Choose the best alternatives in place of ? out of the four given alternatives (a), (b), (c), (d).
B : 16 :: D : ?

Options

A. 120
B. 150
C. 200
D. 256

Explanation

To solve the analogy problem B : 16 :: D : ?, we need to find the relationship between the letters and the numbers.

### Step-by-Step Solution:

1. **Identify the Place Value of B**:
- The letter B is the 2nd letter of the alphabet.
- Therefore, the place value of B is 2.

2. **Determine the Relationship**:
- The number associated with B is 16.
- We can express 16 as \(2^4\) (since \(2 \times 2 \times 2 \times 2 = 16\)).
- This means that the relationship is that the number is the place value of the letter raised to the power of 4.

3. **Identify the Place Value of D**:
- The letter D is the 4th letter of the alphabet.
- Therefore, the place value of D is 4.

4. **Apply the Same Relationship**:
- Now, we need to find the number that corresponds to D using the same relationship.
- We take the place value of D (which is 4) and raise it to the power of 4:
- \(4^4 = 4 \times 4 \times 4 \times 4 = 256\).

5. **Conclusion**:
- Therefore, the number that corresponds to D is 256.
- The answer is option (d) 256.