Simplify the given expression.

​​$$[13 - (-2) \times \{6 - (7 - 3)\}] \div[4 \times \{5 + (-2) \times (-6) \}]$$​​

Correct option is A

Given :

Expression : $$[13 - (-2) \times \{6 - (7 - 3)\}] \div[4 \times \{5 + (-2) \times (-6) \}]$$  

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 : 

=  $$[13 - (-2) \times \{6 - (7 - 3)\}] \div[4 \times \{5 + (-2) \times (-6) \}]$$

= [13 - ( - 2) $$\times$$ { 2 }] $$\div$$ [4 $$\times$$ {17}]

= $$\frac{13 + 4}{4\times 17}$$​​

=  $$\frac {17}{4\times17}= \frac{1}{4}$$

The correct answer is option (a) $$\frac{1}{4}$$​​