Ltcg for gifted property

That's a bit peculiar case.

By virtue of S.64(1)(iv), the income accruing/arising from the transfer of such property by your mother is to be considered in the income of your father [Since this was a transfer of an immovable property to the spouse for an inadequate consideration, that is gift].

Therefore, the income on transfer would accrue arise to someone who does not exist and hence assessment is not possible in the hands of the Father (as held by several court judgements). Therefore, S.159 would become applicable and the legal representative should show that income and pay the tax thereon. The legal representative will also be liable to claim the exemptions which the assessee would have been eligible to. For more details refer to my previous discussion on

https://www.forum.charteredclub.com/threads/deposit-in-capital-gains-account-after-death-of-seller.7108/

[Am there as ZED]

Coming to your other questions, "What is the cost of acquisition while calculating the LTCG for this flat ? "
 

As per S.49(1) and considering the judgement cited by Mr Rakesh Sharma, the cost of acquisition shall be the cost of acquisition in the hands of the previous owner (Father).

Since the period of holding is more than 2 years, it is a long-term capital asset [S.2(42A)]

For the purpose of the computation of the capital gain, as per S.48, cost of acquisition needs to be indexed and for that purpose the fair market value as on 01/04/2001 shall be considered and then indexation shall be applied to such value to arrive at the indexed cost of acqusition.

S.48 Explanation (iii)  "indexed cost of acquisition" means an amount which bears to the cost of acquisition the same proportion as Cost Inflation Index for the year in which the asset is transferred bears to the Cost Inflation Index for the first year in which the asset was held by the assessee or for the year beginning on the 1st day of April, 2001, whichever is later;