If you rent a property on January 1, 2019, the 11-month rent cycle is from January 1st 2019 to November 30th 2019. Although you took possession of the rental property on January 1, 2019 , you shall execute the rent agreement within the rent cycle and as much as possible close to the possession date, say February 1, 2019, but not beyond the rent cycle of November 30, 2019.
Back-dated rent agreement with in rental cycle is accepted by many institutions and organizations in India, like opening bank accounts, gas applications, passport applications, and job applications. The contract has to be executed on or after the date given on the stamp paper, not earlier. However, a clause can be inserted in the contract which considers it effective at an earlier date. The notarial deed only increases the probative value of the contract; it is not mandatory. Using backdated stamp paper will only be useful if you are using it for backdated agreements (although this is not legal).
Nowadays, stamp papers have a date printed at the back, so you can only use them according to their date. e.g., if you want a rent agreement today from March 2008 to February 2009, you can not do so as you need stamp paper from March 2008, which is not available legally. An agreement can be signed in the back-date on a back-dated stamp paper, provided the signatories agree to it. That is to say, at least an oral understanding was reached on the back-date. But such situations should be avoided in case the agreement later on becomes disputed with any third parties that were not signatories to the agreement. Then they may challenge such back-dated agreements as forged documents.
Reference: indian registraction act – 202100499-20210043-14456