The five-day extravaganza will showcase old and new LGBT films.
"Carol", also starring Rooney Mara, is a poignant story of a love affair between a young aspiring photographer and an older woman going through a difficult divorce set in 1950s.
The theme of the fests this year is "7 Shades of Love".
It underlines that at the core of human relationships is the capacity to love each other and offer respect so that each person can like equality and dignity.
The fest had Hollywood star Ian McKellen as the chief guest at the inaugural ceremony.
Over 182 films from 53 countries will be screened at the festival.
The three venues for the fest are Liberty cinema, Alliance de Francaise and Max Mueller Bhavan.
This edition, the 'country in focus' is Brazil with the festival screening 11 films from the country.
American film "Those People" will close the festival.
Anupam Kher's acting academy, Actor Prepares, will sponsor cash prize for the three top competition categories- Rs 30,000 for best narrative feature film, Rs 20,000 for best Indian narrative short film and Rs 20,000 for best performance in a lead role.
