Binomial Theorem: JEE Main MCQ

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

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JEE MainHardQuestion 280010

Question

If the coefficients of x⁷ and x⁸ in (2 + x/3)ⁿ are equal, then n is:

A
55
Correct
B
45
C
56
D
35

Correct answer

Explanation

Coeff of x⁷: ⁿC₇ 2^(n−7) (1/3)⁷. Coeff of x⁸: ⁿC₈ 2^(n−8) (1/3)⁸. Setting equal: ⁿC₇ × 2/1 = ⁿC₈ × (1/3). 2 ⁿC₇ = ⁿC₈/3. 6ⁿC₇ = ⁿC₈ → 6 = ⁿC₈/ⁿC₇ = (n−7)/8 → n−7 = 48 → n = 55.

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