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in Mathematics by (71.2k points)

_______th term is constant term in expansion of (3/x2 + √x/3)10 , x ≠ 0

(a) 4 

(b) 7 

(c) 8 

(d) 9

1 Answer

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Best answer

Correct option: (d) 9

Explanation:

Tr+1 = ncr an–r br 

∴ Tr+1 = 10cr (3 / x2)10–r (√x / 3)r 

10cr (310–r ∙ 3–r) (x(x/2) ∙ x–20+2r)

10cr (310–2r) (x(5r/2)–20)

To have constant term, x(5r / 2) – 20 = x0 

i.e. (5r / 2) – 20 = 0

∴  5r = 40

∴   r = 8

∴ Tr+1 = T9 = i.e. 9th term is constant

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