JEE Mathematics · Medium

Binomial Theorem: Mixed MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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MixedMediumQuestion 280014

Question

The term containing x¹⁰ in (x² + 1/x)¹⁴ is:
  1. A
    T₅ = ¹⁴C₄ x¹⁰
    Correct
  2. B
    T₄
  3. C
    T₆
  4. D
    No such term

Correct answer

T₅ = ¹⁴C₄ x¹⁰

Explanation

T_{r+1} = ¹⁴Cᵣ (x²)^(14−r) (1/x)^r = ¹⁴Cᵣ x^(28−2r−r) = ¹⁴Cᵣ x^(28−3r). For x¹⁰: 28−3r = 10 → r = 6. T₇ = ¹⁴C₆ x¹⁰ = 3003x¹⁰. So T₇, not T₅.