A) \[1\]
B) \[0\]
C) \[-1\]
D) \[\frac{1}{2}\]
Correct Answer: C
Solution :
Expression \[=\frac{\sqrt{({{x}^{2}}+{{y}^{2}}+z)(x+y-3z)}}{\sqrt[3]{x{{y}^{3}}{{z}^{2}}}}\] Putting\[x=1,\,\,y=-3,\,\,z=-1\] \[=\frac{\sqrt{(1+9-1)(1-3+3)}}{\sqrt[3]{1\times 27\times 1}}\] \[=\frac{3}{-3}=-1\] Note: Original question is: \[\sqrt{({{x}^{2}}+{{y}^{2}}+z)(x-y-3z)}\div \sqrt[3]{x{{y}^{3}}{{z}^{2}}}\] which gives answer\[=-\sqrt{7}\] which is not in options.
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