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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

The middle term in the expansion of (1+x)<sup>2n</sup> is:

Answer: (n+1)th term with coefficient 2nCn.

  • A (n+1)th term with coefficient 2nCn
  • B nth term, taken as the halfway point before adjusting for indexing
  • C (2n)th term, the very last term in the expansion
  • D C(n,n), the coefficient of the final term x<sup>2n</sup>

Correct answer: A. (n+1)th term with coefficient 2nCn

Explanation: Expansion of (1+x)<sup>2n</sup> has 2n+1 terms. Middle term is (n+1)th term: C(2n,n) × x<sup>n.</sup>

StartABCBCACAB6 ordered outcomes (permutations); pairing AB/BA etc gives 3 combinations

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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