A) \[\frac{6}{5}\]
B) \[\frac{2}{15}\]
C) \[\frac{18}{5}\]
D) \[\frac{12}{5}\]
Correct Answer: D
Solution :
\[\cos 2x(1-\cos 2x)=0\] \[\cos 2x=1\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\,\,\,\,\,\,\cos 2x=0\] \[\therefore \,\,x=n\pi \,\,\,\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\,\,x=(2n-1)\,\frac{\pi }{4}\] 5 mole of FeS is oxidised by 9 moles of \[0,\,\pi ,\,2\pi \,\,\,\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\frac{\pi }{4},\,\frac{3\pi }{4},\,\frac{5\pi }{4},\,\frac{7\pi }{4}=7\pi \]. \[\Delta =0\] 2 mole of FeS is oxidised by ? moles of \[\Rightarrow \,\left| \,\begin{matrix} k & 1 & 1 \\ 1 & -k & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right|\,=0\Rightarrow \,{{k}^{2}}=1\,\Rightarrow \,k=\pm \,1\] \[=\frac{-3}{4}\] \[y=\frac{-3}{4}\,x+C\] \[C=\sqrt{32\times {{\left( \frac{-3}{4} \right)}^{2}}+18}\,=\sqrt{18+18}=6\] 6 mole of ferrous oxalate is oxidise by 3 moles of \[\therefore \,\,y=\frac{-3}{4}\,x+6\,\Rightarrow \,\,3x+4y\,=24\]. \[\Delta AOB=\frac{1}{2}\,(8)(6)\,=24\] 3 mole of ferrous oxalate is oxidise by \[=\left| \frac{1}{6}[\overline{AD},\,\overline{BD},\,\overline{CD}] \right|\] moles of \[\overline{AD}\,=-6\hat{k},\,\overline{BD}=6\hat{i},\,\overline{CD}=6\hat{j}\]. \[\therefore \,\,V=\frac{1}{6}\times 216\,[\,\hat{i}\,\hat{j}\,\hat{k}]\] \[n=10;\,\,\,p=\frac{1}{2};\,\,\,q=\frac{1}{2}\]
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