A) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C) If Assertion is correct but Reason is incorrect.
D) If Assertion is incorrect but Reason is correct.
Correct Answer: B
Solution :
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion. Assertion: \[\frac{{{2}^{x}}{{.2}^{3}}\times {{3}^{2x}}{{.3}^{-y}}{{.5}^{x}}{{.5}^{y}}{{.5}^{3}}\times {{6}^{y}}{{.6}^{1}}}{{{6}^{x}}{{.6}^{1}}\times {{10}^{y}}{{.10}^{3}}\times {{3}^{x}}{{.5}^{x}}}\] \[=\frac{{{2}^{x}}{{.3}^{x}}{{.3}^{x}}{{.3}^{-y}}{{.5}^{x}}{{.5}^{y}}{{.3}^{y}}{{.2}^{y}}{{.2}^{3}}\times {{5}^{3}}\times {{6}^{1}}}{{{3}^{x}}{{.2}^{x}}{{.5}^{y}}{{.2}^{y}}{{.3}^{x}}{{.5}^{x}}\times 6\times {{10}^{3}}}\] \[=\frac{125\times 6\times 8}{6\times 10\times 10\times 10}=\frac{25\times 8}{2\times 10\times 10}=\frac{25\times 4}{100}=1\] Reason: \[x={{({{8}^{2}})}^{-\frac{1}{2}}}-{{(-{{2}^{5}})}^{-\frac{4}{5}}}={{8}^{-1}}+{{2}^{-4}}\] \[=\frac{1}{8}+\frac{1}{16}=\frac{3}{16}\]
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