Which of the following is $NOT$ true for the $S$ phase?

Given below are the two statements.
Statement $I$: Replication of $DNA$ occurs in the '$S$' phase of interphase in the cell cycle.
Statement $II$: Replication of $DNA$ takes place only once in the cell cycle.
In the light of above statements,choose the correct answer from the options given below:

Select the correct statements regarding $S$-phase of interphase:
$I.$ Occurs between $G_{1}$ and $G_{2}$ phases.
$II.$ $DNA$ replication begins in the nucleus.
$III.$ Centrioles duplicate in the cytoplasm.
$IV.$ As $DNA$ is doubled,the number of chromosomes also doubles.
The option with correct statements is:

$DNA$ replication occurs during

In which phase does $DNA$ replication occur?

Which phase of the cell cycle is characterized by $DNA$ replication,synthesis of histones,and the formation of new nucleosomes?