Solve : 71/2 - [ 21/4 ÷ \ 11/4 - 1/2 ( 11/2 - 1/3 - 1/6 ) \ ] = ?

Answer: Option B

$$=7\frac{1}{2}-$$  $$\left[2\frac{1}{4}÷\left\{1\frac{1}{4}-\frac{1}{2}\left(1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]$$
$$=\frac{15}{2}-$$   $$\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]$$
$$=\frac{15}{2}-$$   $$\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{9-2-1}{6}\right)\right\}\right]$$
$$\begin{array}{rl}& =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\right\}\right]\\ & =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5-2}{4}\right\}\right]\\ & =\frac{15}{2}-\left[\frac{9}{4}÷\frac{3}{4}\right]\\ & =\frac{15}{2}-\left[\frac{9}{4}\times \frac{4}{3}\right]\\ & =\frac{15}{2}-3\\ & =\frac{15-6}{2}\\ & =\frac{9}{2}\\ & =4\frac{1}{2}\end{array}$$