Practice question on triangle for IIT-jee , NDA and Airforce (Set 1 )

triangle

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Question no. 1

∆ABC is a triangle in which AB = 6 cm , BC = 8 cm and CA - 10 cm. What in the value of cot(A/4)?

looks_one √5-2

looks_two √5 + 2

looks_3 √3+1

looks_4 √3-1

Option looks_two √5 + 2

Solution :

Question no. 2

If the sides of a triangle are 6 cm, 10 cm and 14 cm, then what is the largest angle included by the sides?

looks_one 90^o

looks_two 120^o

looks_3 135^o

looks_4 150^o

Option looks_two 120^o

ver soon 2

Question no. 3

For finding the area of a triangle ABC, which of the following entities are required?

looks_one Angles A, B and side a

looks_two Angles A, B and side b

looks_3 Angles A, B and side c

looks_4 Either (a) or (b) or (c)

Option looks_4 Either (a) or (b) or (c)

very soon 3

Question no. 4

If in a ∆ABC, cos B= (sin A)/(2 sin C), then the triangle is

looks_one Isosceles triangle

looks_two Equilateral triangle

looks_3 Right angled triangle

looks_4 Scalene triangle

Option looks_one Isosceles triangle

very soon 4

Question no. 5

In a ∆ABC, a + b = 3 (1 + √3) cm and a-b=3(1-√3) cm. If angle A is 30°, then what is the angle B ?

looks_one 120°

looks_two 60°

looks_3 75°

looks_4 90°

Option looks_two 60°

Solution :
a+b = 3 + 3√3
a - b = 3 - 3√3
a = 3
b = 3√3

Question no. 6

∆ABC is a triangle in which BC=10 cm, CA =6 cm and AB = 8 cm. Which one of the following in correct?

looks_one ABC is an acute angled triangle

looks_two ABC is an obtuse angled triangle

looks_3 ABC is a right angled triangle

looks_4 None of these

Option looks_3 ABC is a right angled triangle

Solution :
BC = 10 cm
CA = 6 cm
AB = 8 cm
(BC)² = (CA)² + (AB)²
100 = 36 + 64 =100
It satisfy the pythogoras theorem

Question no. 7

In a ABC, if c= 2, ∠A= 120°,a = √6, then what is ∠C equal to ?

looks_one 30°

looks_two 60°

looks_3 45°

looks_4 75°

option looks_3 45°

Solution :

Question no. 8

If the angles of a triangle ∆ABC be in A.P. , then

looks_one c² = a² + b² -ab

looks_two b² = a² + c² -ac

looks_3 a² = c² + b² -ac

looks_4 none of these

Option looks_two b² = a² + c² -ac

Solution :
a' - d' = A
a' = B
a' + d' = C
a' - d' + a' + a' + d' = 180^o
3a' = 180⁰
a' = 60^o
B = 60^o
cosB = (a² + c² -b²)/2ac
1/2 = (a² + c² -b²)/2ac
ac = a² + c² -b²
b² = a² + c² -ac

Question no. 9

In ∆ABC , sinB/sin(A+B) =

looks_one b/(a+b)

looks_two b/c

looks_3 c/b

looks_4 none of these

Option looks_two b/c

Solution :

Question no. 10

In a ∆ABC , if b² + c² = 3a² , then cotB + cotC - cotA =

looks_one 1

looks_two 0

looks_3 ab/4∆

looks_4 ac/4∆

Option looks_two 0

Solution :
b² + c² = 3a²

Question no. 11

In a ∆ABC , if c² + a² -b² = ac , then ∠B =

looks_one 60^o

looks_two 45^o

looks_3 30^o

looks_4 none of these

option looks_one 60^o

very soon 11

Question no. 12

In a ∆ABC , if sin²A/2 , sin²B/2, sin²C/2 be in H. P. then a, b , c will be in

looks_one A.P.

looks_two G.P.

looks_3 H.P.

looks_4 none of these

option

very soon 12

Question no. 13

In ∆ABC , b²cos2A - a²cos2B =

looks_one b²-a²

looks_two b²-c²

looks_3 c²-a²

looks_4 a² +b² + c²

option

very son 13

Question no. 14

In ∆ABC , asin(B-C) + bsin(C-A) + csin(A-B) =

looks_one 0

looks_two a + b + c

looks_3 a² + b² + c²

looks_4 none of these

option looks_3 a² + b² + c²

very soon14

Question no. 15

In ∆ABC, if 2( (bc)cosA + (ca)cosB + (ab)cosC) =

looks_one 0

looks_two a + b + c

looks_3 a² + b² + c²

looks_4 none of these

Option looks_3 a² + b² + c²

Solution :
2 bc cosA = b² + c² - a²
2 ca cosB = c² + a² - b²
2 ab cosC = a² + b² - c²
2( (bc)cosA + (ca)cosB + (ab)cosC) = b² + c² - a² + c² + a² - b² + a² + b² - c² = a² + b² + c²

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