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Q.

Let 1+x+2x220=a0+a1x+a2x2+…+a40x40 . Then a1+a3+a5+….+a37 is equal to

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a

219(220+21)

b

220(220−21)

c

220(220+21)

d

219(220−21)

answer is D.

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Detailed Solution

1+x+2x220=a0+a1x+.....a40x40x=1⇒420=a0+a1+……..+a40x=-1⇒220=a0-a1+a2…….+a40420-22020=a1+a3+……a37+a39 But a39= coeff of x39in 1+x+2x220=20!p!q!r!1p.xq.2r.x2rq+2r=39,    p+q+r=20q=1,   r=19,   p=0a39=20!0!  1!   19!.219=20.219 Required =240-2202-20.219=240−220−20.2202=239-219-20.219=219220-21
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