Simplify .

​$$25 \div 10 - \left\{ \frac{7}{4} \times \frac{1}{3} \right\} \times \frac{6}{5} + \frac{14}{3} \times \frac{9}{10} - \left\{ \frac{1}{5} \div \frac{1}{25} \right\}$$​​

Correct option is A

Given:

​$$25 \div 10 - \left\{ \frac{7}{4} \times \frac{1}{3} \right\} \times \frac{6}{5} + \frac{14}{3} \times \frac{9}{10} - \left\{ \frac{1}{5} \div \frac{1}{25} \right\}$$​​

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:

$$25 \div 10 - \left\{ \frac{7}{4} \times \frac{1}{3} \times \frac{6}{5} + \frac{14}{3} \times \frac{9}{10} - \left( \frac{1}{5} \div \frac{1}{25} \right) \right\} \\[5pt]\implies 25 \div 10 - \left( \frac{7}{12} \times \frac{6}{5} + \frac{14}{3} \times \frac{9}{10} - 5 \right) \\[5pt]\implies \frac{25}{10} - \left( \frac{5}{2} - \frac{7}{10} + \frac{21}{5} - 5 \right) \\[5pt]\implies \frac{67}{10} - \frac{7}{10} - 5 \\[5pt]\implies \frac{67}{10} - \frac{57}{10} \\[5pt]\implies \frac{10}{10} \\[5pt]\implies 1$$​

Hence, option (a) is the correct answer.