The law is like that but your case is different since tenant is having bad reputation you have rightly called upon her to vacate. It is better to wait for 2 months and then proceed. Dealing in Courts are still worse. Be confident you will get but not through Courts. The relevant law is as follows:
Section 106 in The Transfer of Property Act, 1882
1[106. Duration of certain leases in absence of written contract or local usage.—
(1) In the absence of a contract or local law or usage to the contrary, a lease of immovable property for agricultural or manufacturing purposes shall be deemed to be a lease from year to year, terminable, on the part of either lessor or lessee, by six months' notice; and a lease of immovable property for any other purpose shall be deemed to be a lease from month to month, terminable, on the part of either lessor or lessee, by fifteen days' notice.
(2) Notwithstanding anything contained in any other law for the time being in force, the period mentioned in sub-section (1) shall commence from the date of receipt of notice.
(3) A notice under sub-section (1) shall not be deemed to be invalid merely because the period mentioned therein falls short of the period specified under that sub-section, where a suit or proceeding is filed after the expiry of the period mentioned in that sub-section.
(4) Every notice under sub-section (1) must be in writing, signed by or on behalf of the person giving it, and either be sent by post to the party who is intended to be bound by it or be tendered or delivered personally to such party, or to one of his family or servants at his residence, or (if such tender or delivery is not practicable) affixed to a conspicuous part of the property.]