Which one of the following cannot be explained on the basis of Mendel's Law of Dominance?

Options

A. The discrete unit controlling a particular character is called a factor
B. Out of one pair of factors one is dominant, and the other is recessive
C. Alleles do not show any blending and both the characters recover as such in `F_2` generation
D. Factors occur in pairs

Answer

To solve the question "Which one of the following cannot be explained on the basis of Mendel's Law of Dominance?", we will analyze each option in relation to Mendel's principles.

### Step-by-Step Solution:

1. **Understand Mendel's Law of Dominance**:
- Mendel's Law of Dominance states that in a heterozygous individual (having two different alleles for a trait), one allele (the dominant allele) will express itself, while the other allele (the recessive allele) will not be expressed.

2. **Evaluate Each Option**:
- **Option 1**: "The discrete unit controlling a particular character is called a vector."
- This statement does not relate to Mendel's Law of Dominance. The term "vector" is not typically used in Mendelian genetics; instead, the term "allele" is used. However, this option does not contradict Mendel's principles directly.

- **Option 2**: "Out of one pair of vectors, one is dominant and the other is recessive."
- This statement directly aligns with Mendel's Law of Dominance, as it describes the relationship between dominant and recessive alleles.

- **Option 3**: "Alleles do not show any blending and both the characters recover as such in F2 generation."
- This statement refers to the concept of segregation and independent assortment, which is explained by Mendel's Law of Segregation and Law of Independent Assortment, not specifically by the Law of Dominance. This option highlights that alleles remain distinct and do not blend, which is not a focus of the Law of Dominance.

- **Option 4**: "Factors occur in pairs."
- This statement is also consistent with Mendel's principles, as it reflects the idea that alleles (factors) exist in pairs (one from each parent).

3. **Conclusion**:
- Based on the analysis, **Option 3** ("Alleles do not show any blending and both the characters recover as such in F2 generation") cannot be explained solely by Mendel's Law of Dominance. It requires an understanding of other laws of inheritance.

### Final Answer:
**Option 3**: Alleles do not show any blending and both the characters recover as such in F2 generation.