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Q.

What is the middle term in the expansion of (xy3−3yx)12 ?

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a

C(12,7)x−3y3

b

C(12,6)x3y−3

c

C(12,7)x3y−3

d

C(12,6)x−3y3

answer is B.

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Detailed Solution

Given expansion   (xy3−3yx)12 is We have general term in the expansion (x+a)n (∴  Tr+1= nCr xn−r (a)r  be the expansion of (x+a)n) Here, index be the n=12 middle term is (122+1)th  i.e. 7th  term.∴  Required middle term =T7 Tr+1= nCr xn−r (a)r  T7=T6+1= 12C6(xy3)6(−3yx)6 .T7=T6+1=  12C6x6y3x3y6= 12C6x3y−3 T7=T6+1= 12C6x3y−3
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