Find the no. of zeros in expression :
`(1 xx 3 xx 5 …….. 99) xx 100`

Options

A. 24
B. 12
C. 10
D. 2

Answer

To find the number of zeros in the expression \( (1 \times 3 \times 5 \times \ldots \times 99) \times 100 \), we need to determine how many times the factors 2 and 5 can be paired together, as each pair contributes to one trailing zero.

### Step-by-step Solution:

1. **Identify the components of the expression**:
The expression consists of the product of all odd numbers from 1 to 99, multiplied by 100.

2. **Count the factors of 2 in the expression**:
- The product \( 1 \times 3 \times 5 \times \ldots \times 99 \) contains only odd numbers.
- Since odd numbers do not contribute any factors of 2, the total count of factors of 2 from this part is **0**.

3. **Count the factors of 5 in the expression**:
- The product of odd numbers \( 1 \times 3 \times 5 \times \ldots \times 99 \) does not include any multiples of 5, hence it contributes **0** factors of 5.
- Now we consider the number 100. The prime factorization of 100 is \( 2^2 \times 5^2 \). This means that 100 contributes **2** factors of 2 and **2** factors of 5.

4. **Combine the factors**:
- From the odd product, we have \( 0 \) factors of 2 and \( 0 \) factors of 5.
- From 100, we have \( 2 \) factors of 2 and \( 2 \) factors of 5.

5. **Determine the number of pairs of (2, 5)**:
- The number of pairs of (2, 5) that can be formed is the minimum of the counts of factors of 2 and factors of 5.
- Here, we have \( 2 \) factors of 2 and \( 2 \) factors of 5. Thus, the number of pairs is \( \min(2, 2) = 2 \).

6. **Conclusion**:
- Therefore, the total number of trailing zeros in the expression \( (1 \times 3 \times 5 \times \ldots \times 99) \times 100 \) is **2**.

### Final Answer:
The number of zeros in the expression is **2**.