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Question

The ratio of the coefficient of x15 to the term independent of x in x2+2x15, is
(a) 12 : 32
(b) 1 : 32
(c) 32 : 12
(d) 32 : 1

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Solution

In x2+2x15 we have Tr+1=15Cr(x2)15-r2xr
i.e. General term is Tr+1=15Cr x30-3r 2r
Hence for the term independent of x,
30 – 3r = 0
i.e. r = 10
hence T11 has coefficient 15C10 210 ...(1)
and term with x15 will have 30 – 3r = 15
i.e. 15 = 3r
i.e. r = 5
∴ coefficient will be 15C5 25 ...(2)
∴ ratio of coefficient of x15 to the term independent of x will be
eqn(2)eqn(1)=25×15C5 210×15C10 =125 15C10=15C5-10=15C5
i.e. ratio will be 1 : 32
Hence, the correct answer is option B.

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