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Let a and b be the coefficients of x^3 i...

Let `a and b` be the coefficients of `x^3` in `(1+x+2x^2+3x^3)^4a n d(1+x+2x^2+3x^3+4x^4)^4,` then respectively. Then the value of `4a//b` is.

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The correct Answer is:
4
We have `b=` coefficient of `x^(3)`in
`((1+x+2x^(3)+3x^(3))+4x^(4))^(4)`
= coefficient of `x^(3)` in `[.^(4)C_(0)(1+x+2x^(2)+3x^(3))^(4)(4x^(4))^(0) + .^(4)C_(1)(1+x+2x^(2)+3x^(3))^(3)(4x^(4))^(1)+"…"]`
= coefficient of `x^(3)` in `(1+x+2x^(2)+3x^(3))^(4) = a`
Hence `4a//b = 4`.
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