| Column - I | Column - II |
| P. \[(3{{x}^{2}}-4xy)\] \[(3{{x}^{2}}-3xy)\] | (i) \[12{{x}^{2}}+53xy+55{{y}^{2}}\] |
| Q. \[({{x}^{2}}+4)\] \[(9{{x}^{2}}+9y)\] | (ii) \[9{{x}^{2}}+2{{y}^{4}}+11x{{y}^{2}}\] |
| R. \[(3x+5y)\] \[(4x+11y)\] | (iii) \[9{{x}^{4}}-21{{x}^{3}}y+12{{x}^{2}}{{y}^{2}}\] |
| S. \[({{y}^{2}}+x)\] \[(2{{y}^{2}}+9x)\] | (iv) \[9{{x}^{4}}+45{{x}^{2}}y+36{{y}^{2}}\] |
A) P \[\to \](iii); Q \[\to \](iv); R\[\to \](i); S \[\to \](ii)
B) P\[\to \](ii); Q\[\to \](i); R\[\to \](iv); S\[\to \](iii)
C) P\[\to \](iv); Q\[\to \](iii); R\[\to \](i): S\[\to \](ii)
D) P\[\to \](iii); Q\[\to \](ii); R\[\to \](iv); S\[\to \](i)
Correct Answer: A
Solution :
\[P.(3{{x}^{2}}-4xy)(3{{x}^{2}}-3xy)\] \[=9{{x}^{4}}-9{{x}^{3}}y-12{{x}^{3}}y+12{{x}^{2}}{{y}^{2}}\] \[=9{{x}^{4}}-21{{x}^{3}}y+12{{x}^{2}}{{y}^{2}}\] \[\text{Q}\text{. (}{{\text{x}}^{2}}+4y)(9{{x}^{2}}+9y)\] \[=9{{x}^{4}}+9{{x}^{2}}y+36{{x}^{2}}y+36{{y}^{2}}=9{{x}^{4}}+45{{x}^{2}}y+36{{y}^{2}}\] \[\text{R}\text{.(3x+5y)(4x+11y)}\] \[\text{=12}{{\text{x}}^{2}}+33xy+20xy+55{{y}^{2}}=12{{x}^{2}}+53xy+55{{y}^{2}}\] \[\text{S}\text{.(}{{\text{y}}^{2}}+x)(2{{y}^{2}}+9x)\] \[=2{{y}^{4}}+9x{{y}^{2}}+2x{{y}^{2}}+9{{x}^{2}}=2{{y}^{4}}+11x{{y}^{2}}+9{{x}^{2}}\]
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