Let $f$ be defined on $D = \mathbb{R} - \{-1, 1\}$ by $f(x) = \frac{|x|}{1-|x|}$,then

The $Ca^{2+}$ and $F^{-}$ ions are located in a $CaF_{2}$ crystal,respectively,at face-centered cubic lattice points and in:

Glycerol $\xrightarrow{KHSO_4} (A)$ $\xrightarrow{LiAlH_4} (B)$; $(A)$ and $(B)$ are respectively:

$A$ sample of $0.1 \text{ g}$ of water at $100^{\circ} \text{C}$ and normal pressure $(1.013 \times 10^5 \text{ Nm}^{-2})$ requires $54 \text{ cal}$ of heat energy to convert to steam at $100^{\circ} \text{C}$. If the volume of the steam produced is $167.1 \text{ cc}$,the change in internal energy of the sample is ....... $\text{J}$.

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring such that it is half-submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is:

If $\frac{dy}{dx} = \frac{xy + y}{xy + x}$,then the solution of the differential equation is