General and middle terms in binomial expansion

Correct answer: B. ¹⁰C₄

The governing concept is the binomial theorem: (1+x)¹⁰ = Σ from r=0 to 10 of ¹⁰Cᵣxʳ. The term containing x⁴ is obtained by taking r=4, so its coefficient is ¹⁰C₄. Equivalently, view the expression as a product of ten factors (1+x). To create x⁴, choose x from exactly four factors and choose 1 from the remaining six. The four factors can be selected in ¹⁰C₄ ways, and each selection contributes one x⁴ term. Thus option B is correct. ¹⁰P₄ incorrectly counts an order among the four selected factors, 10⁴ has no valid binomial-selection interpretation, and 4! counts arrangements that do not produce different terms because multiplication is commutative.