Writing and registering the property will

The property could be disposed or bequeathed by the mother to anyone, at her discretion. No NOC from any of the legal heirs, her daughter included, is not at all necessary. 

It is not mandatory that the Will be registered.

Thank you sir that helps. So after my mother's demise, to execute the will I must be visiting the sub-register's office to have the propery title deed on my name ? Is that it means to executing the will ?

Your mother can transfer her own property to you without taking permission or NOC from your sister and also the unregistered NOC is not legally valid.

She can transfer it by a registered Will which will be more authentic and unchallengeable 

After your mother's death, as the property is in Chennai, you have approach the appropriate court to obtain a probate on the will. The court will take necessary actions including calling the witnesses and taking statements. The original will will be retained by the court and a new order issued. There may be stamp duty. It is better to take the advice of a lawyer.

In the given facts, to my knowledge, it is not mandatory that the Will be probated.

In the three metropolitan cities of Kolkatta, Mumbai and Chennai a will has to be compulsorily probated.  That is the law since British times until very recently. I do not know if the law has been changed. In other places it is not compulsory. The purpose of a will is to authoritatively confirm that the testatee under the will is the new owner owner of the property. The sub-registrar will not do it and he has  not the authority to do it. After the death of the testator, if there are no other claimants and no other person stakes claim, the person in whose favour the property is bequeathed can occupy and enjoy the property. The demand for taxes will continue to be received in the name of the dead person and receipts will be issued in the name of the dead persons. The new owner can get it mutated in his favour and pay the taxes. Problem will come only if and when the new owner wants to alienate the property. Alienation means giving it on rent, or as collateral or outright sale. If he tries to sell,  the purchaser may be hesitant to buy fearing third party claims. Under such circumstances a probate may be required to satisfy the purchaser that no other claimant will dispute the sale.