Cap gains for nri inheritance of shares

I am NRI living outside India who has come into inheritance of shares in Indian compnay thru ancestor who passed (intestate) in 1971. My relative in India got court to award Succession Certificate in 2014, and was able to get shares. I now have shares and want to sell - but want to know tax implications before I sell.

My understanding is that date of acquisition would be pre-1971 (my ancestor acquired these shares prior to their passing in 1971) .Therefore, if I sell now it should qualify as long term gain ?

How do I know the cost basis - I don't know share price pre-1971 ?

I also have read that if shares are in a listed company (which these are) and sold on regular exchange (BSE/NSE) with STT paid, then there is NO long term cap gains tax applied.

If anyone can tell me if this is correct, will be much appreciated ...

Date of acquisition would be the date of acquisition of your ancestor

S 49.[(1)] Where the capital asset became the property of the assessee—

(i) on any distribution of assets on the total or partial partition of a Hindu undivided family;

(ii) under a gift or will;

(iii) (a) by succession, inheritance or devolution, or

[(b) on any distribution of assets on the dissolution of a firm, body of individuals, or other association of persons, where such dissolution had taken place at any time before the 1st day of April, 1987, or]

(d) under a transfer to a revocable or an irrevocable trust, or

(e) under any such transfer as is referred to in clause (iv) [or clause (v)] [or clause (vi)] [or clause (via)] [or clause (viaa)] [or clause (vica) or [clause (vicb)] or [clause (xiii) or clause (xiiib) or clause (xiv) of section 47]];[(iv) such assessee being a Hindu undivided family, by the mode referred to in sub-section (2) of section 64 at any time after the 31st day of December, 1969,]

the cost of acquisition of the asset shall be deemed to be the cost for which the previous owner of the property acquired it, as increased by the cost of any improvement of the assets incurred or borne by the previous owner or the assessee, as the case may be."

For exact date you will to check the details of the account.

NOTE THAT FOR THE PURPOSE OF COMPUTATION WE ARE CONCERNED WITH FAIR MARKET VALUE OF THE SHARES AS ON 01.04.1981, we will index this cost using Cost inflation index and indexation will also be done from this date. Read 2nd proviso to S. 48 for more details.

This long term Capital gain is exempt from tax having regards to

S.10(38) any income arising from the transfer of a long-term capital asset, being an equity share in a company or a unit of an equity oriented fund [or a unit of a business trust] where—

(a) the transaction of sale of such equity share or unit is entered into on or after the date on which Chapter VII of the Finance (No. 2) Act, 2004 comes into force; and

(b) such transaction is chargeable to securities transaction tax under that Chapter