Browse Questions

# The digit at units place in the number $17^{1995}+11^{1995}-7^{1995}$ is

$\begin{array}{1 1}(A)\;0\\(B)\;1\\(C)\;2\\(D)\;3\end{array}$

Toolbox:
• $(a+b)^n=nC_0a^nb^0+nC_1a^{n-1}b^1.......nC_n a^0b^n$
$17^{1995}+11^{1995}-7^{1995}$
$\Rightarrow (7+10)^{1995}+(1+10)^{1995}-7^{1995}$
$\Rightarrow 7^{1995}+1995C_17^{1994}.10+.....1995C_{1995}10^{1995})+(1+1995C_110+.......1995C_{1995}10^{1995})-7^{1995}$
$\Rightarrow 1995C_17^{1994}.10+......10^{1995})+(1995C_110+.....+10^{1995})$
$\Rightarrow$=(some multiple of 10)+1
$\therefore$ Digits at the unit's lace =1
Hence (B) is the correct answer.