# Find the constant term (term independent of x) in the expansion of (x-3x2)10 - Mathematics and Statistics

Sum

Find the constant term (term independent of x) in the expansion of (sqrt(x) - 3/x^2)^10

#### Solution

Let tr+1 be the constant term in the expansion of (sqrt(x) - 3/x^2)^10.

We know that, in the expansion of (a+ b)n,

tr+1 = nCr an–r br

Here a = sqrt(x), b = -3/x^2, n = 10

∴ tr+1 = ""^10"C"_"r" (sqrt(x))^(10-"r") (-(3)/x^2)^"r"

= ""^10"C"_"r"  x^(5-1/2"r")*(-3)^"r"x^(-2"r")

= ""^10"C"_"r" (-3)^"r"* x^(5 - 5/2"r")

But tr+1 is a constant term

∴ power of x = 0

∴ 5 - 5/2"r" = 0

∴ r = 2

∴ the constant term = 10C2 (– 3)2

= (10 xx 9)/(1 xx 2) xx 9

= 405

Concept: General Term in Expansion of (a + b)n
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.3 | Q 3. (iii) | Page 80