An aqueous solution of hydrazine \(\left(\mathrm{N}_2 \mathrm{H}_4\right)\) is electrochemically oxidized by \(\mathrm{O}_2\), thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is \(\mathrm{N}_2(\mathrm{~g})\).
Choose the correct statement(s) about the above process :

The compound(s) with two lone pairs of electrons on the central atom is (are)

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)

The oxidation number of \(\mathrm{Mn}\) in the product of alkaline oxidative fusion of \(\mathrm{MnO}_2\) is

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of ${5.7}^{\mathrm{o}}\mathrm{C}$ was measured for the beaker and its contents (Expt.1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant $(-57.0\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1})$ , this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid $({\mathrm{K}}_{\mathrm{a}}=2.0\times {10}^{-5})$ was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of ${5.6}^{\mathrm{o}}\mathrm{C}$ was measured. (Consider heat capacity of all solutions as $4.2\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{g}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ and density of all solutions as $1.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}{\mathrm{L}}^{-1}$ )
The pH of the solution after Expt. 2 is

The total number of ${\mathrm{sp}}^2$ hybridised carbon atoms in the major product $\mathbf{P}$ (a non-heterocyclic compound) of the following reaction is

Consider the following cell reaction,
\(2 \mathrm{Fe}(\mathrm{s})+\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q) \longrightarrow \)
\( 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{H}_2 \mathrm{O}(l), E^{\circ}=1.67 \mathrm{~V} \)
\( \text {At } {\left[\mathrm{Fe}^{2+}\right]=10^{-3} \mathrm{M}, \mathrm{P}\left(\mathrm{O}_2\right)=0.1 \mathrm{~atm}}\)
and \(\mathrm{pH}=3\), the cell potential at \(25^{\circ} \mathrm{C}\) is

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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:
What is the disadvantage of this system?

Let \(\mathbb{R}\) denote the set of all real numbers. Define the function \(f: \mathbb{R \rightarrow \mathbb { R }}\) by
\(f(\mathrm{x})=\left\{\begin{array}{cc}2-2 x^2-x^2 \sin \frac{1}{x} & \text { if } x \neq 0 \\ 2 & \text { if } x=0\end{array}\right.\)
Then which one of the following statements is TRUE ?

A circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field $\overrightarrow{B}$ points into the plane of the paper. At $t=0$ , the loop starts rotating about the common diameter as axis with a constant angular velocity in the magnetic field. Which of the following options is/are correct?

The arrangement of X^- ions around A⁺ ion in solid AX is given in the figure (not drawn to scale). If the radius of X^- is 250 pm, the radius of A⁺ is

Coefficient of ${\mathrm{x}}^{11}$ in the expansion of ${\left(1+{\mathrm{x}}^2\right)}^4\mathrm{ }{\left(1+{\mathrm{x}}^3\right)}^7\mathrm{ }{\left(1+{\mathrm{x}}^4\right)}^{12}$ is

Aluminium reacts with sulfuric acid to form aluminium sulfate and hydrogen. What is the volume of hydrogen gas in liters $\left(\mathrm{L}\right)$ produced at $300 \mathrm{K}$ and $1.0$ atm pressure, when $5.4 \mathrm{g}$ of aluminium and $50.0 \mathrm{mL}$ of $5.0 \mathrm{M}$ sulfuric acid are combined for the reaction? (Use molar mass of aluminium as $27.0 \mathrm{g} {\mathrm{mol}}^{-1}$, $\mathrm{R}=0.082 \mathrm{atm} \mathrm{L} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$)