Question

If rth term in the expansion of (x + 1/2x)¹² is constant then r =_____

(a) 5 

(b) 6 

(c) 7 

(d) 8

Answer 1

Correct option: (c) 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 = ¹²c_r–1 x^12–r+1 ∙ (1 / 2x)^r–1 

∴ T_r is constant

⇒ x^12–r+1 ∙ x^1–r = x⁰ 

∴ 12 – r + 1 + 1 – r = 0

∴ 14 = 2r

∴ r = 7