positive real numbers,

k = \frac{b + c}{a} [\frac{\sin B}{\sin C} + \frac{\sin C}{\sin B} - 1]

, then

90 k^{3} + 87 k^{2} + 30 k

is equal to...

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 11 - Properties of Triangles>EXERCISE>Q 7

The sides of a quadrilateral are

3, 4, 5

and

6 cms

. The sum of a pair of opposite angles is

120 °

. Then

5 \sqrt{30}

times the area of the quadrilateral is...