A mobile company offered to pay the Indian Cricket Team as much money per run scored by the side as the total number it gets in a one-dayer against Australia. Which one of the following cannot be the total amount to be spent by the company in this deal?

Concept & Logic The company pays an amount equal to the number of runs multiplied by the number of runs. Thus, the total amount spent must be a perfect square. The question is asking us to identify the single option that is **not** a perfect square. Step-by-Step Solution * **Given**: Total amount = (Runs Scored) $\times$ (Runs Scored) = $R^2$. * We need to inspect the unit digits of the given options to rule out non-perfect squares. * A fundamental rule of mathematics: A perfect square can never end in $2$, $3$, $7$, or $8$. * Let us check the last digit of each given option: - Option (a) $21,904$ ends in $4$ (possible perfect square). - Option (b) $56,169$ ends in $9$ (possible perfect square). - Option (c) $1,01,761$ ends in $1$ (possible perfect square). - Option (d) $1,21,108$ ends in $8$ (impossible). * Since no integer squared ends in $8$, $1,21,108$ mathematically cannot be the total amount spent. Exam Strategy & Shortcut Always check the unit digits first when asked if a number is a perfect square! Perfect squares only end in $0, 1, 4, 5, 6,$ or $9$. Option (d) ends in $8$, making it instantly incorrect as a perfect square. Absolutely no calculation is required. Common Pitfall Wasting valuable exam time trying to calculate the exact square root of each large 5- or 6-digit number. Recognizing unit digit rules saves massive amounts of time on these types of questions. Final Answer **Therefore, the correct answer is 1,21,108.**