Properties of Triangles PYQs - Last 5 Years

MHT CET / Mathematics / Trigonometry / 105 recent questions

MathematicsTrigonometry2022-2026

All Properties of Triangles PYQs Last 10 Years Create chapter test

Practice 105 MHT CET Mathematics questions from Properties of Triangles. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

105

PYQs on Page

Mathematics / Trigonometry

2023-2026

Year Range

Based on indexed question metadata

105

Last 5 Years

2022-2026

105

Last 10 Years

2017-2026

Recent Year Trend

2023

2024

2025

2026

202339 max PYQs/year2026

Question Types

105PYQs

MCQ100%

Difficulty Mix

#1 Unknown105

105 in last 5 years105 in last 10 years

Last 5 Years Properties of Triangles Questions

Showing 50 of 105 filtered questions.

1Properties Of Triangles

In a right-angled $\triangle ABC$, the measures of the angles are in an Arithmetic Progression (A.P.) If its smallest side is $4$ units, then the area of $\triangle ABC$ is.....

2Properties Of Triangles

With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

3Properties Of Triangles

The angles of $\triangle ABC$ are in A.P. and $b : c = \sqrt{3} : \sqrt{2}$ then $\angle A =$

4Properties Of Triangles

In $\triangle ABC$, with usual notations, if the sides $a$, $b$ and $c$ are in the ratio $18 : 17 : 7$, then $\cot\dfrac{A}{2} : \cot\dfrac{B}{2} : \cot\dfrac{C}{2} =$

5Properties Of Triangles

If ABC is a triangle of area $\Delta$ with $a = 2, b = \dfrac{7}{2}, c = \dfrac{5}{2}$, where $a, b, c$ are the lengths of the sides of the triangle opposite to angles A, B and C respectively, then $\dfrac{2\sin A - \sin 2A}{2\sin A + \sin ...

6Properties Of Triangles

In $\triangle ABC$, with usual notations, $(a + b + c)(b + c - a)(c + a - b)(a + b - c) = 3b^2c^2$, then $\angle A = $

7Properties Of Triangles

In $\triangle ABC$, with usual notation, if $a = 13, b = 14, c = 15$, then the sum of the values of $\sin\left(\dfrac{A}{2}\right)$ and $\sin A$ is....

8Properties Of Triangles

In triangle ABC, with usual notations, if $(a+b+c)(a+b-c) = ab$, then the measure of angle C is...

9Properties Of Triangles

In $\triangle ABC$, if $\angle C = \dfrac{\pi}{3}$, then the value of $\cos^2 A + \cos^2 B + \cos A\cos B$ is...

10Properties Of Triangles

In $\triangle ABC$, with usual notations, if $\Delta$ denotes the area of triangle $ABC$ then the value of $2s(b+c-a)\tan\left(\dfrac{A}{2}\right)$ is equal to $\ldots$

11Properties Of Triangles

In $\triangle ABC$, if $a = 13, b = 14, c = 15$, then the value of $\sin A + \cos A$ is...

12Properties Of Triangles

With usual notations, in $\triangle ABC$, if $\cos C = \dfrac{\sin A}{2\sin B}$, then which of the following is true ?

13Properties Of Triangles

In $\triangle ABC$, with usual notation, if cot A, cot B, cot C are in arithmetic progression, then

14Properties Of Triangles

In a triangle ABC, with usual notations $a = \sqrt{3} + 1$, $b = \sqrt{3} - 1$ and $\angle C = 60^\circ$ then the values of $\angle A$ and $\angle B$ respectively are

15Properties Of Triangles

With usual notations in $\triangle$ABC, if $b\cos^2\dfrac{C}{2} + c\cos^2\dfrac{B}{2} = \dfrac{3a}{2}$ then

16Properties Of Triangles

In triangle ABC, with usual notations, if $a = 4, b = 5$ and $c = 6$, then angle C is equal to...

