\(3 \;g\) of acetic acid is added to \(250\; \mathrm{mL}\) of \(0.1\; \mathrm{M} \mathrm{HCl}\) and the solution made up to \(500\; \mathrm{mL}\) To \(20 \;\mathrm{mL}\) of this solution \(\frac{1}{2}\; \mathrm{mL}\) of \(5\; \mathrm{M\;NaOH}\) is added. The \(\mathrm{pH}\) of the solution is [Given : \(\mathrm{pK}_{\mathrm{a}}\) of acetic acid \(=4.75,\) molar mass of acetic acid \(=60 \mathrm{g} / \mathrm{mol}, \log 3=0.4771]\) Neglect any changes in volume

\(FeO _4^{2-} \stackrel{+2.2\,V }{\longrightarrow} Fe ^{3+} \stackrel{+0.70\,V }{\longrightarrow} Fe ^{2+} \stackrel{-0.45\,V }{\longrightarrow} Fe ^0\) \(E _{ FeO _4^{2-} / Fe ^{2+}}^\theta\) is \(x \times 10^{-3} V\). The value of \(x\) is \(.........\).

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:

\(4.5\) moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, \(3\) moles of HI were found. The equilibrium constant for \(H _2( g )+ I _2( g ) \rightleftharpoons 2 HI ( g )\) is .......

The ratio of number of oxygen atoms to bromine atoms in the product \(\mathrm{Q}\) is _______ \(\times 10^{-1}\).

Sodium fusion extract of an organic compound \(( Y )\) with \(CHCl _3\) and chlorine water gives violet color to the \(CHCl _3\) layer. 0.15 g of \(( Y )\) gave 0.12 g of the silver halide precipitate in Carius method. Percentage of halogen in the compound \(( Y )\) is _______. (Nearest integer).
(Given : molar mass \(g ~ mol ^{-1} C : 12, H : 1, Cl : 35.5\), \(\operatorname{Br}: 80, I : 127\) )

For the reaction \(\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g}) \rightleftharpoons 2 \ \mathrm{NO}_2(\mathrm{~g})\), \(\mathrm{K}_{\mathrm{p}}=0.492 \mathrm{~atm}\) at \(300 \mathrm{~K}\) . \(\mathrm{K}_{\mathrm{c}}\) for the reaction at same temperature is _______ \( \times 10^{-2}\). (Given : \(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) )

A straight wire carrying a current of \(14\,A\) is bent into a semicircular are of radius \(2.2\,cm\) as shown in the figure. The magnetic field produced by the current at the centre \((O)\) of the arc. is \(.........\,\times 10^{-4}\, T\)

Let \(x _{ i }(1 \leq i \leq 10)\) be ten observations of a random variable \(X .\) If \(\sum \limits_{ i =1}^{10}\left( x _{ i }- p \right)=3\) and \(\sum \limits_{ i =1}^{10}\left( x _{ i }- p \right)^{2}=9\) where \(0 \neq p \in R ,\) then the standard deviation of these observations is 

Total number of moles of \(AgCl\) precipitated on addition of excess of \(AgNO _j\) to one mole each of the following complexes \(\left[ Co \left( NH _3\right)_4 Cl _2\right] Cl\), \(\left[ Ni \left( H _2 O \right)_6\right] Cl _2,\left[ Pt \left( NH _3\right)_2 Cl _2\right]\) and \(\left[ Pd \left( NH _3\right)_4\right] Cl _2\) is \(...............\)

Let \(E_{1}\) and \(E_{2}\) be two events such that the conditional probabilities \(P \left( E _{1} \mid E _{2}\right)=\frac{1}{2}\), \(P \left( E _{2} \mid E _{1}\right)=\frac{3}{4}\) and \(P \left( E _{1} \cap E _{2}\right)=\frac{1}{8}\). Then

If \((a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^{2}-b^{2}\) where \(a>b>0,\) then \(\frac{d x}{d y}\) at \(\left(\frac{\pi}{4}, \frac{\pi}{4}\right)\) is

Let \(\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}\) lie on the plane \(p x-q y+\) \(z=5\), for some \(p, q \in R\). The shortest distance of the plane from the origin is