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← JEE Main 2022 · 26 Jun · Shift 1
MathematicsInteger+4 / -1Question 29 of 90

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 29

Let A=∑i=110∑j=110min⁡{i,j}A=\displaystyle\sum_{i=1}^{10}\sum_{j=1}^{10}\min\{i,j\} and B=∑i=110∑j=110max⁡{i,j}B=\displaystyle\sum_{i=1}^{10}\sum_{j=1}^{10}\max\{i,j\}. Then A+BA+B is equal to ______.

Answer and worked solution

Official answer: 1100

Combine. min⁡{i,j}+max⁡{i,j}=i+j\min\{i,j\}+\max\{i,j\}=i+j.

Sum. ∑i,j(i+j)=2×10×55=1100\displaystyle\sum_{i,j}(i+j)=2\times10\times55=1100.

Answer: 1100