A) \[\frac{5}{7}<\frac{7}{9}<\frac{9}{11}<\frac{11}{13}\]
B) \[\frac{11}{13}<\frac{9}{11}<\frac{7}{9}<\frac{5}{7}\]
C) \[\frac{5}{7}<\frac{11}{13}<\frac{7}{9}<\frac{9}{11}\]
D) \[\frac{5}{7}<\frac{9}{11}<\frac{11}{13}<\frac{7}{9}\]
Correct Answer: A
Solution :
We have, \[\frac{5}{7},\frac{7}{9},\frac{9}{11},\frac{11}{13}\] L.C.M. of 7,9, 11, 13=9009 \[\therefore \frac{5}{7}=\frac{5\times 9\times 11\times 13}{7\times 9\times 11\times 13}=\frac{6435}{9009}\] \[\frac{7}{9}=\frac{7\times 7\times 11\times 13}{9\times 7\times 11\times 13}=\frac{7007}{9009}\] \[\frac{9}{11}=\frac{9\times 7\times 9\times 13}{11\times 7\times 9\times 13}=\frac{7371}{9009}\] \[\frac{11}{13}=\frac{11\times 7\times 9\times 11}{13\times 7\times 9\times 11}=\frac{7623}{9009}\] \[\because \frac{6435}{9009}<\frac{7007}{9009}<\frac{7371}{9009}<\frac{7623}{9009}\] \[\therefore \frac{5}{7}<\frac{7}{9}<\frac{9}{11}<\frac{11}{13}\].
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