Statement I: According to Darwin, variations within a population lead to differential survival and reproduction rates among individuals.

Statement II: Lamarck's theory is centered on the idea that the use or disuse of organs could lead to changes in traits across generations.

Both statements I and II are correct.

The correct answer is Option (3) –Both statements I and II are correct.

Lamarckism, developed by  Lamarck, proposed the theory of the inheritance of acquired characteristics, suggesting that organisms could pass on traits acquired during their lifetime to their offspring. He also proposed that the use or disuse of organs could lead to changes in the organism's traits, asserting that continuous use of an organ would cause it to develop and increase in size, while disuse would lead to its degradation over generations.

The statement "Rate of survival of organisms is different due to variations" is indeed an integral part of evolutionary theory and reflects a fundamental aspect of natural selection proposed by Charles Darwin.

Darwin's theory of natural selection emphasizes that variations within a population lead to differential survival and reproduction rates among individuals. Organisms with advantageous variations or traits that are better suited to their environment tend to survive and reproduce more successfully, passing on these beneficial traits to their offspring. This process ultimately leads to changes in the population over generations.

This concept of natural selection by Darwin is different from Lamarck's theory of inheritance of acquired characteristics, which proposed that organisms pass on traits acquired during their lifetime directly to their offspring.