MUMBAI, India — When Michelle Obama, the first lady, introduced her husband to a group of college students here on Sunday, she urged them to ask him “tough questions.”

They did.

“What is your take or opinion about jihad?” came the first question for President Obama at a town-hall-style meeting at St. Xavier’s College. Next up were queries about spirituality, Gandhi, the American midterm elections and his government’s negotiations with the Taliban.

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