JEE Questions for Maths Properties Of Triangle Quiz 1 - MCQExams.com

In any ∆ABC, c2 sin 2B + b2 sin 2C is equal to
  • ∆/2
  • ∆
  • 2∆
  • 3∆
  • 4∆
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
  • √5 - √6
  • √5 + √6
  • √5 ± √6
  • 5 ± √6
If the bisector of the angle P of a triangle PQR meets QR in S, then
  • QS = SR
  • QS : SR = PR : PQ
  • QS : SR = PQ : PR
  • None of these
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
  • 0
  • 1
  • 3
  • 2

Maths-Properties of Triangle-46407.png
  • sin2 B
  • cos2 A
  • cos2 B
  • sin2 A
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
  • √2 + 2 : √3
  • 3 : 2
  • √3 + 2 : √2
  • √3 + 2 : √3
Angles A, B, C of a ∆ABC are in AP and b : c = √3 : √2, then ∠A is given by
  • 45o
  • 60o
  • 75o
  • 90o
If in a ∆ABC, a tan A + b tan B = (a + b) tan (A + B)/2 , then
  • A = B = C
  • C = A
  • A = B
  • B = C
a3 cos (B - C) + b3 cos (C - A) + c3 cos (A - B) is equal to
  • 3abc
  • 3 (a + b + c)
  • abc (a + b + c)
  • 0
If in a ∆ABC , a/ cos A = b/ cos B, then
  • sin2 A + sin2 B = sin2 C
  • 2 sin A cos B = sin C
  • 2 sin A sin B sin C = 1
  • None of the above
If A + B + C = 180o
Maths-Properties of Triangle-46412.png
  • 1
  • cot A cos B cot C
  • - 1
  • 0
The base BC of a ∆ABC is 6 cm and ∠B = 11 5o , ∠C = 2 5o, then its altitude is
  • 1.2cm
  • 6 cm
  • 1. 5 cm
  • 3 cm

Maths-Properties of Triangle-46413.png
  • a2 - b2
  • 2)
    Maths-Properties of Triangle-46414.png

  • Maths-Properties of Triangle-46415.png
  • a2 + b2
If in a ∆ABC, sin A, sin B, and sin C are in AP, then
  • the radius are in AP
  • the altitudes are in HP
  • the angles are in AP
  • the angles are in HP

Maths-Properties of Triangle-46417.png

  • Maths-Properties of Triangle-46418.png
  • 2)
    Maths-Properties of Triangle-46419.png

  • Maths-Properties of Triangle-46420.png

  • Maths-Properties of Triangle-46421.png
In a ∆ABC, a = 8 cm, h = 10 cm, c = 12 cm Then, relation between angles of the triangle is
  • C = A + B
  • C = 2B
  • c = 2A
  • c = 3A
If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A,B and C respectively, then the value of the expression (a/c) sin 2C + (c/a) sin 2A is
  • 1/2
  • √3/2
  • 1
  • √3
If the sides of a right angled triangle from an AP, then the 'sin' of the acute angles are

  • Maths-Properties of Triangle-46423.png
  • 2)
    Maths-Properties of Triangle-46424.png

  • Maths-Properties of Triangle-46425.png

  • Maths-Properties of Triangle-46426.png
The sides of a triangle are respectively 7 cm, 4√3 cm and √13 cm, then the smallest angle of triangle is
  • π/6
  • π/3
  • π/4
  • π/5
The area (in sq units) of the triangle whose sides are 6, 5, √13, is
  • 5√2
  • 9
  • 6√2
  • 11
  • 13

Maths-Properties of Triangle-46427.png
  • 1/24
  • √3/24
  • 1/8
  • 1/√3
  • 5/12√3

Maths-Properties of Triangle-46429.png
  • 90o
  • 60o
  • 45o
  • 30o

Maths-Properties of Triangle-46430.png
  • Both I and II are correct
  • I is correct, II is incorrect
  • I is incorrect , II is correct
  • Both I and II are incorrect
If in a ∆ABC , a = 6 cm , b = 8 cm , c = 10 cm, then the value of sin 2A is
  • 6/25
  • 8/25
  • 10/25
  • 24/25
If two angles of ∆ABC are 45o and 60o, then the ratio of the smallest and the greatest sides are
  • (√3 -: 1
  • √3 : √2
  • 1 : √3
  • √3 : 1

Maths-Properties of Triangle-46432.png

  • Maths-Properties of Triangle-46433.png
  • 2)
    Maths-Properties of Triangle-46434.png

  • Maths-Properties of Triangle-46435.png

  • Maths-Properties of Triangle-46436.png

Maths-Properties of Triangle-46437.png
  • 1/5
  • 5/7
  • 19/35
  • None of these
In ∆ABC, if (a + b + c) (a - b + c) = 3ac, then
  • ∠B = 60o
  • ∠B = 30o
  • ∠C = 60o
  • ∠A + ∠C = 90o
If in a ∆ ABC, a = 15, b = 36, c = 39, then sin C/2 is equal to
  • √3/2
  • 1/2
  • 1/√2
  • - (1/√2)
  • - (1/2)
In a ∆ABC, if b + c = 2a and ∠A = 60o, then ∆ABC is
  • equilateral
  • right angled
  • isosceles
  • scalene
0:0:1


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