Explanation
Consider the given rational numbers,
$$\dfrac{3}{5}$$ and $$\dfrac{2}{3}$$
Now,
$$\dfrac{3\times 15}{5\times 15}$$ and $$\dfrac{2\times 25}{3\times 25}$$
$$\dfrac{45}{75}$$ and $$\dfrac{50}{75}$$
Now, rational number which does not lie between thes rational numbers is,
$$\dfrac{50}{75}$$
Hence, this is the answer.
.
$$\textbf{Step -1: Find required rational numbers.}$$
$$\text{We need five rational numbers between }1\text{ and }2.$$
$$\text{So, multiply and divide the numbers with a natural number greater or equal to } 5+1=6.$$
$$\text{Lets take }7.$$
$$1=1\times\dfrac{7}{7}=\dfrac{7}{7}$$
$$\text{and }2=2\times\dfrac{7}{7}=\dfrac{14}{7}$$
$$\text{Thus, }1\text{ and }2\text{ becomes }\dfrac{7}{7}\text{ and }\dfrac{14}{7}\text{ respectively.}$$
$$\text{Since, }7<8<9<10<11<12<13<14$$
$$\therefore 1=\dfrac{7}{7}<\dfrac{8}{7}<\dfrac{9}{7}<\dfrac{10}{7}<\dfrac{11}{7}<\dfrac{12}{7}<\dfrac{13}{7}<\dfrac{14}{7}=2$$
$$\text{Hence, five rational numbers between }1\text{ and }2\text{ are }\dfrac{8}{7},\dfrac{9}{7},\dfrac{10}{7},\dfrac{11}{7},\text{ and }\dfrac{12}{7}.$$
$$\textbf{Hence , the correct option is D.}$$
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