The digit in the unit place of the number 200 | vedclass

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(D) The digit in the unit place of $2009!$ is $0$ because $2009!$ contains factors $2$ and $5$,making it a multiple of $10$. Now,consider the powers o

Vedclass · Accepted Answer

$9$

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(D) The digit in the unit place of $2009!$ is $0$ because $2009!$ contains factors $2$ and $5$,making it a multiple of $10$. Now,consider the powers of $3$: $3^1 = 3$ $3^2 = 9$ $3^3 = 27$ $3^4 = 81$ The unit digits follow a cycle of $4$: $(3, 9, 7, 1)$. We divide the exponent $7886$ by $4$: $7886 = 4 	imes 1971 + 2$. Thus,the unit digit of $3^{7886}$ is the same as the unit digit of $3^2$,which is $9$. Therefore,the unit digit of $2009! + 3^{7886}$ is $0 + 9 = 9$.

The digit in the unit place of the number $2009! + 3^{7886}$ is

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