Question : $4^{11}+4^{12}+4^{13}+4^{14}$ is divisible by:
Option 1: 7
Option 2: 14
Option 3: 17
Option 4: 9
Correct Answer: 17
Solution : Given: $4^{11}+4^{12}+4^{13}+4^{14}$ = $4^{11}(1+4+4^2+4^3)$ = $4^{11}(85)$ Since 85 is divisible by 17, Therefore, the above expression is also divisible by 17. Hence, the correct answer is 17.
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