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)

Match the reaction in Column I with appropriate options in Column II

In a metal deficient oxide sample, \(\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4\) ( \(\mathbf{M}\) and \(\mathbf{Y}\) are metals), \(\mathbf{M}\) is present in both +2 and +3 oxidation states and \(\mathbf{Y}\) is in +3 oxidation state. If the fraction of \(\mathbf{M}^{2+}\) ions present in \(\mathbf{M}\) is \(\frac{1}{3}\), the value of \(\mathbf{X}\) is ________.

Reaction of \(\mathbf{x}\) g of \(\mathrm{Sn}\) with \(\mathrm{HCl}\) quantitatively produced a salt. Entire amount of the salt reacted with \(\mathbf{y} g\) of nitrobenzene in the presence of required amount of \(\mathrm{HCl}\) to produce \(1.29 \mathrm{~g}\) of an organic salt (quantitatively).
(Use Molar masses (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of \(\mathrm{H}, \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{Cl}\) and \(\mathrm{Sn}\) as \(1,12,14,16,35\) and 119 , respectively).
The value of $\mathrm{y}$ is_________ .

According to Bohr's theory \(E_n=\) Total energy, \(K_n=\) Kinetic energy, \(V_n=\) Potential energy, \(r_n=\) Radius of \(n\)th orbit

Statement I In water, orthoboric acid behaves as a weak monobasic acid.
Statement II In water, orthoboric acid acts as proton donor.

Scheme $1$ and $2$ describe the conversion of $\mathrm{P}$ to $\mathrm{Q}$ and $\mathrm{R}$ to $\mathrm{S},$ respectively. Scheme $3$ describes the synthesis of $\mathrm{T}$ from $\mathrm{Q}$ and $\mathrm{S}.$ The total number of $\mathrm{B}\mathrm{r}$ atoms in a molecule of $\mathrm{T}$ is
Scheme $1$:

Scheme $2$:

Scheme$3$:

The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match each entry in List-I with the appropriate entry in List-II and choose the correct options.

List - I	List - II
(P) Stephen reaction	(1)
(Q) Sandmeyer reaction	(2)
(R) Hoffmann bromamide degradation reaction	(3)
(S) Cannizzaro reaction	(4)
	(5)

If the normal of the parabola ${\mathrm{y}}^2=4\mathrm{x}$ drawn at the end points of its latus rectum are tangents to the circle ${\left(\mathrm{x}-3\right)}^2+{\left(\mathrm{y}+2\right)}^2={\mathrm{r}}^2,$ then the value of ${\mathrm{r}}^2$ is

Paragraph:
Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS Maglev system.
There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If trains lower down then due to Lenz's law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force disc to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.
Disadvantage of Maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it leviated and as it moves forward according to Lenz law, there is an electromagnetic drag force.
Question:
Which force causes the train to elevate up?

A source of constant voltage $\mathrm{V}$ is connected to a resistance$\mathrm{R}$ and two ideal inductors ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ through a switch $\mathrm{S}$ as shown. There is no mutual inductance between the two inductors. The switch $\mathrm{S}$ is initially open. At $\mathrm{t}=0$ , the switch is closed and current begins to flow. Which of the following options is/are correct?

For every pair of continuous functions $f, g :\left[0, 1\right]\to R$ such that $\max \left\{f\left(x\right):x \in \left[0, 1\right]\right\}=\max \{g\left(x\right) :x \in \left[0, 1\right]\},$then the correct statement (s) is (are)