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Let (2x^(2)+3x+4)^(10)=sum(r=0)^(20)a(r ...

Let `(2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )x^(r )`, then the value of `(a_(7))/(a_(13))` is (a) 6 (b) 8 (c) 12 (d) 16

A

`6`

B

`8`

C

`12`

D

`16`

Text Solution

Verified by Experts

The correct Answer is:
B
`(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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