| Column-l | Column-ll |
| (P) \[({{x}^{2}}+5)\,({{x}^{3}}+3)+5\] | (1) \[-{{x}^{3}}-3{{x}^{2}}+3x+2\] |
| (Q) \[\left( \frac{-10}{3}x{{y}^{3}} \right)\times \left( \frac{6}{5}{{x}^{3}}y \right)\] | (2) \[-{{x}^{2}}+{{x}^{2}}+3x-6\] |
| (R) \[({{x}^{3}}-{{x}^{2}}-x-2)-\]\[(2{{x}^{3}}+2{{x}^{2}}-4x-4)\] | (3) \[{{x}^{5}}+5{{x}^{3}}+3{{x}^{2}}+20\] |
| (S) \[({{x}^{3}}-{{x}^{2}}-x-2)+\]\[(2{{x}^{2}}-2{{x}^{3}}+4x-4)\] | (4) \[-4{{x}^{4}}{{y}^{4}}\] |
A) (P)\[\to \](1), (Q)\[\to \](2), (R)\[\to \](3), (S)\[\to \](4)
B) (P)\[\to \](3), (Q)\[\to \](4), (R)\[\to \](1), (S)\[\to \](2)
C) (P)\[\to \](4), (Q)\[\to \](1), (R)\[\to \](3), (S)\[\to \](2)
D) (P)\[\to \](3), (Q)\[\to \](4), (R)\[\to \](2), (S)\[\to \] (1)
Correct Answer: B
Solution :
\[(P)\,({{x}^{2}}+5)\,({{x}^{3}}+3)+5\] \[={{x}^{5}}+3{{x}^{2}}+5{{x}^{3}}+15+5\] \[={{x}^{5}}+5{{x}^{3}}+3{{x}^{2}}+20\] (Q) \[\left( \frac{-10}{3}\times x{{y}^{3}} \right)\times \left( \frac{6}{5}{{x}^{3}}y \right)\] \[=\left( \frac{-10}{3}\times \frac{6}{5} \right){{x}^{4}}{{y}^{4}}=-4{{x}^{4}}{{y}^{4}}\] (R) \[({{x}^{3}}-{{x}^{2}}-x-2)-(2{{x}^{3}}+2{{x}^{2}}-4x-4)\] \[={{x}^{3}}-{{x}^{2}}-x-2-2{{x}^{3}}-2{{x}^{2}}+4x+4\] \[=-{{x}^{3}}-3{{x}^{2}}+3x+2\] (S) \[({{x}^{3}}-{{x}^{2}}-x-2)+(2{{x}^{2}}-2{{x}^{3}}+4x-4)\] \[={{x}^{3}}-{{x}^{2}}-x-2+2{{x}^{2}}-2{{x}^{3}}+4x-4\] \[=-{{x}^{3}}+{{x}^{2}}+3x-6\]
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