In which phase of meiosis would certain gene segments of the homologous pairs of chromosomes cross over and exchange genetic information?

The correct answer would be prophase I.

Crossing over is the event during which genetic material is exchanged between the non-sister chromatids of homologous chromosomes.

In meiosis-I, this event takes place during the pachytene stage of prophase-I.

The homologous chromosomes aligned them in a synapsis for crossing over to take place.

the statements that apply here about binary star system are

"have stars that might appear to wobble"

"often have one star that is brighter than other"

a binary star is a star system consisting of two stars revolving around their common barycenter. systems of two or more stars are called multiple star systems.