Practice question on triangle for IIT-JEE , NDA and Airforce 16-30 (Set 2 )

Triangle

---

Question no. 16

If cos²A + cos²C = sin²B , then ∆ABC is

looks_one equilateral

looks_two right angled triangle

looks_3 isosceles

looks_4 none of these

Option looks_two right angled triangle

Solution :
let B = 90^o
A + C = 90^o
cos²A = cos²(90⁰ - C) = sin²C
cos²A + cos²C = sin²C + cos²C = 1
sin²B = sin²90^o = 1
Therefore , ∆ABC is right angled triangle

Question no. 17

If in a triangle ∆ABC , C = 60° , then =

looks_one 1/(a+b+c)

looks_two 2/(a+b+c)

looks_3 3/(a+b+c)

looks_4 none of these

option looks_3 3/(a+b+c)

ver soon 2

Question no. 18

In ABC , if tanA/2 tanC/2 = 1/2 , then a,b, c are in

looks_one A.P.

looks_two G.P.

looks_3 H.P.

looks_4 none of these

Option looks_4 none of these

Solution :

Question no. 19

In triangle ABC , if a,b ,c are in AP, then the value of =

looks_one 1

looks_two 2

looks_3 1/2

looks_4 -1

option looks_3 1/2

Solution :
a, b , c are in A.P. , therefore a+c = 2b

Question no. 20

In ABC , if a = 3 , b= 4 , c= 5 then sin2B=

looks_one 4/5

looks_two 3/20

looks_3 24/25

looks_4 1/50

Option looks_3 24/25

Solution :
3,4,5 are the pythogoras tripets , therefore
sinB = 4/5
cosB = 3/5
sin2B = 2sinBcosB = 2*4*3/5*5 = 24/25

Question no. 21

If the length of the sides of a triangle be 7, 4√3 and √13 cm, then the smallest angle is

looks_one 15^o

looks_two 30^o

looks_3 45^o

looks_4 60^o

option looks_two 30^o

Solution :
Smallest angle will be opposite to the smallest side , √13 is the smallest side

Question no. 22

In a ABC , if C = 30° , a = 47 cm and b = 94 cm, then the triangle is

looks_oneright angled triangle

looks_two right angled isosceles

looks_3 isosceles

looks_4 obtuse angled

option looks_4 obtuse angled

Solution :
C = 30^o a = 47 , b = 94

Question no. 23

In ∆ABC , side b is equal to

looks_one ccosA +acosC

looks_two acosB + bcosA

looks_3 bcosC + ccosB

looks_4 none of these

option looks_one b = ccosA +acosC

Solution :
ccosA +acosC

Question no. 24

In ABC , a²( cos²B - cos²C) + b²(cos²C- cos²A) + c²( cos²A - cos²B) =

looks_one 0

looks_two 1

looks_3 a² + b² + c²

looks_4 2(a² + b² + c²)

Option looks_one 0

Solution :
a²( cos²B - cos²C) + b²(cos²C- cos²A) + c²( cos²A - cos²B)
= (a² - c² )cos²B + (b² - a² )cos²C + (c² - b² )cos²A
= (a² - c² )( 1 -sin²B) + (b² - a² )(1 -sin²C) + (c² - b² )(1 -sin²A)
= (a² - c² + b² - a² + c² - b² ) - [(a² - c² )sin²B + (b² - a² )sin²C + (c² - b² )sin²A ]
= - [(a² - c² )sin²B + (b² - a² )sin²C + (c² - b² )sin²A ]
= - [(a² - c² )Kb² + (b² - a² )Kc² + (c² - b² )Ka² ]
= - K[b²a² - b²c² + c²b² - a²c² + a²c² - a² b² ]
= 0

Question no. 25

In triangle ∆ABC, =

looks_one (a-b)/(a-c)

looks_two (a+b)/(a+c)

looks_3 (a²-b²)/(a²-c²)

looks_4 (a² + b²)/(a² + c²)

Option looks_4 (a² + b²)/(a² + c²)

Solution :

Question no. 26

In ∆ABC , =

looks_one (b-c)/a

looks_two (b+c)/a

looks_3 a/(b+c)

looks_4 a/(b-c)

Option looks_two (b+c)/a

Solution :

Question no. 27

In ∆ABC ,( b²- c²)cotA + (c²- a²)cotB + (a²- b²)cotC =

looks_one 0

looks_two 2(a² + b² + c²)

looks_3 a² + b² + c²

looks_4 1/2abc

Option looks_one 0

Solution :

Question no. 28

If in ∆ABC , 2b²= a²+ c² , then =

looks_one

looks_two

looks_3

looks_4

Option looks_4

Solution :

Question no. 29

If the angles of a triangle are in the ratio 1:2:3 , then their corresponding sides are in the ratio

looks_one 1:2:3

looks_two 1:√3 :2

looks_3 √2 : √3 : 3

looks_4 1: √3 : 3

Option looks_two 1:√3 :2

Solution :
∠A = x
∠B = 2x
∠C = 3x
x + 2x + 3x = 180^o
x = 30⁰
∠A = 30⁰ , ∠B = 60⁰ , ∠C = 90⁰
a = λsin30⁰ = λ/2
b = λsin60⁰ = √3λ/2
c = λsin90⁰ = λ
a : b : c = λ/2 : √3λ/2 : λ
a : b : c = 1:√3 :2

Question no. 30

In a triangle ABC , b= √3 cm , c= 1 cm , ∠A= 30° , what is the value of a?

looks_one 2

looks_two 1

looks_3 1/2

looks_4 none of these

Option looks_two 1

Solution :
b= √3 cm
c= 1 cm
∠A= 30°

Previous Next