In each of the following questions , three statements of numbers following same rules are given . Find the rule and accordingly find the value of the number ?
`2 -:3 = 89, 3-:4 = 2716 , 4-:3` = `649` , then `1 -:2 =?`

Options

A. 21
B. 42
C. 14
D. 81

Explanation

To solve the problem, we need to identify the pattern or rule that applies to the given statements. Let's analyze the provided statements step by step.

### Step 1: Analyze the first statement
The first statement is:
\[ 2 -: 3 = 89 \]

From this, we can see:
- The first number is 2.
- The second number is 3.
- The result is 89.

### Step 2: Identify the components of the result
We notice that:
- The first part of the result (8) seems to be related to the first number (2).
- The second part of the result (9) seems to be related to the second number (3).

### Step 3: Find the mathematical relationship
- The first part (8) can be obtained by calculating \(2^3\) (2 cubed).
- The second part (9) can be obtained by calculating \(3^2\) (3 squared).

Thus, we can summarize this as:
\[ 2 -: 3 = 2^3 \, (8) \, \text{and} \, 3^2 \, (9) \]
So, the result is \(89\).

### Step 4: Analyze the second statement
The second statement is:
\[ 3 -: 4 = 2716 \]

Following the same pattern:
- The first part (27) can be obtained by calculating \(3^3\) (3 cubed).
- The second part (16) can be obtained by calculating \(4^2\) (4 squared).

Thus, we can summarize this as:
\[ 3 -: 4 = 3^3 \, (27) \, \text{and} \, 4^2 \, (16) \]
So, the result is \(2716\).

### Step 5: Analyze the third statement
The third statement is:
\[ 4 -: 3 = 649 \]

Following the same pattern:
- The first part (64) can be obtained by calculating \(4^3\) (4 cubed).
- The second part (9) can be obtained by calculating \(3^2\) (3 squared).

Thus, we can summarize this as:
\[ 4 -: 3 = 4^3 \, (64) \, \text{and} \, 3^2 \, (9) \]
So, the result is \(649\).

### Step 6: Apply the rule to find \(1 -: 2\)
Now, we need to find:
\[ 1 -: 2 = ? \]

Using the same pattern:
- The first part will be \(1^3\) (1 cubed), which equals 1.
- The second part will be \(2^2\) (2 squared), which equals 4.

Thus, the result will be:
\[ 1 -: 2 = 1^3 \, (1) \, \text{and} \, 2^2 \, (4) \]
So, the result is \(14\).

### Final Answer:
\[ 1 -: 2 = 14 \]