Question

If sum of the coefficient of second and fourth terms in the expansion of `(2x - 1/(3x^2))^5`, in descending powers of x, is S, Then the value `|81/40"S"|` of is ______.

Options

• 27

• 57

• 72

• 75

Answer 1

If sum of the coefficient of second and fourth terms in the expansion of `(2x - 1/(3x^2))^5`, in descending powers of x, is S, Then the value `|81/40"S"|` of is 57.

Explanation:

⇒ `(2x - 1/(3x^2))^5`

T₂ = `""5"C"_1.(2x)^4(-1/(3x^2))^1`

⇒ Coefficient = `(-80)/3`

T₄ = `""5"C"_3(2x)^2((-1)/(3x^2))^3`

⇒ Coefficient = `(-40)/27`

∴ S = `(-80)/3 + 40/27 = (-760)/27`

⇒  `|81/40"S"|` = 57