Simplify the following.
294 ÷ [10 ÷ 5 × {11 + 12 − (8 + 5 − (10 + 1))}]

Correct Option/Answer:
The correct option is 7.

Step-by-Step Explanation:

To simplify the given numerical expression, we follow the BODMAS / PEMDAS rule, which states the order of operations as follows:
1. Brackets (Innermost first: Parentheses ( ), Curly Brackets { }, Square Brackets [ ])
2. Orders (Exponents, Roots)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

The given expression is:

$294÷[10÷5\times \{11+12-(8+5-(10+1\left)\right)\left\}\right]$

Step 1: Simplify the innermost round brackets (10 + 1)

$10+1=11$

Substitute this back into the expression:

$=294÷[10÷5\times \{11+12-(8+5-11)\left\}\right]$

Step 2: Simplify the remaining round brackets (8 + 5 − 11)

First perform addition, then subtraction inside the round brackets:

$8+5=13$

$13-11=2$

Substitute this back into the expression:

$=294÷[10÷5\times \{11+12-2\left\}\right]$

Step 3: Simplify the curly brackets {11 + 12 − 2}

$11+12=23$

$23-2=21$

Substitute this back into the expression:

$=294÷[10÷5\times 21]$

Step 4: Simplify inside the square brackets [10 ÷ 5 × 21]

Working from left to right, perform the division first:

$10÷5=2$

Next, perform the multiplication:

$2\times 21=42$

Now the expression reduces to:

$=294÷42$

Step 5: Perform the final division

$294÷42=7$

Thus, the simplified value is 7.