A) \[\sqrt{5}:1\]
B) 5 : 2
C) 3 : 5
D) 1 : 2
Correct Answer: A
Solution :
\[y=\frac{a+b{{x}^{3/2}}}{{{x}^{5/4}}}\] Þ \[{y}'=\frac{\frac{3}{2}b{{x}^{7/4}}-\frac{5}{4}(a+b{{x}^{3/2}})\,{{x}^{1/4}}}{{{x}^{5/2}}}\] \[\because \] \[{y}'=0\] at \[x=5\] \ \[\frac{3}{2}b{{x}^{7/4}}-\frac{5}{4}(a+b{{x}^{3/2}}){{x}^{1/4}}=0\] at \[x=5\] Þ \[6b{{x}^{3/2}}-5(a+b{{x}^{3/2}})=0\]at \[x=5\] Þ \[b{{x}^{3/2}}=5a\]at \[x=5\] Þ \[b{{(5)}^{3/2}}=5a\] Þ \[\frac{a}{b}=\frac{{{5}^{3/2}}}{5}\] Þ \[a:b=\sqrt{5}:1\].
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