A) \[\frac{5}{2}{{x}^{2}}+\frac{11}{30}x+2\]
B) \[\frac{3}{2}{{x}^{2}}+\frac{30}{11}x+3\]
C) \[\frac{5}{2}{{x}^{2}}+\frac{13}{30}x+1\]
D) \[\frac{3}{4}{{x}^{2}}+\frac{12}{11}x+5\]
Correct Answer: A
Solution :
Required sum \[=\left( 5{{x}^{2}}-\frac{1}{3}x+\frac{5}{2} \right)+\left( -\frac{1}{2}{{x}^{2}}+\frac{1}{2}x-\frac{1}{3} \right)\] \[+\left( -2{{x}^{2}}+\frac{1}{5}x-\frac{1}{6} \right)\] \[=5{{x}^{2}}-\frac{1}{2}{{x}^{2}}-2{{x}^{2}}-\frac{1}{3}x+\frac{1}{2}x+\frac{1}{5}x\] \[+\frac{5}{2}-\frac{1}{3}-\frac{1}{6}\] [Collecting like terms] \[=\left( 5-\frac{1}{2}-2 \right){{x}^{2}}+\left( -\frac{1}{3}+\frac{1}{2}+\frac{1}{5} \right)x\] \[+\left( \frac{5}{2}-\frac{1}{3}-\frac{1}{6} \right)\] \[=\left( \frac{10-1-4}{2} \right){{x}^{2}}+\left( \frac{-10+15+6}{30} \right)x\] \[+\left( \frac{15-2-1}{6} \right)\] \[=\frac{5}{2}{{x}^{2}}+\frac{11}{30}x+2\]
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