Maharashtra State BoardHSC Science (Electronics) 11th
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Answer the following: x60 in the expansion of (1x2+x4)18 - Mathematics and Statistics

Sum

Answer the following:

x60 in the expansion of `(1/x^2 + x^4)^18`

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Solution

Here a = `1/x^2`, b = x4, n = 18

We have, tr+1 = nCr an–r .br 

= `""^18"C"_"r"(1/(x^2))^(18-"r") (x^4)^"r"`

= 18Cr x2r–36 .x4r

= 18Cr x6r–36

To get the coefficient of x60, we must have

x6r–36 = x60

∴ 6r – 36 = 60

∴ 6r = 96

∴ r = 16

∴ Coefficient of x60

= 18C16

= `(18!)/(16!2!)`

= `(18 xx 17 xx 16!)/(16! xx 2 xx 1)`

= 153

∴  the coefficient of x60 is 153

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
Miscellaneous Exercise 4 | Q II. (9) (ii) | Page 86
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