17Properties Of Triangles

In $\triangle ABC$ with usual notations, if $1 + \tan\left(\dfrac{A}{2}\right)\tan\left(\dfrac{B}{2}\right) = \dfrac{k}{s}$ (where $s$ is the semi-perimeter), then the value of $k$ is...

18Properties Of Triangles

In $\triangle ABC$, with the usual notations, $\angle C = 90^\circ$, then $\sin(A - B)$ is equal to....

19Properties Of Triangles

Let $P_1$, $P_2$, $P_3$ be the altitudes of a triangle ABC from the vertices A, B, C respectively. If $\triangle$ denotes the area of the triangle and s is the semi-perimeter of the triangle, then $\dfrac{\cos A}{P_1} + \dfrac{\cos B}{P_2} ...

20Properties Of Triangles

In a triangle ABC, with the usual notations, $\angle B = \dfrac{\pi}{3}$, $\angle C = \dfrac{\pi}{4}$. If D divides BC internally in the ratio 1:3, then $\dfrac{\sin \angle BAD}{\sin \angle CAD} =$

21Properties Of Triangles

With usual notations, in $\triangle ABC$, $(b - c)^2 \cos^2 \dfrac{A}{2} + (b + c)^2 \sin^2 \dfrac{A}{2} =$

22Properties Of Triangles

With usual notations, in $\triangle ABC$, if $2a^2 = b^2 + c^2$, then $\dfrac{\cos 3A}{\cos A} + 2 =$

23Properties Of Triangles

In a triangle ABC, with usual notations if $\dfrac{s-a}{11} = \dfrac{s-b}{12} = \dfrac{s-c}{13}$ and $\lambda \tan^2 \dfrac{A}{2} = 455$, then $\lambda =$

24Properties Of Triangles

In $\triangle ABC$, with usual notations, if $\cos A = \dfrac{1}{2}, a = 3, \angle B = \dfrac{\pi^c}{6}$, then the values of $b$ and $c$ are.....

25Properties Of Triangles

In triangle ABC, with usual notations, if the angles are in Arithmetic Progression and $3c^2 = 2b^2$, then the measure of angle A is

26Properties Of Triangles

In $\Delta ABC$, if $\angle A = 90^\circ$, then $\sin(B - C) = $

27Properties Of Triangles

In a triangle $A B C$, with usual notations, the sides $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are such that they are roots of the equation $x^3-11 x^2+38 x-40=0$ then $\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\fra...

28Properties Of Triangles

With usual notation, in a triangle ABC $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$, then the value of $\cos B$ is equal to

29Properties Of Triangles

In a triangle $A B C$, with usual notations, if $a=5$, $\mathrm{b}=7 \sin \mathrm{~A}=\frac{3}{4}$, then total number of triangles possible are

30Properties Of Triangles

In a triangle $A B C$, with usual notations, $\cot \left(\frac{A+B}{2}\right) \cdot \tan \left(\frac{A-B}{2}\right)=$

31Properties Of Triangles

In a triangle ABC , with usual notations, $(\mathrm{a}+\mathrm{b}+\mathrm{c})(\mathrm{a}+\mathrm{b}-\mathrm{c})=3 \mathrm{ab}$, then $\angle \mathrm{C}=$

32Properties Of Triangles

If the angles $\mathrm{A}, \mathrm{B}$ and C of a triangle are in A.P. and if $\mathrm{a}, \mathrm{b}$ and c denote the length of the sides opposite to $\mathrm{A}, \mathrm{B}$ and C respectively, then the value of $\frac{a}{b} \sin 2 B+\fr...

