# Properties of Triangles · Mathematics · MHT CET

Start Practice## MCQ (Single Correct Answer)

MHT CET 2023 14th May Evening Shift

In a triangle $$\mathrm{A B C, m \angle A, m \angle B, m \angle C}$$ are in A.P. and lengths of two larger sides are 10 units, 9 units respectively, t...

MHT CET 2023 14th May Morning Shift

In $$\triangle \mathrm{ABC}$$, with usual notations, $$2 \mathrm{ac} \sin \left(\frac{1}{2}(\mathrm{~A}-\mathrm{B}+\mathrm{C})\right)$$ is equal to...

MHT CET 2023 14th May Morning Shift

If the angles $$\mathrm{A}, \mathrm{B}$$, and $$\mathrm{C}$$ of a triangle are in an Arithmetic Progression and if $$\mathrm{a}, \mathrm{b}$$ and $$\m...

MHT CET 2023 13th May Evening Shift

In $$\triangle A B C$$, with usual notations, if $$\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$$, then the value of $$\cos A+\cos B+\cos C$$ is...

MHT CET 2023 13th May Morning Shift

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides of the triangle (in unit...

MHT CET 2023 13th May Morning Shift

In $$\triangle A B C$$ with usual notation, $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$ and $$a=\frac{1}{\sqrt{6}}$$, then the area of tria...

MHT CET 2023 13th May Morning Shift

Angles of a triangle are in the ratio $$4: 1: 1$$. Then the ratio of its greatest side to its perimeter is

MHT CET 2023 12th May Evening Shift

The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the length of the sides...

MHT CET 2023 12th May Evening Shift

If two angles of $$\triangle \mathrm{ABC}$$ are $$\frac{\pi}{4}$$ and $$\frac{\pi}{3}$$, then the ratio of the smallest and greatest sides are

MHT CET 2023 12th May Evening Shift

In $$\triangle \mathrm{ABC}, \mathrm{m} \angle \mathrm{B}=\frac{\pi}{3}$$ and $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{4}$$. Let point $$\mathrm{D}$$...

MHT CET 2023 12th May Morning Shift

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 $$x^2-\mathrm{c}^2=y$$, wher...

MHT CET 2023 11th May Evening Shift

If the vertices of a triangle are $$(-2,3),(6,-1)$$ and $$(4,3)$$, then the co-ordinates of the circumcentre of the triangle are

MHT CET 2023 11th May Evening Shift

In triangle $$\mathrm{ABC}$$ with usual notations $$\mathrm{b}=\sqrt{3}, \mathrm{c}=1, \mathrm{~m} \angle \mathrm{A}=30^{\circ}$$, then the largest an...

MHT CET 2023 11th May Evening Shift

If the angles of a triangle are in the ratio $$4: 1: 1$$, then the ratio of the longest side to its perimeter is

MHT CET 2023 11th May Morning Shift

If in $$\triangle \mathrm{ABC}$$, with usual notations, $$a \cdot \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$$, then

MHT CET 2023 11th May Morning Shift

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathrm{a}=6$$ and $$\mathrm{B}=\sin...

MHT CET 2023 10th May Evening Shift

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{c}=4$$, then value of $$(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}$$ i...

MHT CET 2023 10th May Morning Shift

If one side of a triangle is double the other and the angles opposite to these sides differ by $$60^{\circ}$$, then the triangle is

MHT CET 2023 9th May Evening Shift

In $$\triangle \mathrm{PQR}, \sin \mathrm{P}, \sin \mathrm{Q}$$ and $$\sin \mathrm{R}$$ are in A.P., then

MHT CET 2023 9th May Evening Shift

Let $$a, b, c$$ be the lengths of sides of triangle $$A B C$$ such that $$\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}=k$$. Then $$\frac{(\mathrm{A}(\tri...

MHT CET 2023 9th May Evening Shift

In $$\triangle \mathrm{ABC}$$, with usual notations, $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{2}$$, if $$\tan \left(\frac{A}{2}\right)$$ and $$\tan \...

MHT CET 2023 9th May Morning Shift

Two sides of a triangle are $$\sqrt{3}+1$$ and $$\sqrt{3}-1$$ and the included angle is $$60^{\circ}$$, then the difference of the remaining angles is...

MHT CET 2021 24th September Evening Shift

In a triangle ABC with usual notations a = 2, b = 3, then value of $$\frac{\cos 2 \mathrm{~A}}{\mathrm{a}^2}-\frac{\cos 2 \mathrm{~B}}{\mathrm{~b}^2}$...

MHT CET 2021 24th September Morning Shift

In any $$\triangle A B C$$, with usual notations, $$c(a \cos B-b \cos A)=$$

MHT CET 2021 24th September Morning Shift

If in a $$\triangle A B C$$, with usual notations, $$\mathrm{a}^2, \mathrm{~b}^2, \mathrm{c}^2$$ are in A.P. then $$\frac{\sin 3 B}{\sin B}=$$

MHT CET 2021 23rd September Evening Shift

If $$\mathrm{G}(\overline{\mathrm{g}}), \mathrm{H}(\overline{\mathrm{h}})$$ and $$\mathrm{P}(\overline{\mathrm{p}})$$ are respectively centroid, ortho...

MHT CET 2021 23rd September Evening Shift

With usual notations in $$\triangle$$ABC, if $$\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}$$, then $$a^2, b^2, c^2$$ are in

MHT CET 2021 23rd September Evening Shift

The area of the triangle $$\mathrm{ABC}$$ is $$10 \sqrt{3} \mathrm{~cm}^2$$, angle $$\mathrm{B}$$ is $$60^{\circ}$$ and its perimeter is $$20 \mathrm{...

MHT CET 2021 23th September Morning Shift

In a triangle $$\mathrm{ABC}$$, with usual notations $$\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=5$$, then $$\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\c...

MHT CET 2021 22th September Evening Shift

In $$\Delta ABC$$, with usual notations $$\mathrm{\frac{b\sin B-c\sin C}{\sin(B-C)}}=$$

MHT CET 2021 22th September Evening Shift

With usual notations, in any $$\triangle A B C$$, if $$a\cos B=b \cos A$$, then the triangle is

MHT CET 2021 22th September Morning Shift

In $$\triangle A B C$$, with usual notations, $$2 a b \sin \frac{1}{2}(A+B-C)=$$

MHT CET 2021 22th September Morning Shift

If in $$\Delta$$ABC, with usual notations, the angles are in A.P., then $$\mathrm{\frac{a}{c}}$$ sin 2 C + $$\mathrm{\frac{c}{a}}$$ sin 2 A =

MHT CET 2021 21th September Evening Shift

With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\mathrm{a}=1$$, then measure of ang...

MHT CET 2021 20th September Morning Shift

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio.

MHT CET 2020 16th October Evening Shift

In a $$\triangle A B C$$ if $$2 \cos C=\sin B \cdot \operatorname{cosec} A$$, then

MHT CET 2020 16th October Morning Shift

In a triangle $$A B C$$ with usual notations, if $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$, then area of triangle $$A B C$$ with $$a=\sqr...

MHT CET 2020 16th October Morning Shift

In a triangle $$A B C$$, if $$\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B$$, then $$A, B, C$$, are in