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4 identical bars of mass \(M\) and length \(L\) are connected by pins at \(A,B, C\) and \(D\). The bars are attached to ...

A ring of mass m and radius r and made of an insulating material carries uniform charge. Initially it rests vertically on a frictionless horizontal tabletop on the left side ...

\[x^2 + xy + y^2 = z^2\]

Let \(x,y,\) and \(z\) be prime numbers satisfying the equation above. What is the largest possible product \(xyz\)?

Which day of the week is the 13\(^\text{th}\) day of a month most likely to fall on?

\[ \begin{eqnarray} f(x) &=& p(x)(x-1) +1 \\ f(x) &=& q(x)(x-2) +1 \\ f(x) &=& r(x)(x-3) +1 \end{eqnarray} \]

Let ...

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