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# JEE Main Math Previous Year Papers Properties Solutions of Triangles Questions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Main Math Previous Year Paper Properties and Solutions of Triangles Questions Answer Keys Solutions.

### JEE Mains Mathematics Properties and Solutions of Triangles Questions Bank

JEE Properties and Solutions of Triangles Questions No:1

The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y where x, y > 0 then the triangle is



Option A: Right angled

Option B: Obtuse angled

Option C: Equilateral

Option D: None of these

Option B:  Obtuse angled

JEE Main Properties and Solutions of Triangles Questions No:2

In a triangle with sides a, b, c, r1 > r2> r3 (which are the ex-radii) then



Option A: a > b > c

Option B: a < b < c

Option C: a > b and b < c

Option D: a < b and b > c

Option C:  a > b > c

JEE Mathematics Properties and Solutions of Triangles Questions No: 3

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



Option A: n(a/4) cot (π/2n)

Option B: a cot (π/n)

Option C: (a/2) cot (π/2n)

Option D: a cot (π/2n)

Option B: A (a/2) cot (π/2n)

JEE Main Math Properties and Solutions of Triangles Questions No: 4

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



Option A: 64/3

Option B: 8/3

Option C: 16/3

Option D: 32/3√ 3

Option D: 32/3√3

Properties and Solutions of Triangles JEE Questions No: 5

If in a ∆ABC a cos2  (C/2) + cos2 (A/2) = 3b/2  then the sides a, b and c



Option A: Satisfy a + b =c

Option B: Are in A.P

Option C: Are in G.P

Option D: Are in H.P

Option B: Are in A.P

Properties and Solutions of Triangles JEE Main Questions No: 6

The sides of a triangle are sin α, cos α and √1 + sin α cos α for some 0 < α < (π/2). Then the greatest angle of the triangle is



Option A: 150o

Option B: 90o

Option C: 120o

Option D: 60o

Option C: 120o

Properties and Solutions of Triangles Questions for JEE Mains Questions No: 7

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



Option A: b+ c

Option B: a + b

Option C: a + b + c

Option D: c + a

Option B: a + b

Properties and Solutions of Triangles Questions and Answers No: 8

If in a ∆ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in



Option A: G.P

Option B: A.P

Option C: A.P – G.P

Option D: H.P

Option B: A.P

Properties and Solutions of Triangles Questions with Solutions No:9

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is



Option A: There is a regular polygon with (r/R) = (1/2)

Option B: There is a regular polygon with (r/R) = (3/2)

Option C: There is a regular polygon with (r/R) = (√3/2)

Option D: There is a regular polygon with (r/R) = (1/2)

Option B: There is a regular polygon with (r/R) = (3/2)

JEE Mains Properties and Solutions of Triangles Questions No: 10

In a ∆PQR, If 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to



Option A: π/6

Option B: π/6

Option C: π/4

Option D: 3π/4

Option B: π/6

JEE Mains Math Properties and Solutions of Triangles Questions No: 11

ABCD is a trapezium such that AB and CD are parallel and BC ⟂ CD. If ∠ADB = 0, BC = p and CD = q, then AB is equal to



Option A: ( (p+ q2 ) sinθ / p cosθ + q sinθ)

Option B: ( (p+ q2 ) cosθ / p cosθ + q sinθ)

Option C: ( (p+ q2 ) / p2 cosθ + q2 sinθ)

Option D: ( (p+ q2 ) sinθ / p cosθ + q sinθ)2

Option A:  ( (p+ q2) sinθ / p cos + q sinθ)

Properties and Solutions of Triangles Questions for JEE Questions No:12

Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter is



Option A: 35/2

Option B: √10

Option C: ω20= 1/LC

Option D: 3 √5/√2

Option D: 3 √5 / √2

Properties and Solutions of Triangles Problems for Class 11 Questions No: 13

In a ∆ABC = (a/b) = 2 + √3 and ∠C = 60°. Then the ordered pair (∠A, ∠B) is equal to



Option A: (45°,75°)

Option B: (105°, 15°)

Option C: (15°, 105°)

Option D: (75°, 45°)

Option B: (105°, 15°)

Properties and Solutions of Triangles Problems for Class 12 Questions No: 14

With the usual notation, in ∆ABC, if ∠A + ∠B = 120°, a = √3 + 1 and b = √3 – 1, then the ratio ∠A : ∠B, is:



