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Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately \(6.023 \times 10^{23}\) ) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.
A \(4.0\) molar aqueous solution of \(\mathrm{NaCl}\) is prepared and \(500 \mathrm{~mL}\) of this solution is electrolysed. This leads to the evolution of chlorine gas at one of electrodes (atomic mass: \(\mathrm{Na}=23, \mathrm{Hg}=200 ; 1\) faraday \(=96500\) coulombs).
Question:
If the cathode is a Hg electrode, the maximum weight \((g)\) of amalgam formed from this solution is

Consider the reaction sequence from $\mathrm{P}$ to $\mathrm{Q}$ shown below. The overall yield of the major product $\mathrm{Q}$ from $\mathrm{P}$ $75\%.$ What is the amount in grams of $\mathrm{Q}$ obtained from $9.3 \mathrm{mL}$ $\mathrm{P}$? (Use density of $=1.00{\text{\hspace{0.33em}g\hspace{0.33em}mL}}^{-1};$ Molar mass of $\mathrm{C}=12.0,\mathrm{H}=1.0,\mathrm{O}=16.0$ and $\mathrm{N}=14.0 \mathrm{g} {\mathrm{mol}}^{-1}$)

The correct option(s) regarding the complex ${\left[Co\left(en\right){\left(N{H}_3\right)}_3\left(H_{2}O\right)\right]}^{3+}$ :-
(en $= H_{2}NC{H}_{2}C{H}_{2}N{H}_2$ ) is (are)

The correct statement(s) for the following addition reactions is(are)

The species present in solution when \(\mathrm{CO}_2\) is dissolved in water are

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 $1.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}{\mathrm{L}}^{-1}$ )
Enthalpy of dissociation $\left(\mathrm{i}\mathrm{n}\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\right)$ of acetic acid obtained from the Expt. 2 is

Match the specified conditions in solids listed in Column I with their properties in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

Column I	Column II
A. Simple cubic and face-centered cubic	p. Have these cell parameters \(a=b=c \text { and } \alpha=\beta=\gamma\)
B. Cubic and rhombohedral	q. Are two crystal systems
C. Cubic and tetragonal	r. Have only two crystallographic angles of \(90^{\circ}\)
D. Hexagonal and monoclinic	s. Belong to same crystal system

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A special metal \(S\) conducts electricity without any resistance. A closed wire loop, made of \(S\), does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius \(a\), with its center at the origin. A magnetic dipole of moment \(m\) is brought along the axis of this loop from infinity to a point at distance \(r(\gg a)\) from the center of the loop with its north pole always facing the loop, as shown in the figure below.

The magnitude of magnetic field of a dipole \(m\), at a point on its axis at distance \(r\), is \(\frac{\mu_{0}}{2 \pi} \frac{m}{r^{3}}\), where \(\mu_{0}\) is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, \(m_{1}\) and \(m_{2}\), separated by a distance \(r\) on the common axis, with their north poles facing each other, is \(\frac{k m_{1} m_{2}}{r^{4}}\), where \(k\) is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

Question :
The work done in bringing the dipole from infinity to a distance$r$from the centre of the loop by the given process is proportional to:

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $\mathrm{\theta }$ with the horizontal floor. The coefficient of friction between the wall and the ladder is ${\mathrm{\mu }}_1$ and that between the floor and the ladder is ${\mathrm{\mu }}_2$ . The normal reaction of the wall on the ladder is ${\mathrm{N}}_1$ and that of the floor is ${\mathrm{N}}_2$ If the ladder is about to slip, then

A block of mass \(5 \mathrm{~kg}\) moves along the \(x\)-direction subject to the force \(F=(-20 x+10) \mathrm{N}\), with the value of \(x\) in metre. At time \(t=0 \mathrm{~s}\), it is at rest at position \(x=1 \mathrm{~m}\). The position and momentum of the block at \(t=(\pi / 4) \mathrm{s}\) are

A container with $1 \mathrm{kg}$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 \mathrm{W} {\mathrm{m}}^{-2}$ and it is absorbed by the water over an effective area of $0.05 {\mathrm{m}}^2.$ Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${}^{\circ }\mathrm{C}$) in the temperature of water and the surroundings after a long time will be_________. (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 {\mathrm{s}}^{-1},$ Heat capacity of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

The Henry's law constant for the solubility of \(\mathrm{N}_2\) gas in water at \(298 \mathrm{~K}\) is \(1.0 \times 105 \mathrm{~atm}\). The mole fraction of \(\mathrm{N}_2\) in air is \(0.8\). The number of moles of \(\mathrm{N}_2\) from air dissolved in 10 moles of water of \(298 \mathrm{~K}\) and \(5 \mathrm{~atm}\) pressure is

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$, at a height $L$ above the hinge at point $O$. A block of weight $\alpha W$ is attached at the point $P$ of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of  $\left(2\sqrt{2}\right)W$. Which of the following statement(s) is(are) correct?