$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1-\cos x^2}}{1-\cos x}=$$

If $$\mathrm{A}=\left[\begin{array}{cc}\lambda & \mathrm{i} \\ \mathrm{i} & -\lambda\end{array}\right]$$ and $$\mathrm{A}^{-1}$$ does not exist, then $$\lambda=$$ (where $$\mathrm{i}=\sqrt{-1}$$)

The distance 's' in meters covered by a particle in t seconds is given by $$s=2+27 t-t^3$$. The particle will stop after _________ distance.

If the polar co-ordinates of a point are $$\left(2, \frac{\pi^{\mathrm{c}}}{4}\right)$$, then its Cartesian co-ordinates are