# The digits at unit’s place in the number $17^{1995} + 11^{1995} – 7^{1995}$ is

Q: The digits at unit’s place in the number $\large 17^{1995} + 11^{1995} – 7^{1995}$ is

(A) 0

(B) 1

(C) 2

(D) 3

Sol: $\large 17^{1995} + 11^{1995} – 7^{1995}$

$\large = (7+10)^{1995} + (1+10)^{1995} – 7^{1995}$

$\large = [ 7^{1995} + 1995_{C_1} 7^{1994} 10^1 + 1995_{C_2} 7^{1993} 10^2 + ……+ 1995_{C_{1995}} 10^{1995}]$

$\large + [ 1995_{C_0} + 1995_{C_1} 10^1 + 1995_{C_2} 10^2 + ……+ 1995_{C_{1995}} 10^{1995} ] -7^{1995}$

$\large [ 1995_{C_1} 7^{1994} 10^1 + ….+ 10^{1995}]$ $\large + [1995_{C_1} 10^1 + ….+ 1995_{C_{1995}} 10^{1995} ] + 1$

= a multiple of 10 + 1

Thus, the unit’s place digits is 1

Hence (B) is the correct answer.