$\frac{d}{dx}{\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^2} = $

After losing a number of $\alpha$ and $\beta$ particles,$_{92}U^{238}$ is changed to $_{82}Pb^{206}$. The total number of $\alpha$-particles lost in this process is:

Give the correct order of initials $T$ or $F$ for the following statements. Use $T$ if the statement is true and $F$ if it is false.
$(I)$ Sulphide ions react with $Na_2[Fe(CN)_5(NO)]$ to form a purple-coloured compound $Na_4[Fe(CN)_5(NOS)]$. In the reaction,the oxidation state of iron changes.
$(II)$ $Pt(IV)$ compounds are relatively more stable than $Ni(IV)$ compounds.
$(III)$ The welding of magnesium can be done in the atmosphere of Helium.
$(IV)$ $LiAlH_4$ on hydrolysis will give $H_2$.

If $0.5 \ mol$ of $CaBr_2$ is mixed with $0.2 \ mol$ of $K_3PO_4$,then the maximum number of moles of $Ca_3(PO_4)_2$ obtained will be:

The period of revolution of planet $A$ around the sun is $8$ times that of planet $B$. The distance of planet $A$ from the sun is how many times greater than that of planet $B$ from the sun?

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $(R=8.30 \ J \ mol^{-1} \ K^{-1})$.