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Does anybody here know that at any time instant there exist two antipodal points on the earth's equator that have the same temperature? The proof of this fact does ...

There are four boxes. Each contains 2 balls. The first box has a red and a white ball in it. The remaining three boxes each have two white balls in ...

Consider a circuit that consists of an ideal inductor of inductance \(L\), an ideal capacitor of capacitance \(C\) and a linear resistor of resistance \(R\) in series.

Let the capacitor ...

Find the value of

\[ \displaystyle I=\int_{C} x^{2}dy - y^{2}dx \]

where ...

A circuit is built by connecting \(1\ \Omega\) wires in a pattern of triangles, as shown above. Point \(A\) is the common vertex of all triangles, and point \(B\) is ...

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