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Question

The coefficient x12 in (x3 + x4 + x5 +...)3 ____
  1. 10

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Solution

The correct option is A 10
We wish to find coefficient of x12 in (x3 + x4 + x5 +...)3
= (x3 (1 + x1 + x2 + ...))3
= x9 (1 + x + x2.....)3

= x9(1x)3

= x9 r=0 31+rCrXr

= x9 r=0 r+2CrXr

Now to make x12 we need put r = 3
So coefficient to x12 is 3+2C3 = 5C3 = 5C2 = 10

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