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

Answer

4

Explanation

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`.