Maharashtra State BoardHSC Science (General) 11th
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Find the middle term in the expansion of (xy+yx)12 - Mathematics and Statistics

Sum

Find the middle term in the expansion of `(x/y + y/x)^12`

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Solution

Here, a = `x/y`, b = `y/x`, n = 12

Now, n is even

∴  `("n" + 2)/2 = (12 + 2)/2` = 7

∴ Middle term is t7, for which r = 6.

We have, tr+1 = nCr an–r .br

∴ t7 = `""^12"C"_6 (x/y)^6.(y/x)^6 = (12!)/(6!6!)`

= `(12 xx 11 xx 10 xx 9 xx 8 xx 7)/(6 xx 5 xx 4 xx 3 xx 2 xx 1)`

= 924

∴ Middle term is 924

Concept: Middle term(s) in the 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 4. (i) | Page 80
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