Read the following statements carefully and select the correct ones.
() Alfred wallace, a naturalist who worked in Malay Archipelago had also come to similar conclusions as Darwin around the same time.
(ii) August Weismann by carefull experimentation demonstrated that life comes only from pre-existing life.
(iii) The organs which have the same fundamental structure but are different in functions are called homologous organs.
(iv) Rate of appearance of new form is inversely proportional to life spain of organism.

Options

A. i and iii
B. i and ii
C. ii and iv
D. iii and iv

Explanation

To solve the question, we need to analyze each statement carefully and determine whether they are correct or incorrect based on biological principles and historical facts.

### Step-by-Step Solution:

1. **Statement (i)**: "Alfred Wallace, a naturalist who worked in Malay Archipelago had also come to similar conclusions as Darwin around the same time."
- **Analysis**: This statement is correct. Alfred Wallace independently developed a theory of natural selection that was similar to Darwin's. Both scientists contributed to the understanding of evolution, and Wallace's work in the Malay Archipelago was significant in this context.

2. **Statement (ii)**: "August Weismann by careful experimentation demonstrated that life comes only from pre-existing life."
- **Analysis**: This statement is incorrect. The correct scientist associated with demonstrating that life comes only from pre-existing life is Louis Pasteur, not August Weismann. Pasteur's experiments, particularly with the swan-neck flask, disproved the theory of spontaneous generation.

3. **Statement (iii)**: "The organs which have the same fundamental structure but are different in functions are called homologous organs."
- **Analysis**: This statement is correct. Homologous organs are those that share a common structural origin but have evolved to perform different functions due to adaptation to different environments or lifestyles. Examples include the forelimbs of mammals, which have similar bone structures but serve different purposes.

4. **Statement (iv)**: "Rate of appearance of new form is inversely proportional to lifespan of organism."
- **Analysis**: This statement is incorrect. The rate of evolution is generally faster in organisms with shorter lifespans because they can reproduce more quickly and have more generations in a given time frame. Therefore, the relationship is directly proportional; shorter lifespans lead to faster evolution.

### Conclusion:
Based on the analysis:
- **Correct Statements**: (i) and (iii)
- **Incorrect Statements**: (ii) and (iv)

**Final Answer**: The correct statements are (i) and (iii).