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Question

The coefficient of x30 in the expansion of (1+2x+3x2+.....21x20)2 is

A
2706
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B
2450
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C
1481
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D
256
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Solution

The correct option is B 2706
(1+2x+3x2+....21x20)(21x20+20x19+19x18+.....2x+1)
coeff. of x30 is 11.21+12.20+......+21.11
=2[11.21+12.20+13.19+14.18+15.17]+16.16
=2[231+240+247+252+255]+256
=2[1225]+256
=2450+256
=2706

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