The correct order of \(pK _{ a }\) values for the following compounds is:

The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is:

X and Y are the number of electrons involved, respectively during the oxidation of \( I^{-} \) to \( I_{2} \) and \( S^{2-} \) to S by acidified \( K_{2}Cr_{2}O_{7} \). The value of X + Y is ______.

Given \(\left( i \right)\,2F{e_2}{O_3}\left( s \right) \to 4Fe\left( s \right) + 3{O_2}\left( g \right)\)          \({\Delta _r}{G^o} =  + 1487.0\,kJ\,mo{l^{ - 1}}\) \(\left( {ii} \right)\,2CO\left( g \right) + {O_2}(g) \to 2C{O_2}\left( g \right)\)         \({\Delta _r}{G^o} =  - 514.4\,kJ\,mo{l^{ - 1}}\) Free energy change, \(\Delta_rG^o\)  for the reaction \(\,2F{e_2}{O_3}\left( s \right) + 6CO\left( g \right) \to 4Fe\left( s \right) + 6C{O_2}\left( g \right)\) will be .....\(kJ\, mol^{-1}\)

Consider the following half cell reaction
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})\) \(\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
The reaction was conducted with the ratio of \(\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}\). The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
\(\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]\)

At \(27^{\circ}\,C\), a solution containing \(2.5\,g\) of solute in \(250.0\,mL\) of solution exerts an osmotic pressure of \(400\,Pa\). The molar mass of the solute is \(..............g\) \(mol ^{-1}\) (Nearest integer)(Given : \(R =0.083\,L\,bar\,K ^{-1}\,mol ^{-1}\) )

The exact volumes of \(1\, M\, NaOH\) solution required to neutralise \(50 \,mL\) of \(1 \,M \,H _{3} PO _{3}\) solution and \(100\, mL\) of \(2 \,M\, H _{3} PO _{2}\) solution, respectively, are :

A vector \(\vec A \) is rotated by a small angle \(\Delta \theta\) radian \(( \Delta \theta << 1)\) to get a new vector \(\vec B\) In that case \(\left| {\vec B - \vec A} \right|\) is

For a cell, \(Cu ( s ) \mid Cu ^{2+}\left(0.001 M || Ag ^{+}(0.01\,M ) \mid Ag ( s )\right.\) the cell potential is found to be \(0.43\,V\) at \(298 K\). The magnitude of standard electrode potential for \(Cu ^{2+} / Cu\) \(.........\times 10^{-2}\,V\) \(\left[\text { Given }: E _{ Ag ^{+} / Ag }^{\Theta}=0.80 V \text { and } \frac{2.303 \,RT }{ F }=0.06\,V \right]\)

Two wires \(A\) and \(B\) are carrying currents \(I_1\) and \(I_2\) as shown in the figure. The separation between them is \(d\). A third wire \(C\) carrying a current \(I\) is to be kept parallel to them at a distance \(x\) from \(A\) such that the net force acting on it is zero. The possible values of \(x\) are

Let \(f : [-1,3] \to  R\) be defined as \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
  {\left| x \right| + \left[ x \right],}&{ - 1 \leq x < 1} \\ 
  {x + \left| x \right|,}&{1 \leq x < 2} \\ 
  {x + \left| x \right|,}&{2 \leq x \leq 3} 
\end{array}} \right.\)  where \([t]\) denotes the greatest integer less than or equal to \(t\). Then, \(f\) is discontinuous at:

If  \(\int {\frac{{dx}}{{{{\cos }^3}\,x\sqrt {2\,\sin \,2x} }} = {{(\tan \,\,x)}^A} + C{{(\tan \,\,x)}^B} + k,} \) where \(k\) is a constant of integration, then \(A+ B + C\) equals

\([image]\) Maleic anhydride Maleic anhydride can be prepared by :