Consider the following reaction,
\(2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})\)
which follows the mechanism given below:
\(2 \mathrm{NO}(\mathrm{g}) \stackrel{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})\) \(\quad\) (fast equlibrium)
\(\mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_2} \mathrm{~N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})\) \(\quad\)(slow reaction)
\(\mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_3} \mathrm{~N}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})\) \(\quad\) (fast reaction)
The order of the reaction is_____

A positron is emitted from \({ }_{11}^{23} \mathrm{Na}\). The ratio of the atomic mass and atomic number of the resulting nuclide is

On dissolving $0.5\mathrm{ }\mathrm{g}$ of a non-volatile non-ionic solute to $39\mathrm{ }\mathrm{g}$ of benzene, its vapor pressure decreases from $650\mathrm{ }\mathrm{m}\mathrm{m}\mathrm{ }\mathrm{H}\mathrm{g}$ to $640\mathrm{ }\mathrm{m}\mathrm{m}\mathrm{ }\mathrm{H}\mathrm{g}.$ The depression of freezing point of benzene (in $\mathrm{K}$ ) upon addition of the solute is _______
(Given data: Molar mass and the molal freezing point depression constant of benzene are $78\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$ and $5.12\mathrm{ }\mathrm{K}\mathrm{ }\mathrm{k}\mathrm{g}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1},$ respectively)

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

Among the complex ions,
\(\left[\mathrm{Co}\left(\mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{NH}_{2}\right)_{2} \mathrm{Cl}_{2}\right]^{+},\)\(\left[\mathrm{CrCl}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{OH})_{2}\right]^{+}\), \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{CN})_{4}\right]^{-},\)\(\left[\mathrm{Co}(\mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{NH}_{2})_{2}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}\right]^{2+}\) and \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right]^{2+}\), the number of complex ion(s) that show(s) cis-trans isomerism is

Match each of the compounds is Column I with its characteristic reaction(s) is Column II.

An organic compound \(\mathbf{P}\) having molecular formula \(\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}_3\) gives ferric chloride test and does not have intramolecular hydrogen bond. The compound \(\mathbf{P}\) reacts with 3 equivalents of \(\mathrm{NH}_2 \mathrm{OH}\) to produce oxime \(\mathbf{Q}\). Treatment of \(\mathbf{P}\) with excess methyl iodide in the presence of \(\mathrm{KOH}\) produces compound \(\mathbf{R}\) as the major product. Reaction of \(\mathbf{R}\) with excess iso-butylmagnesium bromide followed by treatment with \(\mathrm{H}_3 \mathrm{O}^{+}\)gives compound \(\mathrm{S}\) as the major product.
The total number of methyl \(\left(-\mathrm{CH}_3\right)\) group(s) in compound \(\mathbf{S}\) is ________. (consider maximum value if there are two values)

Paragraph:
An aqueous solution of metal ion \(\mathbf{M} 1\) reacts separately with reagents \(\mathbf{Q}\) and \(\mathbf{R}\) in excess to give tetrahedral and square planar complexes, respectively. An aqueous solution of another metal ion M2 always forms tetrahedral complexes with these reagents. Aqueous solution of \(\mathbf{M} 2\) on reaction with reagent \(\mathbf{S}\) gives white precipitate which dissolves in excess of \(\mathbf{S}\). The reactions are summarized in the scheme given below:


Question:
Reagent \(\mathbf{S}\) is

Two inductors $L_i$ (inductance $1 \mathrm{mH}$, internal resistance $3 \mathrm{\Omega }$ ) and $L_2$ (inductance $2 \mathrm{mH}$, internal resistance $4 \mathrm{\Omega }$ ), and a resistor $R$(resistance $12 \mathrm{\Omega }$ ) are all connected in parallel across a $5 \mathrm{V}$ battery. The circuit is switched on at time $t=0$. The ratio of the maximum current $\left(\frac{I_{max}}{I_{min}}\right)$ drawn from the battery is:

The coefficient of $x^9$ in the expansion of $\left(1+x\right) \left(1+x^2\right) \left(1+x^3\right)\dots \dots \left(1+x^{100}\right)$ is

A thin convex lens is made of two materials with refractive indices ${\mathrm{n}}_1$ and ${\mathrm{n}}_2,$ as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. $\mathrm{f}$ is the focal length of the lens when ${\mathrm{n}}_1={\mathrm{n}}_2=\mathrm{n}.$ The focal length is $\mathrm{f}+\mathrm{\Delta }\mathrm{f}$ when ${\mathrm{n}}_1=\mathrm{n}$ and ${\mathrm{n}}_2=\mathrm{n}+\mathrm{\Delta }\mathrm{n}.$ Assuming $\mathrm{\Delta }\mathrm{n}<<\left(\mathrm{n}-1\right)$ and $1<\mathrm{n}<2,$ the correct statement(s) is/are:

Let $\overrightarrow{u},\overrightarrow{v}$ and $\overrightarrow{w}$ be vectors in three-dimensional space, where $\overrightarrow{u}$ and $\overrightarrow{v}$ are unit vectors which are not perpendicular to each other and $\overrightarrow{u}·\overrightarrow{w}=1, \overrightarrow{v}·\overrightarrow{w}=1, \overrightarrow{w}·\overrightarrow{w}=4$.
If the volume of the parallelopiped, whose adjacent sides are represented by the vectors $\overrightarrow{u},\overrightarrow{v}$ and $\overrightarrow{w}$, is $\sqrt{2}$, then the value of $|3\overrightarrow{u}+5\overrightarrow{v}|$ is

For a non-zero complex number $z$, let arg$\left(z\right)$ denote the principal argument with $-\pi <\mathrm{a}\mathrm{r}\mathrm{g}\left(z\right)\le \pi$ then, which of the following statement(s) is (are) FALSE?