NEW DELHI—Indian Prime Minister Narendra Modi prepares this week to address global business and political leaders in Davos, Switzerland, as his country passes France and the U.K. to become the world’s fifth-largest economy, underscoring the South Asian nation’s drive for recognition as a great power.

Some economists calculate that India’s gross domestic product jumped into the top five last quarter as it continued to outgrow every country in Europe—and for that matter most of the rest of the world.

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