​Simplify the following.

​$$1 + \frac{3}{7} \times [6 + 8 \times (3 - 2)] + \{(\frac{1}{5} \div \frac{7}{25}) - (\frac{3}{7} + \frac{4}{14})\}$$​​

Correct option is A

Given:

​$$1 + \frac{3}{7} \times [6 + 8 \times (3 - 2)] + \{(\frac{1}{5} \div \frac{7}{25}) - (\frac{3}{7} + \frac{4}{14})\}$$ 

Concept Used: 

BODMAS rule:

$$\begin{array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline Brackets &[],{}, () \\ \hline Orders, of & ² (power), √ (root) , of \\ \hline Division & ÷ \\ \hline Multiplication & × \\ \hline Addition & + \\ \hline Subtraction & - \\ \hline \end{array}$$​​​

Solution:

​$$1 + \frac{3}{7} \times [6 + 8 \times (3 - 2)] + \{(\frac{1}{5} \div \frac{7}{25}) - (\frac{3}{7} + \frac{4}{14})\}$$

= $$1+\frac37\times[6+8\times(1)]+[(\frac15\times\frac{25}7)-(\frac{6+4}{14})]$$

= 1 +$$\frac37$$ $$\times$$ [6 + 8] + {($$\frac57$$) - ($$\frac57$$)}

= 1 + $$\frac37$$ $$\times$$ 14

= 1 + 6

= 7