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\( \vec{a},\vec{b}\) and \(\vec{c}\) are three non coplanar unit vectors inclined at an angle \(\alpha (\leq \dfrac{\pi}{2} ) \) to each other . If volume of the tetrahedron ...

\[\large (a-b)^{2}+\left(\sqrt{\theta-a^{2}} -\dfrac{16}{b}\right)^{2}\]

Given that \(a \in [0,\sqrt{\theta}]\), \(b\in \mathbb R^{+}\) and the minimum value of the expression ...

A uniform disc is rolling on rough ground as shown in the figure.

The disc is about to collide with a frictionless wall. Find the maximum value of the coefficient ...

\[\large I = \int_0^1 \dfrac{(2x-1)\ln x}{1-x^2} \, dx\]

Find the value of the closed form of the above integral \(I\). Submit your answer as ...

In an isosceles \(\triangle ABC\), \(\angle A\) is measured as \(108^\circ\). \(A,C\) and \(D\) are collinear, while \(AD=BC\). \(M\) is the midpoint of \(BD\). What is the ...

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