Properties of Triangle PYQs - Last 5 Years
JEE Main / Mathematics / Trigonometry / 20 recent questions
MathematicsTrigonometry2021-2025
Practice 20 JEE Main Mathematics questions from Properties of Triangle. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Trigonometry
2021-2025
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20
Last 5 Years
2021-2025
20
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2016-2025
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INTEGER40%
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#2 Hard3
20 in last 5 years20 in last 10 years
Last 5 Years Properties of Triangle Questions
Showing 20 of 20 filtered questions.
1Properties Of Triangle
Let the area of a $\triangle P Q R$ with vertices $P(5,4), Q(-2,4)$ and $R(a, b)$ be 35 square units. If its orthocenter and centroid are $O\left(2, \frac{14}{5}\right)$ and $C(c, d)$ respectively, then $c+2 d$ is equal to
MCQ+4 / -12025
2Properties Of Triangle
Let $\mathrm{A}(6,8), \mathrm{B}(10 \cos \alpha,-10 \sin \alpha)$ and $\mathrm{C}(-10 \sin \alpha, 10 \cos \alpha)$, be the vertices of a triangle. If $L(a, 9)$ and $G(h, k)$ be its orthocenter and centroid respectively, then $(5 a-3 h+6 k+...
INTEGER+4 / -12025
3Properties Of Triangle
Two vertices of a triangle \(\mathrm{ABC}\) are \(\mathrm{A}(3,-1)\) and \(\mathrm{B}(-2,3)\), and its orthocentre is \(\mathrm{P}(1,1)\). If the coordinates of the point \(\mathrm{C}\) are \((\alpha, \beta)\) and the centre of the of the c...
MCQ+4 / -12024
4Properties Of Triangle
In a triangle \(\mathrm{ABC}, \mathrm{BC}=7, \mathrm{AC}=8, \mathrm{AB}=\alpha \in \mathrm{N}\) and \(\cos \mathrm{A}=\frac{2}{3}\). If \(49 \cos (3 \mathrm{C})+42=\frac{\mathrm{m}}{\mathrm{n}}\), where \(\operatorname{gcd}(m, n)=1\), then ...
INTEGER+4 / -12024
5Properties Of Triangle
Consider a triangle \(\mathrm{ABC}\) having the vertices \(\mathrm{A}(1,2), \mathrm{B}(\alpha, \beta)\) and \(\mathrm{C}(\gamma, \delta)\) and angles \(\angle A B C=\frac{\pi}{6}\) and \(\angle B A C=\frac{2 \pi}{3}\). If the points $$\math...
INTEGER+4 / -12024
6Properties Of Triangle
Let \(\left(5, \frac{a}{4}\right)\) be the circumcenter of a triangle with vertices \(\mathrm{A}(a,-2), \mathrm{B}(a, 6)\) and \(C\left(\frac{a}{4},-2\right)\). Let \(\alpha\) denote the circumradius, \(\beta\) denote the area and $$\gamma$...
MCQ+4 / -12024
7Properties Of Triangle
A straight line cuts off the intercepts \(\mathrm{OA}=\mathrm{a}\) and \(\mathrm{OB}=\mathrm{b}\) on the positive directions of \(x\)-axis and \(y\) axis respectively. If the perpendicular from origin \(O\) to this line makes an angle of $$...
MCQ+4 / -12023
8Properties Of Triangle
For a triangle \(ABC\), the value of \(\cos 2A + \cos 2B + \cos 2C\) is least. If its inradius is 3 and incentre is M, then which of the following is NOT correct?
MCQ+4 / -12023
9Properties Of Triangle
If the line $x=y=z$ intersects the line
$x \sin A+y \sin B+z \sin C-18=0=x \sin 2 A+y \sin 2 B+z \sin 2 C-9$,
where $A, B, C$ are the angles of a triangle $A B C$, then $80\left(\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}\right)$
...
$x \sin A+y \sin B+z \sin C-18=0=x \sin 2 A+y \sin 2 B+z \sin 2 C-9$,
where $A, B, C$ are the angles of a triangle $A B C$, then $80\left(\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}\right)$
...
INTEGER+4 / -12023
10Properties Of Triangle
In a triangle ABC, if \(\cos \mathrm{A}+2 \cos \mathrm{B}+\cos C=2\) and the lengths of the sides opposite to the angles A and C are 3 and 7 respectively, then \(\mathrm{\cos A-\cos C}\) is equal to
MCQ+4 / -12023
11Properties Of Triangle
In the figure, \(\theta_{1}+\theta_{2}=\frac{\pi}{2}\) and \(\sqrt{3}(\mathrm{BE})=4(\mathrm{AB})\). If the area of \(\triangle \mathrm{CAB}\) is \(2 \sqrt{3}-3\) unit \({ }^{2}\), when \(\frac{\theta_{2}}{\theta_{1}}\) is the largest, then...
INTEGER+4 / -12023
12Properties Of Triangle
The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 \(-\) 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :
MCQ+4 / -12022
13Properties Of Triangle
Let a, b and c be the length of sides of a triangle ABC such that \({{a + b} \over 7} = {{b + c} \over 8} = {{c + a} \over 9}\). If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the va...
MCQ+4 / -12022
14Properties Of Triangle
Let \({{\sin A} \over {\sin B}} = {{\sin (A - C)} \over {\sin (C - B)}}\), where A, B, C are angles of triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then :
MCQ+4 / -12021
15Properties Of Triangle
The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :
MCQ+4 / -12021
16Properties Of Triangle
If a rectangle is inscribed in an equilateral triangle of side length \(2\sqrt 2\) as shown in the figure, then the square of the largest area of such a rectangle is _____________.
INTEGER+4 / -12021
17Properties Of Triangle
Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be \(\left( {{{10} \over 3},{7 \over 3}} \right)\). If \(\alpha\), \(\beta\) are the roots of the equation $$a{x^2} + bx + 1 ...
MCQ+4 / -12021
18Properties Of Triangle
If in a triangle ABC, AB = 5 units, \(\angle B = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)\) and radius of circumcircle of \(\Delta\)ABC is 5 units, then the area (in sq. units) of \(\Delta\)ABC is :
MCQ+4 / -12021
19Properties Of Triangle
Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the ci...
INTEGER+4 / -12021
20Properties Of Triangle
In \(\Delta\)ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of \(\Delta\)ABC is 30 cm2 and R and r are respectively the radii of circumcircle and incircle of \(\Delta\)ABC, then the value of 2R + r (in cm)...
INTEGER+4 / -12021