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All years 2023 2022 2021

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Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is $ \frac{\pi}{2} $ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius $ 1 $.
Then the inradius of the triangle $ ABC $ is:

Let $ X=\left\{(x,y)\in \mathbb{Z}\times \mathbb{Z} : \frac{x^2}{8}+\frac{y^2}{20}<1 \text{ and } y^2<5x\right\} $. Three distinct points $ P, Q $ and $ R $ are randomly chosen from $ X $. Then the probability that $ P, Q $ and $ R $ form a triangle whose area is a positive integer, is:

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Consider an obtuse angled triangle $ABC$ in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius $1$.
Let $a$ be the area of the triangle $ABC$. Then the value of $(64a)^2$ is:

Let $ PQRS $ be a quadrilateral in a plane, where $ QR=1 $, $ \angle PQR=\angle QRS=70^\circ $, $ \angle PQS=15^\circ $ and $ \angle PRS=40^\circ $. If $ \angle RPS=\theta^\circ $, $ PQ=\alpha $ and $ PS=\beta $, then the interval(s) that contain(s) the value of $ 4\alpha\beta\sin\theta^\circ $ is/are:

In a triangle $ ABC $, let $ AB = \sqrt{23} $, $ BC = 3 $ and $ CA = 4 $. Then the value of $ \dfrac{\cot A + \cot C}{\cot B} $ is _____.

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JEE Advanced 2023 Paper - 2

Consider a triangle $ PQR $ having sides of lengths $ p,q$ are $r $ opposite to the angles $ P,Q $ and $ R $, respectively. Then which of the following statements is (are) TRUE?

JEE MainsJEE AdvanceBITSATJEE Advance | PYQ

JEE Mains JEE Advance BITSAT
JEE Advance | PYQ