Question

The digit at thousand place in the expansion of ${251}^{1000}$ is

• A. $0$
• B. $1$
• C. $5$
• D. $6$

Answer 1

The correct option is A $0$

Digit at thousand place in the expansion of ${251}^{1000}$,

For knowing the thousand place, we will have to divide the number by 1000 and then the unit digit of the quotient would be the required answer.

$\Rightarrow {(1+251)}^{1000}=1+{{}^{1000}C}_{1}250+{{}^{1000}C}_2{\left(250\right)}^2......$

We can see that from 2nd term, all the terms equate to numbers with at least four zeroes in the end.

That means ${251}^{1000}$ will be like

$=(...........)0001$

Implies that the thousand place will be $0$.