Among \(\mathrm{CrO}, \mathrm{Cr}_2 \mathrm{O}_3\) and \(\mathrm{CrO}_3\), the sum of spin-only magnetic moment values of basic and amphoteric oxides is _______ \(10^{-2} \mathrm{BM}\) (nearest integer). (Given atomic number of \(\mathrm{Cr}\) is 24 )

For the reaction, \( N_{2}O_{4}\rightleftharpoons 2NO_{2}, \) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is -5.40 kJ mol⁻¹.
B. As \( \Delta G^{\ominus} \) in graph is positive, \( N_{2}O_{4} \) will not dissociate into \( NO_{2} \) at all.
C. Reverse reaction will go to completion.
D. When 1 mole of \( N_{2}O_{4} \) changes into equilibrium mixture, value of \( \Delta G^{\ominus}=-0.84 \, kJ \, mol^{-1} \).
E. When 2 mole of \( NO_{2} \) changes into equilibrium mixture, \( \Delta G^{\ominus} \) for equilibrium mixture is -6.24 kJ mol⁻¹.

Choose the correct answer from the options given below:

Given below are two statements: Statement \(I\): Group \(13\) trivalent halides get easily hydrolyzed by water due to their covalent nature. Statement \(II\): \(\mathrm{AlCl}_3\) upon hydrolysis in acidified aqueous solution forms octahedral \(\left[\mathrm{Al}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}\) ion. In the light of the above statements, choose the correct answer from the options given below :

Among \((a) - (d)\) the complexes that can display geometrical isomerism are \((a)\) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}\right]^{+}\) \((b)\) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}_{5}\right]^{-}\) \((c)\) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}\left(\mathrm{NO}_{2}\right)\right]\) \((d)\) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{ClBr}\right]^{2+}\)

The order of stability of the following carbocations is : \((I)\,\,C{H_2} = CH - \mathop C\limits^ \oplus  {H_2}\) \((II)\,\,C{H_3} - CH_2 - \mathop C\limits^ \oplus  {H_2}\)

What quantity (in \(mL\)) of a \(45\%\) acid solution of a mono-protic strong acid must be mixed with a \(20\%\) solution of the same acid to produce \(800\, mL\) of a \(29.875\%\) acid solution?

x mg of pure HCl was used to make an aqueous solution. 25.0 mL of \(0.1 M Ba ( OH )_2\) solution is used when the HCl solution was titrated against it. The numerical value of x is _________ \(\times 10^{-1}\). (Nearest integer)
Given : Molar mass of HCl and \(Ba ( OH )_2\) are 36.5 and \(171.0 g mol ^{-1}\) respectively.

The standard enthalpy of formation \((\Delta _f\,H^o_{298})\) for methane, \(CH_4\) is \(-74.9\,kJ\,mol^{-1}\) . In order to calculate the average energy given out in the formation of a \(C - H\) bond from this it is necessary to know which one of the following?

The value \(\sum \limits_{ r =0}^{22}{ }^{22} C _{ r }{ }^{23} C _{ r }\) is \(.......\)

Given below are the statements about diborane. \((a)\) Diborane is prepared by the oxidation of \(\mathrm{NaBH}_{4}\) with \(\mathrm{I}_{2}\). \((b)\) Each boron atom is in sp \(^{2}\) hybridized state. \((c)\) Diborane has one bridged \(3\) centre\(-2-\)electron bond. \((d)\) Diborane is a planar molecule. The option with correct statement(s) is :

The locus of the mid point of the line segment joining the point \((4,3)\) and the points on the ellipse \(x^{2}+2 y^{2}=4\) is an ellipse with eccentricity

The sum of the cubes of all the roots of the equation \(x^{4}-3 x^{3}-2 x^{2}+3 x+1=10\) is

Two charges \(7 \mu C\) and \(-2 \mu C\) are placed at \((-9,0,0) cm\) and \((9,0,0) cm\) respectively in an external field \(E=\frac{ A }{ r ^2} \hat{ r }\), where \(A=9 \times 10^5 N / C . m ^2\).
Considering the potential at infinity is 0 , the electrostatic energy of the configuration is ___________ J .