One Self Occupied House property is exempted from tax under the Head “Income from House Property”. All other house properties are deemed to be let-out and thus taxable even if those are not actually rented out. Thus, an assessee can opt any one house property at his choice as “Self-Occupied” and take the benefit of exemption.
If an assessee resides at a place (another city) away from his residence due to employment, that property is deemed to be “Self-Occupied” and hence exempted. Thus in effect you can opt the property at Bangalore Self-Occupied and claim exemption.
Also note that the Interest on Capital Borrowed for self-occupied/deemed to be self-occupied property is limited to Rs.150000 p.a (subject of course to actual payment of interest) i.e., actual interest paid or Rs 150000 whichever is lower.
Also note that the interest paid/payable on other let-out/deemed to be let-out properties can be claimed without limit (subject of course to actual payment). i.e., you can claim all the interest paid/payable against let-out/deemed to be let-out property i.e, even more than 150000. But you have to show income from such property also.
Thus, in effect you can claim exemption against only one house property of your choice.
Also, you can claim principal re-payment u/s 80C. You can also claim HRA against rent paid for Bangalore rented house (if actually paid).