Values of $\lambda$ for which $(\lambda^2-5\lambda+6)x^2+(\lambda-3\lambda+2)x+\lambda^2-4=0$ is an identity in x is:

$\begin{array}{1 1}(A)\;1&(B)\;0\\(C)\;2&(D)\;-2\end{array}$

For equation to be identity
$\lambda^2-5\lambda+6=0\Rightarrow \lambda=2$
$\lambda^2-3\lambda+2=0\Rightarrow \lambda=2$
$\lambda^2-4=0\Rightarrow \lambda=2$
Hence (C) is the correct answer.