JEE Questions for Maths Properties Of Triangle Quiz 3 - MCQExams.com

In a ∆ABC, 2a2 + 4b2 + c2 = 4ab + 2ac , then cos B is
  • 0
  • 1/8
  • 3/8
  • 7/8
In a ∆ABC, if sin2 A/2, sin2 B/2 and sin2 C/2 are in HP. Then, a, b and c will be in
  • AP
  • GP
  • HP
  • None of these

Maths-Properties of Triangle-46463.png

  • Maths-Properties of Triangle-46464.png
  • 2)
    Maths-Properties of Triangle-46465.png

  • Maths-Properties of Triangle-46466.png

  • Maths-Properties of Triangle-46467.png
In ∆ABC, (a - b)2 cos2 C/2 + (a + b)2 sin2 C/2 is equal to
  • a2
  • b2
  • c2
  • None of these
If in a ∆ABC, 2b2 = a2 + c2, then (sin 3B/ sin B) is equal to

  • Maths-Properties of Triangle-46468.png
  • 2)
    Maths-Properties of Triangle-46469.png

  • Maths-Properties of Triangle-46470.png

  • Maths-Properties of Triangle-46471.png
In a ∆ABC , if (√3 - 1)a = 2b, A = 3B, then ∠C is equal to
  • 60o
  • 120o
  • 30o
  • 45o
If in a ∆ABC, 4 sin A = 4 sin B = 3 sin C, the cos C is equal to
  • 1/3
  • 1/9
  • 1/27
  • 1/18
In ∆ABC, if cot A, cot B and cot C are in AP, then a2 , b2 and c2 are in
  • HP
  • GP
  • AP
  • None of these
In a ∆ABC , (b + c) (bc) cos A + (a + c) (ac) cos B + (a + b)(ab) cos C is equal to
  • a2 + b2 + c2
  • a3 + b3 + c3
  • (a + b + c) (a2 + b2 + c2)
  • (a + b + c) (ab + bc + ca)
  • abc
If in ∆ABC, sin A/2 sin C/2 = sin B/2 and 2s is the perimeter of the triangle, then s is equal to
  • 2b
  • b
  • 3b
  • 4b
  • 3b/2
In a ∆ABC, if tan A/2 = 5/6, tan C/2 = 2/5, then
  • a, c and b are in AP
  • a, b and c are in GP
  • b, a and c are in AP
  • a, b and c are in AP
  • a, c and b are in GP
The sides of triangle are in the ratio 1 : √3 : 2, then the angles of the triangle are in ratio
  • 1 : 3 : 5
  • 2 : 3 : 1
  • 3 : 2 : 1
  • 1 : 2 : 3
Points D, and E are taken on the side BC of the ∆ABC, such that BD = DE = EC. If ∠BAD = x, ∠DAE = y and ∠EAC = z, then the value of
Maths-Properties of Triangle-46472.png
  • 1
  • 2
  • 4
  • None of these
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

  • Maths-Properties of Triangle-46473.png
  • 2)
    Maths-Properties of Triangle-46474.png

  • Maths-Properties of Triangle-46475.png

  • Maths-Properties of Triangle-46476.png
In a ∆ABC, a, c, A are given and b1, b2 are two values of the third side b such that b2 = 2b1, then sin A is equal to

  • Maths-Properties of Triangle-46477.png
  • 2)
    Maths-Properties of Triangle-46478.png

  • Maths-Properties of Triangle-46479.png
  • None of these
In a ∆ABC, if the sides are a = 3, b = 5 and c = 4, then sin B/2 + cos B/2 is equal to
  • √2
  • 2)
    Maths-Properties of Triangle-46480.png

  • Maths-Properties of Triangle-46481.png
  • 1
If in the ∆ABC, ∠B = 45o, then a4 + b4 + c4 is equal to
  • 2a2 (b2 + c2)
  • 2c2 (a2 + b2)
  • 2b2 (a2 + c2)
  • 2(a2b2 + b2c2 + c2a2)
  • 2a2b2 + 2b2c2 + 2a2c2
In a ∆ABC, among the following which one is correct ?

  • Maths-Properties of Triangle-46482.png
  • 2)
    Maths-Properties of Triangle-46483.png

  • Maths-Properties of Triangle-46484.png

  • Maths-Properties of Triangle-46485.png
If in a ∆ABC, the altitudes from the vertices A, B, C on opposite side are in HP, then sin A, sin B and sin C are in
  • HP
  • Arithmetico - Geometric Progression
  • AP
  • GP
If the sides of the triangles are p, q, √(P2 + q2 + pq) , then the greatest angle is
  • π/2
  • 5π/4
  • 2π/3
  • 7π/4
  • 5π/3
In a ∆PQR, P is the largest angle and cos P = 1/3, Further in circle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers, Then, possible length(s) of the side (s) of the triangle is (are)
  • 16
  • 18
  • 24
  • 22
The area of a circle and the area of a regular polygon of n sides of the perimeter equal to that of that circle are in the ratio
  • tan π/n : π/n
  • cos π/n : π/n
  • sin π/n : π/n
  • cot π/n : π/n
If A, A1, A2 and A3 and the areas of the incricle and excricles, then 1/√A1 + 1/√A2 + 1/√A3 is equal to
  • 1/√A
  • 2/√A
  • 3/√A
  • 4/√A

Maths-Properties of Triangle-46486.png
  • 0
  • 2)
    Maths-Properties of Triangle-46487.png

  • Maths-Properties of Triangle-46488.png

  • Maths-Properties of Triangle-46489.png
In a triangle, if r1 = 2r2 = 3r3, then a/b + b/c + c/a is equal to
  • 75/60
  • 155/60
  • 176/60
  • 191/60
In a ∆ABC, a : b : c = 4 : 5 : 6. The ratio of the radius of the circumcircle to that of the incircle is
  • 15/4
  • 11/5
  • 16/7
  • 16/3
In radius of a circle which is inscribed in an isosceles triangle one of whose angle is 2π/ 3 , is √3, then area of triangle is
  • 4√3
  • 12 - 7√3
  • 12 + 7√3
  • None of these
The circumradius of the triangle whose sides are 13, 12 and 5 is
  • 15
  • 13/2
  • 15/2
  • 6
If p1, p2, p3 are respectively the perpendiculars from the vertices of a triangle to the opposite side, then p1, p2, p3 is equal to
  • a2b2c2
  • 2 a2b2c2
  • 4 a2b2c3 / R2
  • a2b2c2/ 8R3
In a ∆ABC, let ∠C = π/2, if r is the inradius and R is the circumraidus of the ∆ABC, then 2 (r + R) equals
  • c + a
  • a + b + c
  • a + b
  • b + c
0:0:1


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