$\lim _{x \rightarrow 0} x^2 \sin \left(\frac{\pi}{x}\right)$ is equal to

Consider the general reaction given below at $400 \ K$: $xA_{(g)} \rightleftharpoons yB_{(g)}$. The values of $K_p$ and $K_c$ are studied under the same condition of temperature but variation in $x$ and $y$. $(i)$ $K_p = 85.87$ and $K_c = 2.586$ (appropriate units). $(ii)$ $K_p = 0.862$ and $K_c = 28.62$ (appropriate units). The values of $x$ and $y$ in $(i)$ and $(ii)$ respectively are:

$A$ renewable exhaustible natural resource is

An iron sphere of mass $20 \times 10^{-3} \ kg$ falls through a viscous liquid with terminal velocity $0.5 \ ms^{-1}$. The terminal velocity (in $ms^{-1}$) of another iron sphere of mass $54 \times 10^{-2} \ kg$ is (in $.5$)

Which of the following is an aldohexose?

Which of the following monosaccharides is a pentose?