A solution of $0.1\mathrm{M}$ weak base $\left(\mathrm{B}\right)$ is titrated with $0.1\mathrm{M}$ of a strong acid $\left(\mathrm{HA}\right)$. The variation of $\mathrm{pH}$ of the solution with the volume of $\mathrm{HA}$ added is shown in the figure below. What is the ${\mathrm{pK}}_{\mathrm{b}}$ of the base? The neutralization reaction is given by$\mathrm{B}+\mathrm{HA}\to {\mathrm{BH}}^{+}+{\mathrm{A}}^{-}$.

The electrochemical cell shown below is a concentration cell. \(\mathrm{M} \mid \mathrm{M}^{2+}\) (saturated solution of a sparingly soluble salt, \(\left.\mathrm{MX}_{2}\right) \| \mathrm{M}^{2 \perp}\left(0.001 \mathrm{~mol} \mathrm{dm}^{-3}\right) \mid \mathrm{M}\).
The emf of the cell depends on the difference in concentrations of \(\mathrm{M}^{2+}\) ions at the two electrodes. The emf of the cell at \(298 \mathrm{~K}\) is \(0.059 \mathrm{~V}\).
Question:
The value of \(\Delta \mathrm{G}\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\) for the given cell is (take 1 \(\mathrm{F}=96500 \mathrm{Cmol}^{-1}\) )

Ozonolysis of ${\mathrm{ClO}}_2$ produces an oxide of chlorine. The average oxidation state of chlorine in this oxide is ______ .

Consider the following complex ions, P, Qand R.

The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is

For the process ${\mathrm{H}}_2\mathrm{O}\mathrm{ }\left(\mathcal{l}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\mathrm{ }$ at $\mathrm{T}={100}^{\mathrm{o}}\mathrm{C}\mathrm{ }$ and 1 atmosphere pressure, the correct choice is

Among ${\mathrm{B}}_2{\mathrm{H}}_6,\mathrm{ }{\mathrm{B}}_3{\mathrm{N}}_3{\mathrm{H}}_6,\mathrm{ }{\mathrm{N}}_2\mathrm{O},\mathrm{ }{\mathrm{N}}_2{\mathrm{O}}_4,\mathrm{ }{\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_3$ and ${\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_8,$ the number of molecules containing covalent bond between two atoms of the same kind is __________

The ionization isomer of \(\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}\) is

Statement 1 Bromobenzene, upon reaction with \(\mathrm{Br}_2 / \mathrm{Fe}\) gives 1, 4-dibromobenzene as the major product.
Statement 2 In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile.

The vector(s) which is/are coplanar with vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\), are perpendicular to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) is/are

Paragraph:
p-amino-N, N-dimethylaniline is added to a strongly acidic solution of \(X\). The resulting solution is treated with a few drops of aqueous solution of \(Y\) to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of \(Y\) with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of \(Y\) with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of \(Z\).
Question:
The compound \(X\), is

Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.

Which of the following statement(s) is(are) correct in SI units?

Let \(f(x)=x^2\) and \(g(x)=\sin x\) for all \(x \in R\). Then, the set of all \(x\) satisfying \((\) fogogof \()(x)=(\operatorname{gogof})(x)\), where \((f \circ g)(x)=f(g(x))\) is

Given, that the abundances of isotopes, \({ }_{54} \mathrm{Fe},{ }_{56} \mathrm{~F}\) and \({ }_{57} \mathrm{Fe}\) are \(5 \%\), \(90 \%\) and \(5 \%\), respectively, the atomic mass of \(\mathrm{Fe}\) is