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Question

If the coefficient of x2 and x3 are both zero, in the expansion of the expression (1+ax+bx2)(13x)15 in powers of x, then the ordered pair (a,b) is equal to :

A
(21,714)
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B
(54,315)
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C
(28,861)
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D
(28,315)
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Solution

The correct option is D (28,315)
Coefficient of x2 in (1+ax+bx2)(13x)15
15C2(3)2+a (15C1)(3)+b (15C0)(3)0=0
1514293a15+b=0156345a+b=0 (1)

Coefficient of x3 in (1+ax+bx2)(13x)15
15C3(3)3+a(15C2)(3)2+b(15C1)(3)=0
15141332132a315142+15b=0211321a+b=0 (2)

On subtracting (1)(2) , we have
1563211324a=0a=28b=315

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