If $\lim_{x \rightarrow 0} \frac{e^{(a-1)x} + 2 \cos(bx) + (c-2)e^{-x}}{x \cos x - \log_{e}(1+x)} = 2$, then $a^{2} + b^{2} + c^{2}$ is equal to:

If $\mathop {\lim }\limits_{x \to 0} \frac{{\ln \left( {1 + x} \right) - ax}}{{{x^2}}} = l$,then the value of $(a + l)$ is equal to (where $l$ is a finite number).

If $\alpha, \beta$ are the roots of the equation $ax^2 + bx + c = 0$, then $\lim_{x \rightarrow \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2}$ is

If $\lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right)$ is finite,then the values of $a, b$ are respectively :

If $\lim _{x \rightarrow 0} \frac{\alpha e^{x}+\beta e^{-x}+\gamma \sin x}{x \sin ^{2} x}=\frac{2}{3}$,where $\alpha, \beta, \gamma \in R$,then which of the following is $NOT$ correct?

If $\lim _{x \rightarrow 1} \frac{x^2-ax+b}{x-1}=7$,then $a+b$ is equal to