To solve this problem, we need to identify which event never occurs during mitotic cell division. Let's analyze each option:$\newline \bullet$Option 1: Spindle fibres attach to kinetochores of chromosomes.$\newline$ - During mitosis, spindle fibres form and attach to the kinetochores of chromosomes to help segregate them into daughter cells.$\newline$ - This is a normal part of mitosis.$\newline \bullet$Option 2: Movement of centrioles towards opposite poles.$\newline$ - In mitosis, centrioles move to opposite poles of the cell to help organize the spindle apparatus.$\newline$ - This is a typical event in mitosis.$\newline \bullet$Option 3: Pairing of homologous chromosomes.$\newline$ - Pairing of homologous chromosomes occurs during meiosis, not mitosis.$\newline$ - In meiosis, homologous chromosomes pair up during prophase I for crossing over.$\newline$ - This event does not occur in mitosis.$\newline \bullet$Option 4: Coiling and condensation of the chromatids.$\newline$ - During mitosis, chromatids coil and condense to become visible as distinct chromosomes.$\newline$ - This is a normal part of mitotic prophase.$\newline$Therefore, the event that never occurs during mitotic cell division is:$\newline$Option 3: Pairing of homologous chromosomes.$\newline$This corresponds to the correct option, which is Option 3.