The radius of the \(2^{\text {nd }}\) orbit of \(Li ^{2+}\) is \(x\). The expected radius of the \(3^{\text {rd }}\) orbit of \(Be ^{3+}\) is

Consider the following reaction : The product \('P'\) gives positive ceric ammonium nitrate test. This is because of the presence of which of these \(-OH\) group(s)\(?\)

The correct order of the spin only magnetic moment of metal ions in the following low spin complexes, \({\left[ {V\,{{\left( {CN} \right)}_6}} \right]^{4 - }}\) , \({\left[ {Fe\,{{\left( {CN} \right)}_6}} \right]^{4 - }}\) , \({\left[ {Ru\,{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }}\) , and \({\left[ {Cr\,{{\left( {N{H_3}} \right)}_6}} \right]^{2 + }}\) , is

In neutral or faintly alkaline medium, \(KMnO _{4}\) being a powerful oxidant can oxidize, thiosulphate almost quantitatively, to sulphate. In this reaction overall change in oxidation state of manganese will be

The correct statements from the following are : \((A)\) The decreasing order of atomic radii of group \(13\) elements is \(\mathrm{Tl}>\mathrm{In}>\mathrm{Ga}>\mathrm{Al}>\mathrm{B}\). \((B)\) Down the group \(13\) electronegativity decreases from top to bottom. \((C)\) \(\mathrm{Al}\) dissolves in dil. \(\mathrm{HCl}\) and liberate \(\mathrm{H}_2\) but conc. \(\mathrm{HNO}_3\) renders Al passive by forming a protective oxide layer on the surface. \((D)\) All elements of group \(13\) exhibits highly stable +1 oxidation state. \((E)\) Hybridisation of \(\mathrm{Al}\) in \(\left[\mathrm{Al}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}\) ion is \(\mathrm{sp}^3 \mathrm{~d}^2\). Choose the correct answer from the options given below:

Fluorination of an aromatic ring is easily accomplished by treating a diazonium salt with \(HBF_4\). Which of the following conditions is correct about this reaction?

\(\mathrm{FeO}_4^{2-} \xrightarrow{+2.0 \mathrm{v}} \mathrm{Fe}^{3+} \xrightarrow{0.8 \mathrm{v}} \mathrm{Fe}^{2+} \xrightarrow{-0.5 \mathrm{v}} \mathrm{Fe}^0\)
In the above diagram, the standard electrode potentials are given in volts (over the arrow).
The value of \(\mathrm{E}_{\mathrm{FeO}_4^{2-} / \mathrm{Fe}^{2+}}^{\mathrm{O}}\) is _______.

Electromagnetic waves travel in a medium with speed of \(1.5 \times 10^8 \mathrm{~ms}^{-1}\). The relative permeability of the medium is \(2.0\) . The relative permittivity will be _______.

Which one of the following molecules is polar ?

The bulk moduli of ethanol, mercury and water are given as \(0.9, 25\) and \(2 .2\) respectively in units of \(10^9\, Nm^{-2}\) . For a given value of pressure, the fractional compression in volume is \(\frac{{\Delta V}}{V}\). Which of the following statements about \(\frac{{\Delta V}}{V}\) for these three liquids is correct ?

A point charge of \(10\,\mu C\) is placed at the origin. At what location on the \(X\)-axis should a point charge of \(40\,\mu\,C\) be placed so that the net electric field is zero at \(x =2\,cm\) on the \(X\)-axis ?

The correct order of basic nature on aqueous solution for the bases \(\mathrm{NH}_3, \mathrm{H}_2 \mathrm{~N}-\mathrm{NH}_2, \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{NH}_2\), \(\left(\mathrm{CH}_3 \mathrm{CH}_2\right)_2 \mathrm{NH}\) and \(\left(\mathrm{CH}_3 \mathrm{CH}_2\right)_3 \mathrm{~N}\) is _______.

Two coherent point sources \(S_1\) and \(S_2\) are separated by a small distance '\(d\)' as shown. The fringes obtained on the screen will be