Don't Rely Completely on answers. First refer the definition of a government company which is defined under sub section (45) of section 2 of companies act 2013.
Later refer the provision of appointment of auditor in case of government and non government company.
sometimes they print incorrectly. Here 60% of the shares are held by Government then obviously CAG will appoint the auditor.
So in the above case Board should APPOINT the auditor within prescribe time.
As per the definition shares held by government company is not considered to be a share held by government indirectly UNLESS it is a subsidiary of such government company or wholly owned subsidiary company.
I think this question was asked in CA final in November 2016.