Question

If rth term in expansion of (3x²/2 - 1/3x)⁹ , x ≠ 0 is constant then r = _____

(a) 6 

(b) 7 

(c) 8 

(d) 9

Answer 1

Correct option: (b) 7

Explanation:

T_r+1 = ⁿc_r a^n–r b^r 

T_r = ⁿc_r–1 a^n–r+1 ∙ b^r–1 

∴ T_r = ⁹c_r–1 [(3x²) / 2]^9–r+1 ∙ [– (1 / 3x)]^r–1 

given T_r is constant

⇒ x^18–2r+2 ∙ x^–r+1 = x⁰ 

∴ 18 – 2r + 2 – r + 1 = 0

∴ 21 = 3r

∴ r = 7