If 17200 is divided by 18, the remainder is -
A. 17
B. 16
C. 1
D. 2
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & = {17^{200}} \div 18 \cr & = {\left( {18 - 1} \right)^{200}} \div 18 \cr} $$Apply Binomial theorem
$$ = {\left( {18} \right)^{200}}{\left( { - 1} \right)^0} + {\left( {18} \right)^{199}}{\left( { - 1} \right)^1} + $$ $$..... + \, {\left( {18} \right)^1}{\left( { - 1} \right)^{199}}$$ $$ \, + \, {\left( {18} \right)^0}{\left( { - 1} \right)^{200}}$$
$$ \Rightarrow $$ Remainder always comes from last term is (18)0 (- 1)200
$$\eqalign{ & = \frac{{{{\left( {18} \right)}^0}{{\left( { - 1} \right)}^{200}}}}{{18}} \cr & = 1 \times {1^{200}} \cr & = 1 \cr & {\text{So, remainder}} = 1 \cr} $$
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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