If $f(x)=\left\{\begin{array}{cc}\frac{a \sin x-b x+c x^2+x^3}{2 \log (1+x)-2 x^3+x^4} &, x \neq 0 \\ 0 &, x=0\end{array}\right.$ is continuous at $x=0$, then

• A

  $a=2 b$
• Correct answer
  B

  $a=b$
• C

  $a=b=c$
• D

  $b=c$

Hence, the correct answer is option: 'B'.