What will come in place of question mark (?) in the following questions.
`84 xx (1)/(4) div 21^(2) + ? = (7)/(147) xx 21 - (20)/(21)`

Options

A. 2
B. 1
C. 0
D. 3

Answer

To solve the equation \( 84 \times \frac{1}{4} \div 21^2 + ? = \frac{7}{147} \times 21 - \frac{20}{21} \), we will follow the order of operations (BODMAS/BIDMAS).

### Step 1: Simplify the left side of the equation
First, we will simplify \( 84 \times \frac{1}{4} \div 21^2 \).

1. Calculate \( 21^2 \):
\[ 21^2 = 441 \]

2. Now, calculate \( 84 \times \frac{1}{4} \):
\[ 84 \times \frac{1}{4} = \frac{84}{4} = 21 \]

3. Now, perform the division:
\[ 21 \div 441 = \frac{21}{441} = \frac{1}{21} \]

So, the left side simplifies to:
\[ \frac{1}{21} + ? \]

### Step 2: Simplify the right side of the equation
Now, we will simplify the right side \( \frac{7}{147} \times 21 - \frac{20}{21} \).

1. Calculate \( \frac{7}{147} \):
\[ \frac{7}{147} = \frac{1}{21} \]

2. Now, calculate \( \frac{1}{21} \times 21 \):
\[ \frac{1}{21} \times 21 = 1 \]

3. Now, subtract \( \frac{20}{21} \):
\[ 1 - \frac{20}{21} = \frac{21}{21} - \frac{20}{21} = \frac{1}{21} \]

So, the right side simplifies to:
\[ \frac{1}{21} \]

### Step 3: Set the two sides equal
Now we have:
\[ \frac{1}{21} + ? = \frac{1}{21} \]

### Step 4: Solve for ?
To find \( ? \), we can rearrange the equation:
\[ ? = \frac{1}{21} - \frac{1}{21} = 0 \]

Thus, the value of \( ? \) is:
\[ \boxed{0} \]