33Properties Of Triangles

In a triangle PQR with usual notations, $\angle \mathrm{R}=\frac{\pi}{2}$. If $\tan \frac{\mathrm{P}}{2}$ and $\tan \frac{\mathrm{Q}}{2}$ are the roots of the equation $a x^2+b x+c=0(a \neq 0)$, then

34Properties Of Triangles

In a triangle $A B C$ with usual notations if $\angle A=30^{\circ}$, then the value of $\left(1+\frac{a}{c}+\frac{b}{c}\right)\left(1+\frac{c}{b}-\frac{a}{b}\right)=$

35Properties Of Triangles

If in triangle ABC , with usual notations $\sin \frac{\mathrm{A}}{2} \cdot \sin \frac{\mathrm{C}}{2}=\sin \frac{\mathrm{B}}{2}$ and 2 s is the perimeter of the triangle, then the value of $s$ is

36Properties Of Triangles

In a triangle ABC , with usual notations. $\frac{2 \cos \mathrm{~A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\frac{2 \cos \mathrm{C}}{\mathrm{c}}=\frac{\mathrm{a}}{\mathrm{bc}}+\frac{\mathrm{b}}{\mathrm{ca}}$. Then $\angle \mathrm{A}...

37Properties Of Triangles

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is

38Properties Of Triangles

With usual notations in $\triangle \mathrm{ABC}$, if $\angle \mathrm{B}=\frac{\pi}{2}$, and $\tan \frac{\mathrm{A}}{2}, \tan \frac{\mathrm{C}}{2}$ are roots of equation $\mathrm{p} x^2+\mathrm{qx}+\mathrm{r}=0$, $\mathrm{p} \neq 0$, then

39Properties Of Triangles

In $\triangle \mathrm{ABC}$, with usual notations, if $\cos \frac{B}{2}=\sqrt{\frac{c+a}{2 a}}$, then $a^2=$

40Properties Of Triangles

In a triangle ABC , with usual notations, if $\mathrm{a}=5, \mathrm{~b}=4, \cos (\mathrm{~A}-\mathrm{B})=\frac{31}{32}$, then $\mathrm{c}=$

41Properties Of Triangles

In a triangle ABC with usual notations, $\cot \frac{\mathrm{A}}{2}+\cot \frac{\mathrm{B}}{2}+\cot \frac{\mathrm{C}}{2}=$

42Properties Of Triangles

With usual notations, in $\triangle \mathrm{ABC}$, the lengths of two sides are 10 cm and 9 cm respectively. If angles $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are in A.P. then perimeter of $\triangle \mathrm{ABC}$ is

43Properties Of Triangles

In a triangle ABC with usual notations if $b \sin C(b \cos C+c \cos B)=42$, then area of triangle $\mathrm{ABC}=$

44Properties Of Triangles

Let $\mathrm{A} \equiv(0,0), \mathrm{B}(3,0), \mathrm{C}(0,-4)$ are vertices of $\triangle A B C$, then the co-ordinates of incentre of $\triangle \mathrm{ABC}$ is

45Properties Of Triangles

In a triangle with one of the angles $120^{\circ}$, the lengths of the sides form an A.P. If length of the greatest side is 7 m , then the area of the triangle is

46Properties Of Triangles

In $\triangle A B C$, with usual notations, if $\mathrm{a}^4+\mathrm{b}^4+\mathrm{c}^4-2 \mathrm{a}^2 \mathrm{c}^2-2 \mathrm{c}^2 \mathrm{~b}^2=0$, then $\angle \mathrm{C}=\ldots$

47Properties Of Triangles

In a triangle ABC with usual notations if, $\tan \left(\frac{\mathrm{B}-\mathrm{C}}{2}\right)=x \cot \frac{\mathrm{~A}}{2}$, then $x=$

48Properties Of Triangles

In a triangle ABC with usual notations, if $3 \mathrm{a}=\mathrm{b}+\mathrm{c}$, then $\cot \frac{\mathrm{B}}{2} \cdot \cot \frac{\mathrm{C}}{2}=$

49Properties Of Triangles

In a triangle ABC with usual notations if, $\cot \frac{A}{2}=\frac{b+c}{a}$, then the triangle $A B C$ is

50Properties Of Triangles

In $\triangle A B C$, with usual notations, $a \cos B=b \cos A, a \cos C \neq c \cos A$ then $\mathrm{A}(\triangle \mathrm{ABC})$ $\qquad$ sq. units.