Properties of Triangle Test

Result

Properties of Triangle Test - 4

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Weekly Quiz Competition

Question 1
4 / -1

In a triangle, the lengths of two larger sides are 10 cm and 9 cm. If the angles of the triangle are in AP, then the length of the third side is

A
√5 - √6

B
√5 + √6

C
√5 ± √6

D
5 ± √6
Question 2
4 / -1

If the bisector of the angle P of a triangle PQR meets QR in S, then

A
QS = SR

B
QS : SR = PR : PQ

C
QS : SR = PQ : PR

D
None of these

Solution
Question 3
4 / -1

In a ∆ABC, a,b, c are the sides of the triangle opposite to the angles A, B, C, respectively. Then, the value of a³ sin (B - C) + b³ (C - A) + c³ (A - B) is

A
0

B
1

C
3

D
2

Solution
Question 4
4 / -1

A
sin² B

B
cos² A

C
cos² B

D
sin² A

Solution
Question 5
4 / -1

If the angles of a triangle are in the ratio 1 : 1 : 4, then the ratio of the perimeter of the triangle to its largest side is

A
√2 + 2 : √3

B
3 : 2

C
√3 + 2 : √2

D
√3 + 2 : √3

Solution
Question 6
4 / -1

Angles A, B, C of a ∆ABC are in AP and b : c = √3 : √2, then ∠A is given by

A
45^o

B
60^o

C
75^o

D
90^o
Question 7
4 / -1

If in a ∆ABC, a tan A + b tan B = (a + b) tan (A + B)/2 , then

A
A = B = C

B
C = A

C
A = B

D
B = C

Solution
Question 8
4 / -1

a³ cos (B - C) + b³ cos (C - A) + c³ cos (A - B) is equal to

A
3abc

B
3 (a + b + c)

C
abc (a + b + c)

D
0
Question 9
4 / -1

If in a ∆ABC , a/ cos A = b/ cos B, then

A
sin² A + sin² B = sin² C

B
2 sin A cos B = sin C

C
2 sin A sin B sin C = 1

D
None of the above

Solution
Question 10
4 / -1

If A + B + C = 180^o

A
1

B
cot A cos B cot C

C
- 1

D
0