Description

This mock test of Competition Level Test: Solution Of Triangles- 3 for JEE helps you for every JEE entrance exam.
This contains 27 Multiple Choice Questions for JEE Competition Level Test: Solution Of Triangles- 3 (mcq) to study with solutions a complete question bank.
The solved questions answers in this Competition Level Test: Solution Of Triangles- 3 quiz give you a good mix of easy questions and tough questions. JEE
students definitely take this Competition Level Test: Solution Of Triangles- 3 exercise for a better result in the exam. You can find other Competition Level Test: Solution Of Triangles- 3 extra questions,
long questions & short questions for JEE on EduRev as well by searching above.

QUESTION: 1

AA_{1}, BB_{1} and CC_{1} are the medians of triangle ABC whose centroid is G. If points A, C_{1}, G and B_{1} are concyclic, then

Solution:

AA_{1}, BB_{1} and CC_{1} are the medians of triangle ABC whose centroid is G.

Since A, C_{1}, G and B_{1} are concyclic, then

BG⋅BB_{1} = BC_{1}⋅BA

2/3 ( BB_{1})^{2} = (c/2).c

(2/3).(1/4).(2a^{2} + 2c^{2} - b^{2}) = c^{2}/2

2a^{2} + 2c^{2} - b^{2} = 3c^{2}

b^{2} + c^{2} = 2a^{2}

QUESTION: 2

If l is the median from the vertex A to the side BC of a ΔABC, then

Solution:

QUESTION: 3

In a ΔABC, a = 1 and the perimeter is six times the A.M. of the sines of the angles. Then measure of ∠A is

Solution:

QUESTION: 4

If the median AD of a triangle ABC divides the angle ∠BAC in the ratio 1 : 2, then is equal to

Solution:

QUESTION: 5

In a triangle ABC, let ∠C = π/2, if r is the inradius and R is the circumradius of the triangle ABC, then 2(r + R) equals

Solution:

QUESTION: 6

If in a ∠ABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sinA, sinB, sinC are in

Solution:

QUESTION: 7

The sides of a triangle are sina, cosa, and for some 0 < a < π/2. Then the greatest angle of the triangle is

Solution:

QUESTION: 8

The sum of the radii of inscribed and circumscribed circle for an n sided regular polygon of side a, is

Solution:

QUESTION: 9

If in a triangle ABC a cos^{2}+ c cos^{2}=3b/2, then the sides a, b and c

Solution:

QUESTION: 10

In a triangle ABC, medians AD and BE are drawn. If AD = 4, ∠DAB = π/6 and ∠ABE =π/3, then the area of the ΔABC is

Solution:

QUESTION: 11

If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ = PR then the angle P is

Solution:

QUESTION: 12

Given an isosceles triangle, whose one angle is 120º and radius of its incircle is √3, then the area of the triangle in sq. units is

Solution:

Let the angles be A,B,C

Given:∠A=120∘

and since it is an isosceles Triangle, other two angles must be equal

We have B=C

= √3(4 + 3 + 4√3)

= 7√3 + 12

QUESTION: 13

The sides a, b, c of a triangle ABC are the roots of x^{3} – 11x^{2} + 38x – 40 = 0, then =

Solution:

QUESTION: 14

In a triangle ABC = 4, ∠C = π/3, then a^{2} + b^{2} – c^{2} =

Solution:

QUESTION: 15

In a triangle cot A : cot B : cot C = 30 : 19 : 6, then a : b : c

Solution:

QUESTION: 16

If twice the square of the diameter of a circle is equal to sum of the squares of the sides of the inscribed triangle ABC, then sin^{2}A + sin^{2}B + sin^{2}C is equal to

Solution:

QUESTION: 17

In a triangle ABC if a/1 = b/√3 = c/2, then

Solution:

QUESTION: 18

In a triangle ABC, if s – a, s – b, s – c are in GP, then =

Solution:

QUESTION: 19

If cos A = , then ΔABC is

Solution:

QUESTION: 20

In a triangle ABC if = , then sin (B+C) is equal to

Solution:

QUESTION: 21

In a triangle ABC, 1 – tan (A/2) tan (B/2) is equal to

Solution:

QUESTION: 22

The angles of a triangle ABC are in A.P. The largest angle is twice the smallest angle and the median to the largest side divides the angle at the vertex in the ratio 2 : 3. If length of the median in 2√3 cm, length of the largest side is

Solution:

QUESTION: 23

The vertices angle of a triangle is divided into two parts, such that the tangent of one part is 3 times the tangent of the other and the difference of these parts is 30º, then the triangle is

Solution:

QUESTION: 24

In a triangle ABC, if tan (A/2) = p, tan (B/2) = q, then is equal to

Solution:

QUESTION: 25

If I is the incentre of a triangle whose in raidus and circumradius are r and R respectively; I_{1} I_{2} I_{3} is its ex-centre triangle, then I I_{1} . I I_{2} . I I_{3} is equal to

Solution:

QUESTION: 26

If R is the circumradius of a triangle ABC then the area of its pedal triangle is

Solution:

QUESTION: 27

In an isosceles triangle with base angle a and lateral side 4, Rr =

Solution:

### Solution- Evolution Test-3

Doc | 3 Pages

### Solution- Vectors Test-3

Doc | 3 Pages

### Solution- Matrices Test-3

Doc | 3 Pages

### Allen Test Paper 3 Solution

Doc | 8 Pages

- Competition Level Test: Solution Of Triangles- 3
Test | 27 questions | 54 min

- Competition Level Test: Solution Of Triangles- 2
Test | 30 questions | 60 min

- Competition Level Test: Solution Of Triangles- 1
Test | 30 questions | 60 min

- Test: Limit With Solution (Competition Level) - 2
Test | 30 questions | 60 min

- Test: Area Under Curve With Solution (Competition Level)
Test | 30 questions | 60 min