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.