Find the value of  $$[(42 ÷ 7) × \{(\frac{42}{3}) + (\frac{19}{4}) × (8 − 4)\}]$$​​

Correct option is C

Given: 

$$[(42 ÷ 7) × \{(\frac{42}{3}) + (\frac{19}{4}) × (8 − 4)\}]$$​

Concept Used:  

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

Solution: 

$$\begin{aligned}& \left[ \frac{42}{7} \times \left\{ \frac{42}{3} + \frac{19}{4} \times (8 - 4) \right\} \right] \\&= \left[ 6 \times \left\{ 14 + \frac{19}{4} \times 4 \right\} \right] \quad \text{(since } 42 \div 7 = 6, \quad 42 \div 3 = 14, \quad 8-4=4 \text{)} \\&= \left[ 6 \times (14 + 19) \right] \quad \text{(since } \frac{19}{4} \times 4 = 19 \text{)} \\&= 6 \times 33 \\&= 198\end{aligned}$$​