How many different
six-digit numbers are there whose three digits are even and three digits are
odd?
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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, ...
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Find the number of pairs \((m,n)\) of positive integers with \(1 \le m
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Let S be a set of n points in the plane such that any two points of S are at least 1 unit apart. Prove there is a subset T of S with at le...
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