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Question

# If the coefficients of x3 and x4 in the expansion (1+ax+bx2)(1âˆ’2x)18 in powers of x are both zero, then (a,b) is equal to

A
(16,2723)
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B
(16,2513)
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C
(14,2513)
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D
(14,2723)
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Solution

## The correct option is A (16,2723)This can be written as (1−2x)18+ax(1−2x)18+bx2(1−2x)18Hence coefficient of x4=18C424−a18C323+b18C222=0Hence 18C422−a18C321+b18C2=0 ...(i)The coefficient of x3=−18C323+a18C222−b18C121=0−18C322+a18C221−b18C1=0 ..(ii)Solving the above equations, we get a=16 and b=2723

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