Option A: 7 : 1

Option B:  5 : 3

Option C: 9 : 7

Option D: 3 : 1

Option A: 7 : 1

Properties and Solutions of Triangles Problems for Class 11 JEE Questions No: 15

Given (b + c / 11) = (c + a / 12) = (a + b / 13) for a ∆ABC with usual notation. If (cosA  /α) = (cosB / β) = (cosC / γ) then the ordered traid (α, β, γ) has a value



Option A: (7,19,25)

Option B: (3,4,5)

Option C: (5, 12, 13)

Option D: (19,7,25)

Option A: (7,19,25)

Properties and Solutions of Triangles Problems for Class 12 JEE Questions No: 16

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x2 – c2 = y, where c is the length of the third side of the triangle, then the circumradius of the triangle is



Option A: 3/2y

Option B: c/√3

Option C: c/3

Option D: y/√3

Option B: c/√3

JEE Properties and Solutions of Triangles Questions No:17

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is



Option A: 5 : 9 : 13

Option B:  4 : 5 : 6

Option C: 3 : 4 : 5

Option D: 5 : 6 : 7

Option B: 4 : 5 : 6

JEE Main Properties and Solutions of Triangles Questions No:18

The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : √3. If c = 4 cm, then the area (in sq.cm) of this triangle is:



Option A: 2/√3

Option B: 4√3

Option C: 2√3

Option D: 4√3

Option C: 23

JEE Mathematics Properties and Solutions of Triangles Questions No: 19

Let A (3, 0, -1), B (2, 10, 6) and C (1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2:1, then cos (O being the origin) is equal to



Option A: 1/2√15

Option B: 1/√15

Option C: 1/6√10

Option D: 1/√30

Option B: 1/√15

JEE Main Math Properties and Solutions of Triangles Questions No: 20

The area bounded by the lines y = | |x – 1| – 2| is



Correct Ans : Bonus

Properties and Solutions of Triangles JEE Questions No: 21

In ∆ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of ∆ABC is 30 cm2 and R and r are respectively the radii of circumcircle and incircle of ABC, then the value of 2R + r (in cm) is equal to



Correct Ans : 15

Properties and Solutions of Triangles JEE Main Questions No: 22

Let A(-1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of ∆ABC and ∆PQC respectively, such that A1 = 3A2, then the value of m is equal to



Option A: 2

Option B: 3

Option C: 4/15

Option D: 1

Option D: 1

Properties and Solutions of Triangles Questions for JEE Mains Questions No: 23

A square ABCD has all its vertices on the curve x2y2 = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is



Correct Ans : 80

Properties and Solutions of Triangles Questions and Answers No: 24

Consider a triangle having vertices A(-2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point then the value of real number  α is



Correct Ans : 9

Properties and Solutions of Triangles Questions with Solutions No:25

If in a triangle ABC, AB = 5 units, and radius of circumcircle of ∆ABC is 5 units, then the area (in sq. units) of ∆ABC is



Option A: 10 + 6√2

Option B: 8 + 2√2

Option C: 6 + 8√3

Option D: 4 + 2√3

Option C:  6 + 8√3

JEE Mains Properties and Solutions of Triangles Questions No: 26

If a rectangle is inscribed in an equilateral triangle of side length as shown in the figure, then the square of the largest area of such a rectangle is Correct Ans : 3

JEE Mains Math Properties and Solutions of Triangles Questions No: 27

Two tangents are drawn from the point P(-1, 1) to the circle x2 + y2 – 2x – 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to



Option A: 2

Option B: (3√2 + 2)

Option C: 4

Option D: (3√2 -1)

Option C: 4

Properties and Solutions of Triangles Questions for JEE Questions No:28

The  Let (sin A/ sin B) = (sin (A – C) / sin (C – B) ) where A, B, C are angles of a  triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then



Option A: b2 – a2 = a2 + c2

Option B: b2 , c2 , a2 are in A.P

Option C: c2 , a2 , b2 are in A.P

Option D: a2 , b2 , c2 are in A.P

Option B: b2, c2, a2 are in A.P

Properties and Solutions of Triangles Problems for Class 11 Questions No: 29

If the minimum area of the triangle formed by a tangent to the ellipse (x2 / b2) + (y2 / 4a2) = 1 and the co-ordinate axis is kab, then k is equal to



Correct Ans : 2

Properties and Solutions of Triangles Problems for Class 12 Questions No: 30

The Let B be the centre of the circle x2 + y2 – 2x + 4y + 1 = 0. Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then 8 (area ∆APQ / area ∆BPQ) is equal to



Correct Ans : 18

Properties and Solutions of Triangles Problems for Class 11 JEE Questions No: 31

A man starts walking from the point P(-3, 4), touches the x axis at R. and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then 50 ( (PR)2 + (RQ)2 ) is equal to