JEE Mains JEE Advance BITSAT
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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 _____.

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?

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JEE Advance 2021 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?