Answer should be 4.
Telomerase helps to replicate the DNA at its terminals. but telomerase inhibitors prevent the telomerase to divide.
cancerous cells have the property of continuous division. so what we can say in cancerous cells telomerase is continuous dividing and it only happens if mutation destroy telomerase inhibitors.

Mutations in Cancer Cells

Introduction:
Cancer is a complex disease characterized by uncontrolled cell growth and the ability to invade and spread to other parts of the body. It arises due to a multitude of genetic alterations that accumulate in a cell over time, resulting in the disruption of normal cellular processes. Mutations play a crucial role in the development and progression of cancer. However, not all statements regarding mutations in cancer cells are true. Let's examine each statement in detail to identify the false statement.

Statement 1: Mutations inactivate the cell control.
Mutations can indeed disrupt the normal control mechanisms within a cell, leading to loss of cell cycle regulation, impaired DNA repair, and evasion of cell death pathways. These alterations can result in uncontrolled cell growth and division, which are characteristic of cancer cells. Therefore, this statement is true.

Statement 2: Mutations inhibit the production of telomerase.
Telomerase is an enzyme that helps maintain the length of telomeres, which are protective caps at the ends of chromosomes. In most normal cells, telomerase production is repressed, leading to gradual telomere shortening with each cell division. However, cancer cells often exhibit reactivation of telomerase, allowing them to maintain their telomere length and achieve immortality. Therefore, this statement is false. Mutations in cancer cells can actually lead to increased production or activation of telomerase.

Statement 3: Mutations in proto-oncogenes accelerate the cell cycle.
Proto-oncogenes are normal genes that regulate cell growth and division. However, when these genes undergo specific mutations, they can become oncogenes, which promote excessive cell growth and proliferation. Mutations in proto-oncogenes often result in hyperactivation of the corresponding protein products, leading to accelerated cell cycle progression. Therefore, this statement is true.

Statement 4: Mutations destroy telomerase inhibitor.
Telomerase inhibitors are molecules that can potentially limit the activity of telomerase and prevent the maintenance of telomere length in cancer cells. However, mutations in cancer cells do not destroy telomerase inhibitors. Rather, they can render these inhibitors ineffective by activating alternative telomere maintenance mechanisms or upregulating telomerase production. Therefore, this statement is false.

Conclusion:
Among the given statements, the false statement is "Mutations destroy telomerase inhibitor." Mutations in cancer cells can modulate various cellular processes, such as cell cycle regulation and telomere maintenance, which are essential for their uncontrolled growth and survival. Understanding these molecular alterations is crucial for developing effective strategies to target and treat cancer.