Do Indian parents ever apologize to their kids when they themselves are at fault?

I do not think so that majority of them do, but yes, since with every generation things change, so I think this change too is coming. I mean, I apologise to my kids if I am wrong. And trust that seeking forgiveness from little kids is such an exhilarating experience. And you learn also from them that how they forgive you so easily without keeping anything in their hearts. I think adults should do it when they are at fault as this is also a step towards fair parenting and would make your kids and yours understanding better over the period of time.

Lol! What kind of a question is this! Yes, in today's time you can at least think of asking this question, in my time, when I was growing up, we could even think of lifting up our face in front of our parents, especially in front of our father. I do not know how much things have changed in parenting now, but I as a parent when wrong, do analyse myself but do not like, verbally say, sorry to my kids. I do things to make up for whatever bad or wrong I may have done.

my parents have always been very fair, so when i was a kid, and then a teen and later, i remember they would readily say sorry if they were not right. as a parent today, i also practice the same. there is nothing to be ashamed of in saying sorry or acknowledging your mistake when you know you are not right, even if it is from a parent to a child.