We know that if we are taking any electrically charged object near to uncharged body, then in the uncharged body, charges are getting induce.
Opposite charges are getting induce near to the charged object side and same type of charges are getting induce on the other side of the body.
So on the outer surface of the conducting sphere should be negative if we are putting the negative charges at the center of the spherical conducting body.
Hence the given statement is false.
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