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As we know the charge in conducting body remains on its surface because  the electric field is zero inside the conductor, as same charges repeal eachother. As per  Coulomb's Law it  demands that the charges be as far apart as possible. So in this case negatively charges sphere touched conducting bucket then half part  the negative charge of sphere got transferred to bucket. As bucket is conducting so charge will reside on it's surface. For this question the negative charge spread equally over the sphere and inside and outside surfaces of bucket and cover  Hence option (e) is correct. ...