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Question

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

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

## The correct option is B (16,2723)Consider (1+ax+bx2)(1−2x)18=(1+ax+bx2)[18C0−18C1(2x)+18C2(2x)2−18C3(2x)3+18C4(2x)4−...]Coeff. of x3=18C3(−2)3+a.(−2)2.18C2+b(−2).18C1=0Coeff. of x3=−18C3.8+a×418C2−2b×18=0=−18×17×166⋅8+4a×18×172−36b=0=−51×16×8+a×36×17−36b=0=−34×16+51a−3b=0=51a−3b=34×16=544=51a−3b=544 .....(i) Only option number (b) satisfies the equation number (i)

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