Is cloudnine a good hospital? The staff mentioned the child birth package costs 2 lacs whether normal or c-section. Doesn't it seem 2 much?
Insurance is the way to go. Try to get asap as you can't claim them initially for a month or so.
Did you book the package beforehand or just walked in on the day and asked them to admit with cashless insurance?
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It is around 2L in almost all Tier 1 cities. U can take it. U can use company health insurance. Just check with health insurance company if package is reimbursable.