Jan 27 (Reuters) - Indian shares rallied on Tuesday after a volatile trading session, as a landmark trade deal with the European Union scrapped all tariffs on 90% of Indian goods.

The Nifty 50 rose 0.51% to 25,175.4 and the BSE Sensex gained 0.39% to 81,857.48.

Volatility jumped to a seven-month high with investors on the edge about U.S. tariff policy and ahead of India's federal budget, which is due on February 1.

Eleven of the 16 major sectors logged gains. The broader small-caps and mid-caps rose 0.4% and 0.6%, respectively.

The long-pending trade deal with the EU will see India eliminating or reducing tariffs on 96.6% of traded goods while the EU will cut tariffs on 99.5% goods traded over seven years.

"The deal will potentially diversify India's trade base, accelerate sectoral growth, and strengthen global investor confidence by signalling policy stability and deeper integration into global value chains," said Ravi Singh, chief research officer from Master Capital Services.

"The deal is structurally positive for trade and investment outlook and an overall positive for Indian stock market."

Bucking the broader trend, auto stocks fell 0.9% as tariffs on cars from EU will be cut steeply over five years, benefiting European automakers such as Volkswagen, Renault, Mercedes-Benz and BMW.

Mahindra & Mahindra fell 4.2%, while the country's biggest carmaker Maruti Suzuki India and Tata Motors Passenger Vehicle fell 1.5% and 1.1%, respectively.

"The near-term pressure is less about volumes and more about perception and pricing power in the premium end" of the auto market, Bhavik Joshi, business head of portfolio management services firm INVasset, said.

Metal shares rose 3.1% on strong results from JSW Steel and higher base metal prices.

Adani group stocks reversed some of the losses after Friday's selloff.

Axis Bank and UltraTech Cement gained 4.6% and 1.8%, respectively, following strong quarterly results, while Kotak Mahindra Bank fell 3.3% after missing profit estimates.

(Reporting by Vivek Kumar M and Bharath Rajeswaran; Editing by Sherry Jacob-Phillips, Sonia Cheema and Mrigank Dhaniwala)

By Vivek Kumar M and Bharath Rajeswaran