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JEE Questions for Maths Properties Of Triangle Quiz 3 - MCQExams.com
JEE
Maths
Properties Of Triangle
Quiz 3
In a ∆ABC, 2a
2
+ 4b
2
+ c
2
= 4ab + 2ac , then cos B is
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0%
0
0%
1/8
0%
3/8
0%
7/8
In a ∆ABC, if sin
2
A/2, sin
2
B/2 and sin
2
C/2 are in HP. Then, a, b and c will be in
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0%
AP
0%
GP
0%
HP
0%
None of these
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0%
0%
2)
0%
0%
In ∆ABC, (a - b)
2
cos
2
C/2 + (a + b)
2
sin
2
C/2 is equal to
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0%
a2
0%
b2
0%
c2
0%
None of these
If in a ∆ABC, 2b
2
= a
2
+ c
2
, then (sin 3B/ sin B) is equal to
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0%
0%
2)
0%
0%
In a ∆ABC , if (√3 - 1)a = 2b, A = 3B, then ∠C is equal to
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0%
60o
0%
120o
0%
30o
0%
45o
If in a ∆ABC, 4 sin A = 4 sin B = 3 sin C, the cos C is equal to
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0%
1/3
0%
1/9
0%
1/27
0%
1/18
In ∆ABC, if cot A, cot B and cot C are in AP, then a
2
, b
2
and c
2
are in
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0%
HP
0%
GP
0%
AP
0%
None of these
In a ∆ABC , (b + c) (bc) cos A + (a + c) (ac) cos B + (a + b)(ab) cos C is equal to
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0%
a2 + b2 + c2
0%
a3 + b3 + c3
0%
(a + b + c) (a2 + b2 + c2)
0%
(a + b + c) (ab + bc + ca)
0%
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
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0%
2b
0%
b
0%
3b
0%
4b
0%
3b/2
In a ∆ABC, if tan A/2 = 5/6, tan C/2 = 2/5, then
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0%
a, c and b are in AP
0%
a, b and c are in GP
0%
b, a and c are in AP
0%
a, b and c are in AP
0%
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
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0%
1 : 3 : 5
0%
2 : 3 : 1
0%
3 : 2 : 1
0%
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
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0%
1
0%
2
0%
4
0%
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
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0%
0%
2)
0%
0%
In a ∆ABC, a, c, A are given and b
1
, b
2
are two values of the third side b such that b
2
= 2b
1
, then sin A is equal to
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0%
0%
2)
0%
0%
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
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0%
√2
0%
2)
0%
0%
1
If in the ∆ABC, ∠B = 45
o
, then a
4
+ b
4
+ c
4
is equal to
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0%
2a2 (b2 + c2)
0%
2c2 (a2 + b2)
0%
2b2 (a2 + c2)
0%
2(a2b2 + b2c2 + c2a2)
0%
2a2b2 + 2b2c2 + 2a2c2
In a ∆ABC, among the following which one is correct ?
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0%
0%
2)
0%
0%
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
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0%
HP
0%
Arithmetico - Geometric Progression
0%
AP
0%
GP
If the sides of the triangles are p, q, √(P
2
+ q
2
+ pq) , then the greatest angle is
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0%
π/2
0%
5π/4
0%
2π/3
0%
7π/4
0%
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)
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0%
16
0%
18
0%
24
0%
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
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0%
tan π/n : π/n
0%
cos π/n : π/n
0%
sin π/n : π/n
0%
cot π/n : π/n
If A, A
1
, A
2
and A
3
and the areas of the incricle and excricles, then 1/√A
1
+ 1/√A
2
+ 1/√A
3
is equal to
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0%
1/√A
0%
2/√A
0%
3/√A
0%
4/√A
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0%
0
0%
2)
0%
0%
In a triangle, if r
1
= 2r
2
= 3r
3
, then a/b + b/c + c/a is equal to
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0%
75/60
0%
155/60
0%
176/60
0%
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
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0%
15/4
0%
11/5
0%
16/7
0%
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
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0%
4√3
0%
12 - 7√3
0%
12 + 7√3
0%
None of these
The circumradius of the triangle whose sides are 13, 12 and 5 is
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0%
15
0%
13/2
0%
15/2
0%
6
If p
1
, p
2
, p
3
are respectively the perpendiculars from the vertices of a triangle to the opposite side, then p
1
, p
2
, p
3
is equal to
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0%
a2b2c2
0%
2 a2b2c2
0%
4 a2b2c3 / R2
0%
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
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0%
c + a
0%
a + b + c
0%
a + b
0%
b + c
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