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Question

The coefficient of x28 in the expansion of (1+x3x6)30 is
  1. 30C6
  2. 30C3
  3. 1
  4. 0


Solution

The correct option is D 0
(1+x3x6)30=k1+k2+k3=3030!k1!k2!k3!(1)k1(x3)k2(x6)k3=k1+k2+k3=3030!k1!k2!k3!(1)k3x3k2+6k3

Now, for coefficient of x28
3k2+6k3=28k2+2k3=283
As k2,k3W, so it is not possible
Therefore, coefficient of x28 is 0.

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