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Let `X`be the setconsisting of the first 2018 terms of the arithmetic progression `1, 6, 11 , ddot,`and `Y`be the setconsisting of the first 2018 terms of the arithmetic progression `9, 16 , 23 , ddot`. Then, thenumber of elements in the set `XuuY`is _____. |
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Answer» Correct Answer - 3748 Here `X={1,6,11, …, 10086}" "[because a_(n)=a+(n-1)d]` and `Y={9,16,23, …, 14128}` `X cap Y=[16,51,86, …}` `t_(n) " of " X cap Y` is less than or equal to 10086 `therefore t_(n)=16+(n-1)35 le 10086 rArr n le 288.7` `therefore n=288` `because n (X cap Y) =n(X) +n(Y)-n(X cap Y)` ` therefore n(X cap Y)=2018 +2018+288=3748` |
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