A) 330
B) 332
C) 333
D) 334
Correct Answer: D
Solution :
\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz\] \[=\,\,\,\,\,\frac{1}{2}\,(x+y+z)\,\,[{{(x-y)}^{2}}+{{(y-z)}^{2}}+{{(z-x)}^{2}}]\] \[=\,\,\,\,\,\frac{1}{2}\,(111+111+112)\,[{{(111-111)}^{2}}+\] \[{{(111-112)}^{2}}+{{(112-111)}^{2}}]\] \[=\,\,\,\,\,\frac{1}{2}\times 334\,\,[0+1+1]\] \[=\,\,\,\,\,\frac{1}{2}\times 334\,\times 2=\underline{\mathbf{334}}\]
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