Question : Simplify the following expression.
$\frac{7}{10} \div \frac{3}{7}$ of $\left(2 \frac{3}{10}+2 \frac{3}{5}\right)+\frac{1}{5} \div 1 \frac{2}{5}-\frac{2}{7}$

Option 1: $-\frac{4}{21}$

Option 2: $\frac{5}{21}$

Option 3: $\frac{4}{21}$

Option 4: $-\frac{5}{21}$

Question : Let $x=\frac{5 \frac{3}{4}-\frac{3}{7} \times 15 \frac{3}{4}+2 \frac{2}{35} \div 1 \frac{11}{25}}{\frac{3}{4} \div 5 \frac{1}{4}+5 \frac{3}{5} \div 3 \frac{4}{15}}$. When $y$ is added to $x$, the result is $\frac{7}{13}$. What is the value of $y$?

Option 1: $\frac{1}{13}$

Option 2: $\frac{9}{13}$

Option 3: $\frac{2}{13}$

Option 4: $\frac{4}{13}$

Question : If $3\sqrt{\frac{1-a}{a}}+9=19-3\sqrt{\frac{a}{1-a}};$ then, what is the value of $a?$

Option 1: $\frac{3}{10}$ and $\frac{7}{10}$

Option 2: $\frac{1}{10}$ and $\frac{9}{10}$

Option 3: $\frac{2}{5}$ and $\frac{3}{5}$

Option 4: $\frac{1}{5}$ and $\frac{4}{5}$

Question : Find the fraction which bears the same ratio to $\frac{1}{27}$ that $\frac{3}{7}$ does to $\frac{5}{9}$.

Option 1: $\frac{5}{9}$

Option 2: $\frac{1}{35}$

Option 3: $\frac{45}{7}$

Option 4: $\frac{7}{45}$

Question :  The value of $1 \frac{3}{4}+1 \frac{5}{7} \div 2 \frac{3}{7} \times 2 \frac{3}{7}=$?

Option 1: $1 \frac{11}{28}$

Option 2: $2 \frac{13}{28}$

Option 3: $3 \frac{13}{28}$

Option 4: $4 \frac{23}{28}$