Monday, 26 August 2019

PRMO August 25, 2019 (Second Round) Answer Key

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Location: India

PRMO August 25, 2019 (Second Round) Question Paper

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Location: India

PRMO August 11, 2019 Answer Key

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Location: Agartala, Tripura, India

PRMO 2019 examination held on August 11, 2019

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Location: India

Sunday, 19 May 2019

ISI 2019 SOLUTIONS

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Two solid cylinders are mathematically similar. The sum of their heights is 1. The sum of their surface areas is 8π. The sum of their volumes is 2π. Find all possibilities for the dimensions of each cylinder.


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Ares multiplies two integers which differ by 9. Grace multiplies two integers which differ by 6. They obtain the same product T. Determine all possible values of T.


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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 all polynomial \(P(x)\) with degree \(\leq n\) and non negative coefficients such that \[P(x)P(\frac{1}{x})\leq P(1)^2\]for all positiv...
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    Find the number of ways \(66\) identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile th...
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