The correct order for acidity of the following hydroxyl compound is: Choose the correct answer from the options given below:

Two \(5\) molal solutions are prepared by dissolving a non-electrolyte, non-volatile solute separately in the solvents \(X\) and \(Y\). The molecular weights of the solvents are \(M_X\) and \(M_Y\), respectively where \(M_X\, = \frac{3}{4} M_Y\). The relative lowering of  vapour pressure of the solution in \(X\) is \(''m''\) times that of the solution in \(Y\). Given that the number of moles of solute is very small in comparison to that of solvent, the value of \(''m''\)  is

Given below are two statements :
Statement (I): Experimentally determined oxygen-oxygen bond lengths in the \(\mathrm{O}_3\) are found to be same and the bond length is greater than that of a \(\mathrm{O}=\mathrm{O}\) (double bond) but less than that of a single \((O-O)\) bond.
Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond \((\mathrm{O}=\mathrm{O})\) but more than that of a single bond \((\mathrm{O}-\mathrm{O})\).
In the light of the above statements, choose the correct answer from the options given below :

The large difference between the melting and boiling points of oxygen and sulphur may be explained on the basis of _______.

For the following Assertion and Reason, the correct option is Assertion \((A)\) \(:\) When Cu \((II)\) and sulphide ions are mixed, they react together extremely quickly to give a solid. Reason \((R)\) \(:\) The equilibrium constant of \(Cu ^{2+}( aq )+ S ^{2-}( aq ) \rightleftharpoons \operatorname{CuS}( s )\) is high because the solubility product is low.  

Which of the following combination of statements is true regarding the interpretation of the atomic orbitals? \((1)\) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum. \((2)\) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number \((3)\) According to wave mechanics, the ground state angular momentum is equal to \(\frac {h}{2\pi }\) \((4)\) The plot of \(\Psi \,\,Vs\,\,r\) for various azimuthal quantum numbers, shows peak shifting towards higher \(r\) value

Consider two Group IV metal ions \( X^{2+} \) and \( Y^{2+} \).
A solution containing 0.01 \( MX^{2+} \) and 0.01 \( MY^{2+} \) is saturated with \( H_{2}S \). The pH at which the metal sulphide YS will form as a precipitate is _______
(Nearest integer)
(Given:
\(K _{ sp }( XS )=1 \times 10^{-22}\) at \(25^{\circ} C , K _{ sp }( YS )=4 \times 10^{-16}\) at \(25^{\circ} C\), \(\left[ H _2 S\right]=0.1 M\) in solution, \(K _{ al } \times K _{22}\left( H _2 S\right)=1.0 \times 10^{-21}\), \(\log 2=0.30, \log 3=0.48, \log 5=0.70)\)

Let \(\quad f(x)=x+\frac{a}{\pi^2-4} \sin x+\frac{b}{\pi^2-4} \cos x\) \(x \in R\) be a function which satisfies \(f(x)=x+\int \limits_0^{\pi / 2} \sin (x+y) f(y) d y\). Then \(( a + b )\) is equal to \(............\)

The sum \(1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\ldots\) upto \(\infty\) terms, is equal to

The number of real roots of the equation \(x | x |-5| x +2|+6=0\), is

\(\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right)\) is equal to:

The correct order of the first ionization enthalpy is _______.

\(1\, gram\) of a carbonate \((M_2CO_3)\) on treatment with excess \(HCl\) produces \(0.01186\, mole\) of \(CO_2.\) The molar mass of \(M_2CO_3\) in \(g\, mol^{-1}\) is :