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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Step $1$: The unit digit of $2009!$ is $0$ because $2009!$ contains factors $2$ and $5$, making it a multiple of $10$.Step $2$: Consider the power

Vedclass · Accepted Answer

$9$

Vedclass · Answer

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

Similar Questions

If $n$ is an integer with $0 \leq n \leq 11$,then the minimum value of $n!(11-n)!$ is attained when a value of $n$ equals to

The number of $4$-digit numbers that are not divisible by $5$ is:

The total number of ways in which $5$ balls of different colours can be distributed among $3$ persons so that each person gets at least one ball is

The tens digit of the sum $1! + 4! + 7! + 10! + 12! + 13! + 16! + 17!$ is divisible by which of the following?

If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero,then $n$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module