In the questions, select the pair in which the numbers are similarly related as in the given pair.
17:290 :: ?: ?

Options

A. `5:26`
B. `7:345`
C. `11 : 120`
D. `7:51`

Explanation

To solve the problem, we need to identify the relationship between the numbers in the given pair (17:290) and then apply the same relationship to find the missing pair.

### Step-by-Step Solution:

1. **Identify the relationship in the given pair (17:290)**:
- We need to find a mathematical operation that relates 17 to 290.
- Calculate the square of 17:
\[ 17^2 = 289 \]
- Now, add 1 to this result:
\[ 289 + 1 = 290 \]
- Thus, the relationship can be expressed as:
\[ \text{If } x = 17, \text{ then } x^2 + 1 = 290 \]

2. **Apply the same relationship to find the missing pair**:
- We need to find a number \( y \) such that \( y^2 + 1 \) gives us a specific result.
- We will check the options provided to find a pair that follows the same pattern.

3. **Check the options**:
- **Option 1: 5:26**
- Calculate \( 5^2 + 1 \):
\[ 5^2 = 25 \quad \Rightarrow \quad 25 + 1 = 26 \]
- This option follows the same pattern.

- **Option 2: 7:345**
- Calculate \( 7^2 + 1 \):
\[ 7^2 = 49 \quad \Rightarrow \quad 49 + 1 = 50 \]
- This does not match 345.

- **Option 3: 11:120**
- Calculate \( 11^2 + 1 \):
\[ 11^2 = 121 \quad \Rightarrow \quad 121 + 1 = 122 \]
- This does not match 120.

- **Option 4: 7:51**
- Calculate \( 7^2 + 1 \):
\[ 7^2 = 49 \quad \Rightarrow \quad 49 + 1 = 50 \]
- This does not match 51.

4. **Conclusion**:
- The only option that follows the same pattern as the original pair (17:290) is **Option 1: 5:26**.

### Final Answer:
The correct answer is **5:26**.