Properties of Triangles

JEE Advanced · Mathematics · 13 past questions

1. Q1 2021 Paper 1

   In a triangle $ABC$, let $AB=\sqrt{23}$, $BC=3$ and $CA=4$. Then the value of…

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2. Q2 2020 Paper 1

   Let $x, y$ and $z$ be positive real numbers. Suppose $x, y$ and $z$ are the lengths of the sides of a…

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3. Q3 2019 Paper 1

   In a non-right-angled triangle $\Delta PQR$, let $p,q,r$ denote the lengths of the sides opposite to the…

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4. Q4 2018 Paper 1

   In a triangle $PQR$, let $\angle PQR = 30^\circ$ and the sides $PQ$ and $QR$ have lengths $10\sqrt{3}$ and…

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5. Q5 2016 Paper 1

   In a triangle $XYZ$, let $x,y,z$ be the lengths of sides opposite to the angles $X,Y,Z$, respectively, and…

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6. Q6 2014 Paper 2

   In a triangle the sum of two sides is $x$ and the product of the same two sides is $y$. If $x^2 - c^2 = y$…

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7. Q7 2013 Paper 2

   In a triangle $PQR$, $P$ is the largest angle and $\cos P = \frac{1}{3}$. Further the incircle of the…

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8. Q8 2012 Paper 2

   Let $PQR$ be a triangle of area $\Delta$ with $a = 2$, $b = \frac{7}{2}$ and $c = \frac{5}{2}$, where $a$…

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9. Q9 2010 Paper 1

   Let ABC be a triangle such that $\angle ACB = \frac{\pi}{6}$ and let a, b and c denote the lengths of the…

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10. Q10 2010 Paper 2

    Consider a triangle $ABC$ and let $a$, $b$ and $c$ denote the lengths of the sides opposite to vertices $A$…

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11. Q11 2009 Paper 1

    In a triangle $ABC$ with fixed base $BC$, the vertex $A$ moves such that…

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12. Q12 2009 Paper 2

    Let $ABC$ and $ABC'$ be two non-congruent triangles with sides $AB = 4$, $AC = AC' = 2\sqrt{2}$ and angle…

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13. Q13 2007 Paper 2

    Let $ABCD$ be a quadrilateral with area 18, with side $AB$ parallel to the side $CD$ and $AB = 2CD$. Let $AD$…

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