Sunday 19 May 2019
A list of five two-digit positive integers is written in increasing order on a blackboard. Each of the five integers is a multiple of 3, and each digit 0,1,2,3,4,5,6,7,8,9 appears exactly once on the blackboard. In how many ways can this be done? Note that a two-digit number cannot begin with the digit 0.
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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, &a...
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Find the number of pairs \((m,n)\) of positive integers with \(1 \le m < n \le 30\) such that there exists a real number \(x\) satisfying...
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