A) 1
B) 3
C) 7
D) 9
Correct Answer: C
Solution :
[c] \[{{(1073)}^{71}}-m={{(73+1000)}^{71}}-m\] \[={{\,}^{71}}{{C}_{0}}{{(73)}^{71}}+{{\,}^{71}}{{C}_{1}}{{(73)}^{70}}(1000)+{{\,}^{71}}{{C}_{2}}{{(73)}^{69}}\] \[{{(1000)}^{2}}+.....+{{\,}^{71}}{{C}_{71}}{{(1000)}^{71}}-m\] Above will be divisible by 10 if \[^{71}{{C}_{0}}{{(73)}^{71}}\] is divisible by 10 Now \[^{71}{{C}_{0}}{{(73)}^{71}}={{(73)}^{70}}.73={{({{73}^{2}})}^{35}}.73\] The last digit of \[{{73}^{2}}\] is 9, so the last digit of \[{{\left( {{73}^{2}} \right)}^{35}}\] is 9. \[\therefore \] Last digit of \[{{\left( {{73}^{2}} \right)}^{35}}.73\] is 7 Hence, the minimum positive integral value of m is 7, so that is divisible by 10.
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