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JEE Advanced Mathematics question

MathematicsPermutations and CombinationsJEE Advanced

There are identical balls on which the numbers are written, each ball carrying a different number. The total number of ways in which the balls can be arranged in a row so that the values of numbers on the first and the last are equal, is

Answer: (A),(B)

Solution

The balls carry different labels , so they are distinct objects. Only the *values* can repeat: exactly when or . So a ball can be matched only with its "mirror" ball .

** even, .** The middle ball has no partner. The

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Question ID VK-110132