Permutations & Combinations · JEE Advanced previous year questions

2023 1 question

1. Q102023 · 4 Jun 2023 · Paper 1· Numerical answer

   Let $7\stackrel{r}{\overbrace{5\cdots 5}}7$ denote the $(r+2)$ digit number where the first and the last digits are 7 and the remaining $r$ digits are 5. Consider the sum $S=77+757+7557+\cdots +7\stackrel{98}{\overbrace{5\cdots 5}}7$. If $S=\frac{7\stackrel{99}{\overbrace{5\cdots 5}}7+m}{n}$, where $m$ and $n$ are natural numbers less than 3000, then the value of $m+n$ is ____.

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   Answer: 1219