MCQ
If $a = i - 2j$ and $b = 2i + \lambda j$ are parallel, then $\lambda $ is
- A$4$
- B$2$
- C$-2$
- ✓$-4$
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$f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x<-1 \\ \left|a x^{2}+x+b\right|, & \text { if }-1 \leq x \leq 1 \\ \sin (\pi x), & \text { if } x>1\end{array}\right.$
If $f(x)$ is continuous on $R,$ then $a+b$ equals ..... .
$f(x)=\left\{\begin{array}{ll}\frac{x^{3}}{(1-\cos 2 x)^{2}} \log _{e}\left(\frac{1+2 x e^{-2 x}}{\left(1-x e^{-x}\right)^{2}}\right), & x \neq 0 \\ \,\alpha & , x=0\end{array}\right.$ If $\mathrm{f}$ is continuous at $\mathrm{x}=0$, then $\alpha$ is equal to :