1.

Let (2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )x^(r ), then the value of (a_(7))/(a_(13)) is

Answer»

`6`
`8`
`12`
`16`

Solution :`(b)` Given `(2x^(2)+3x=4)^(10)=sum_(R=0)^(20)a_(r )x^(r )`
Replacing `x` by `(2)/(x)`, we get
`((8)/(x^(2))+(6)/(x)+4)^(10)=sum_(r=0)^(20)a_(r )((2)/(x))^(r )`
`implies2^(10)(2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )2^(r )x^(20-r)`
`impliessum_(r=0)^(20)a_(r )x^(r )=sum_(r=0)^(20)a_(r )2^(r-10)x^(20-r)`
Comparing coefficient `x^(7)` both SIDES , we get `a_(7)=a_(13)xx2^(3)`.


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