$11^{9} + 9^{11}$ is divisible by

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answer is B.

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Detailed Solution

$11^{9} + 9^{11} = {(10 + 1)}^{9} + {(10 - 1)}^{11}$

$\begin{array}{l} =^{9} C_{0} 10^{9} +^{9} C_{1} 10^{8} + \dots + 1 +^{11} C_{0} 10^{11} -^{11} C_{1} 10^{10} + \dots + (- 1) \\ = 10 k_{1} + 1 + 10 k_{2} - 1 \\ = 10 (k_{1} + k_{2}) \end{array}$

Hence it is divisible by 10

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