During the Abbasid dynasty, what event marked the permanent end of the caliphate?
A. The Umayyads took over and established a different kind of government.
B. Mongols entered the city of Baghdad and killed the caliph.
C. The Fatimids took power and established a new capital in Kabul.
D. The Abbasids themselves declared an end to the caliphate. .
The best answer to this question depends on how you define the “permanent end” of the caliphate.
In 1258, Mongols under the command of Hulagu Khan besieged Baghdad. This city was, at that time, the capital of the Abbasid Dynasty. The Mongol siege of the city was successful and they entered and sacked the city. As a part of this sack, they executed the Abbasid caliph, Al-Musta'sim. You can call this the end of the Abbasid Caliphate, though the Abbasids did set up rule in Egypt and continued to rule from there until the 1500s. If you consider the Abbasid Caliphate to have ended at this time, B is the best answer.
However, the Abbasids did at least claim to still be in control of the Muslim world. They continued to make this claim until the 1500s. At that point, they transferred power to the Ottoman Empire. If you consider this to be the permanent end of the caliphate, Option D is the best.
Neither of the other options is correct. The Abbasids replaced the Umayyads. This means Option A is wrong. The Fatimids were conquered by the Abbasids, so Option C is wrong.
I would argue that Option B is the best answer, but a case can be made for Option D.