Triangles (IPMAT/JIPMAT) - Free PYQs + Solutions

Q1:

Indore 2024

Geometry

>

Triangles

Hard

Q1:

The side AB of a triangle ABC is c. The median BD is of length k. If

\angle BDA = \theta

and

\theta < 90^\circ

, then the area of triangle ABC is

\dfrac{k^2 \sin \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}

\dfrac{k^2 \sin 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}

\dfrac{k^2 \cos 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}

\dfrac{k^2 \cos \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}

Correct Answer

Option: 2

Correct Answer

Explanation →

Q2:

Indore 2024

Geometry

>

Triangles

Medium

Q2:

Let

\triangle ABC

be a triangle with

AB = AC

and

D

be a point on

BC

such that

\angle BAD = 30^\circ

. If

E

is a point on

AC

such that

AD = AE

, then

\angle CDE

equals

60^\circ

30^\circ

10^\circ

15^\circ

Correct Answer

Option: 4

Correct Answer

Explanation →

Q3:

Indore 2024

Geometry

>

Triangles

Hard

Q3:

Let ABC be an equilateral triangle, with each side of length

k

. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is

\left(3\sqrt{3} + \pi\right) \frac{k^2}{24}

\left(3\sqrt{3} + \pi\right) \frac{k^2}{6}

\left(3\sqrt{3} - \pi\right) \frac{k^2}{24}

\left(3\sqrt{3} + \pi\right) \frac{k^2}{6}

Correct Answer

Option: 1

Correct Answer

Explanation →

Q4:

Indore 2024

Geometry

>

Triangles

Easy

Q4:

Let

\triangle ABC

be a triangle right-angled at

B

with

AB = BC = 18

. The area of the largest rectangle that can be inscribed in this triangle and has

B

as one of the vertices is:

Entered answer:

Correct Answer

81

Correct Answer

Explanation →

Q5:

Indore 2024

Geometry

>

Triangles

Easy

Q5:

The number of triangles with integer sides and with perimeter 15 is:

Entered answer:

Correct Answer

7

Correct Answer

Explanation →

Q6:

Indore 2023

Geometry

>

Triangles

Medium

Q6:

In a triangle ABC, let D be the midpoint of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be

11:4\sqrt{10}

12:11

11:12

4\sqrt{10}:11

Correct Answer

Option: 1

Correct Answer

Explanation →

Q7:

Indore 2022

Geometry

>

Triangles

Easy

Q7:

The lengths of the sides of a triangle are

x, 21

and

40

, where

x

is the shortest side. A possible value of

x

is:

18

20

19

16

Correct Answer

Option: 2

Correct Answer

Explanation →

Q8:

Indore 2022

Geometry

>

Triangles

Medium

Q8:

In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is

12

cm

5

cm

2 \sqrt{3}

cm

8

cm

Correct Answer

Option: 1

Correct Answer

Explanation →

Q9:

Indore 2020

Geometry

>

Triangles

Hard

Q9:

The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

28

29

31

33

Correct Answer

Option: 2

Correct Answer

Explanation →

Q10:

Indore 2019

Geometry

>

Triangles

Medium

Q10:

The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices

(0, 0), (0, 31),

and

(31, 0)

is

435

465

450

464

Correct Answer

Option: 1

Correct Answer

Explanation →

Q11:

JIPMAT 2024

Geometry

>

Triangles

Easy

Q11:

The sides of four triangles are given below. Which of them forms a right triangle ?

(A)

20 \mathrm{~cm}, 22 \mathrm{~cm}, 24 \mathrm{~cm}

(B)

15 \mathrm{~cm}, 32 \mathrm{~cm}, 37 \mathrm{~cm}

(C)

11 \mathrm{~cm}, 60 \mathrm{~cm}, 61 \mathrm{~cm}

(D)

6 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm}

(A) and (B) only

(C) only

(D) only

(C) and (D) only

Correct Answer

Option: 4

Correct Answer

Explanation →

Q12:

JIPMAT 2024

Geometry

>

Triangles

Medium

Q12:

The points

(2,2),(6,3)

and

(4,11)

are vertices of :

Equilateral triangle

Isosceles triangle

Right-angled triangle

Scalene triangle

Correct Answer

Option: 3

Correct Answer

Explanation →

Q13:

JIPMAT 2024

Geometry

>

Triangles

Medium

Q13:

An equilateral triangle

A B C

is inscribed in a circle of radius

20 \sqrt{3} \mathrm{~cm}

. The centroid of the triangle

A B C

is at a distance

d

from the vertex

A

. then

d

is equal to ?

15 \mathrm{~cm}

20 \mathrm{~cm}

20 \sqrt{3} \mathrm{~cm}

30 \sqrt{3} \mathrm{~cm}

Correct Answer

Option: 3

Correct Answer

Explanation →

Q14:

JIPMAT 2024

Geometry

>

Triangles

Easy

Q14:

An equilateral triangle

\mathrm{ABC}

is inscribed in a circle of radius

20 \sqrt{3} \mathrm{~cm}

. What is the length of the side of the triangle ?

30 \mathrm{~cm}

40 \mathrm{~cm}

50 \mathrm{~cm}

60 \mathrm{~cm}

Correct Answer

Option: 4

Correct Answer

Explanation →

Q15:

JIPMAT 2022

Geometry

>

Triangles

Easy

Q15:

Given below are two statements:

Statement I: In

\triangle A B C, A B=6 \sqrt{3} \mathrm{~cm}, A C=12 \mathrm{~cm}

and

B C=6 \mathrm{~cm}

, then angle

B=90^{\circ}

Statement II: In

\triangle A B C

, is an isosceles with

A C=B C

. If

A B^{2}=2 AC^{2}

, Then angle

C=90^{\circ}

In the light of the above statement, choose the correct answer form the question below.

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Correct Answer

Option: 1

Correct Answer

Explanation →

Q16:

JIPMAT 2021

Geometry

>

Triangles

Conceptual

Q16:

ABC is right angled triangle at C. Let BC = a, CA = b and AB = c and let p be the length of perpendicular from C on AB, then cp is equal to

a + b

ab

ac

bc

Correct Answer

Option: 2

Correct Answer

Explanation →

Q17:

Rohtak 2019

Geometry

>

Triangles

Medium

Q17:

A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of the remaining portion of the triangle?

144\sqrt{3} - 48\pi cm^2

121\sqrt{3} - 36\pi cm^2

144\sqrt{3} - 36\pi cm^2

121\sqrt{3} - 48\pi cm^2

Correct Answer

Option: 1

Correct Answer

Explanation →

Triangles - Past Year Questions

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Triangles - Past Year Questions (Free PDF Download)