Maharashtra State BoardHSC Science (General) 11th
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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`

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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
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