A) \[\text{A}\to (s);\,B\to (r);\,C\to (q);\,D\to (p)\]
B) \[\text{A}\to (r);\,B\to (s);\,C\to (q);\,D\to (p)\]
C) \[\text{A}\to (r);\,B\to (s);\,C\to (p);\,D\to (q)\]
D) \[\text{A}\to (s);\,B\to (r);\,C\to (p);\,D\to (q)\]
Correct Answer: D
Solution :
\[5a-[3b-\{a-3\,(2a-b)\}]\] \[=5a-[3b-\{a-6a+3b\}]\] \[=5a-[3b-a+6a-3b]\,=5a\,-[5a]=0\] \[-a-[a+\{a+b-2a-(a-2b)\}\,-b]\] \[=-a-\,[a+\{a+b-2a-a+2b\}-b]\] \[=-a-\,[a+\{-2a+3b\}-b]\] \[=-a-\,[-a+2b]\,=-a+a-2b=-2b\] \[\left( \frac{1}{5}x-\frac{1}{6}y \right)\,\left( 5x+6y \right)\] \[={{x}^{2}}+\frac{6}{5}xy-\frac{5}{6}xy-{{y}^{2}}\] \[={{x}^{2}}-{{y}^{2}}+\frac{11xy}{30}\] \[{{x}^{2}}(3-5{{y}^{2}})\,+x(x{{y}^{2}}-3x)\,-2y\,(y-2{{x}^{2}}y)\] \[=3{{x}^{2}}-5{{x}^{2}}{{y}^{2}}+{{x}^{2}}{{y}^{2}}-3{{x}^{2}}-2{{y}^{2}}+4{{x}^{2}}{{y}^{2}}\] \[=-2{{y}^{2}}\]
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