Find the value of the following.

​$$\frac{1}{6} + \frac{2}{6} + \frac{1}{12} + \frac{2}{6} - 2$$​​

Correct option is C

Given:

​$$\frac{1}{6} + \frac{2}{6} + \frac{1}{12} + \frac{2}{6} - 2$$

Concept Used:

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

Solution:

$$\frac{1}{6} + \frac{2}{6} + \frac{1}{12} + \frac{2}{6} - 2$$

= $$\frac{1\times2 +2\times 2 + 1 \times 1 + 2 \times 2 - 2 \times 12}{12}$$

= $$\frac{2+4+1+4-24}{12}$$

= $$\frac{11-24}{12}$$

= $$\frac{-13}{12}$$​​

Thus, the correct answer is (c).