Simplify the given expression.

$\left[\right\{9\times 81+(142÷2)\}+350-155+5]÷\left[\right(25\times 25)-125]$

The correct option is 2.

To simplify the given expression, we follow the order of operations (BODMAS/PEMDAS rule), which dictates performing operations in the following order: Parentheses/Brackets, Order/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

The expression to simplify is:
$\left[\right\{9\times 81+(142÷2)\}+350-155+5]÷\left[\right(25\times 25)-125]$

Step 1: Simplify the innermost parentheses.
Inside the first main term, simplify the division in the parentheses:
$142÷2=71$
Inside the second main term, simplify the multiplication in the parentheses:
$25\times 25=625$

Substituting these values back into the expression gives:
$\left[\right\{9\times 81+71\}+350-155+5]÷[625-125]$

Step 2: Simplify the curly braces and the right bracket.
First, evaluate the expression inside the curly braces:
$\{9\times 81+71\}$
Perform the multiplication first:
$9\times 81=729$
Then add 71:
$729+71=800$
Next, evaluate the subtraction inside the rightmost bracket:
$625-125=500$

Now, substitute these simplified parts back:
$[800+350-155+5]÷500$

Step 3: Simplify the expression inside the remaining bracket.
Perform the operations inside the left bracket from left to right:
$800+350=1150$
$1150-155=995$
$995+5=1000$

The expression now simplifies to:
$1000÷500$

Step 4: Perform the final division.
$1000÷500=2$

Thus, the simplified value of the expression is 2.