The total number(s) of stable conformers with non-zero dipole moment for the following compound is(are)

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\(\mathbf{X}\) and \(\mathbf{Y}\) are two volatile liquids with molar weights of \(10 \mathrm{~g} \mathrm{~mol}^{-1}\) and \(40 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively. Two cotton plugs, one soaked in \(\mathbf{X}\) and the other soaked in \(\mathbf{Y}\), are simultaneously placed at the ends of a tube of length \(L=24 \mathrm{~cm}\), as shown in the figure. The tube is filled with an inert gas at \(1\) atmosphere pressure and a temperature of \(300 \mathrm{~K}\). Vapours of \(\mathbf{X}\) and \(\mathbf{Y}\) react to form a product which is first observed at a distance \(\mathbf{d} \mathrm{~cm}\) from the plug soaked in \(\mathbf{X}\). Take \(\mathbf{X}\) and \(\mathbf{Y}\) to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.



Question:

The value of \(\mathbf{d}\) in \(\mathbf{c m}\) (shown in the figure), as estimated from Graham's law, is

The correct statement $\left(\mathrm{s}\right)$ related to colloids is(are)

Consider the following molecules : ${\mathrm{Br}}_3{\mathrm{O}}_8, {\mathrm{F}}_2\mathrm{O},{\mathrm{H}}_2 {\mathrm{S}}_4{\mathrm{O}}_6,{\mathrm{H}}_2 {\mathrm{S}}_5{\mathrm{O}}_6$, and ${\mathrm{C}}_3{\mathrm{O}}_2$. Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure$1$). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure $2$), the volume (in ${\mathrm{m}}^3$) of the compartment A after the system attains equilibrium is _________.

If the bond length of \(\mathrm{CO}\) bond in carbon monoxide is \(1.128 \mathrm{~A}^{\circ}\), then what is the value of \(\mathrm{CO}\) bond length in \(\mathrm{Fe}(\mathrm{CO})_5\) ?

In the following reaction sequence, the major product \(\mathbf{P}\) is formed.

Glycerol reacts completely with excess \(\mathbf{P}\) in the presence of an acid catalyst to form \(\mathbf{Q}\). Reaction of \(\mathbf{Q}\) with excess \(\mathrm{NaOH}\) followed by the treatment with \(\mathrm{CaCl}_2\) yields Ca-soap \(\mathbf{R}\), quantitatively. Starting with one mole of \(\mathbf{Q}\), the amount of \(\mathbf{R}\) produced in gram is ________.
[Given, atomic weight: \(\mathrm{H}=1, \mathrm{C}=12,\) \(\mathrm{~N}=14, \mathrm{O}=16, \mathrm{Na}=23, \mathrm{Cl}=35,\) \(\mathrm{Ca}=40\)]

A mixture of 2 moles of helium gas (atomic mass \(=4 \mathrm{amu}\) ) and 1 mole of argon gas (atomic mass \(=40 \mathrm{amu}\) ) is kept at \(300 \mathrm{~K}\) in a container. The ratio of the rms speeds \(\left(\frac{v_{\mathrm{rms}}(\text { helium })}{v_{\mathrm{rms}}(\operatorname{argon})}\right)\) is

In a study about a pandemic, data of $900$ persons was collected. It was found that $190$ persons had symptom of fever, $220$ persons had symptom of cough, $220$ persons had symptom of breathing problem, $330$ persons had symptom of fever or cough or both, $350$ persons had symptom of cough or breathing problem or both, $340$ persons had symptom of fever or breathing problem or both, $30$ persons had all three symptoms (fever, cough and breathing problem). If a person is chosen randomly from these $900$ persons, then the probability that the person has at most one symptom is ______.

The work done on a particle of mass m by a force $\text{K}\left[\frac{\text{x}}{{\left({\text{x}}^2+{\text{y}}^2\right)}^{3/2}}\widehat{\text{i}}+\frac{\text{y}}{{\left({\text{x}}^2+{\text{y}}^2\right)}^{3/2}}\widehat{\text{j}}\right]$ (K being a constant of appropriate dimensions, when the particle is taken from the point (a,0) to the point (0,a) along a circular path of radius a about the origin in the x-y plane is

Paragraph : In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $\left[E\right] \mathrm{a}\mathrm{n}\mathrm{d} \left[B\right]$ stand for dimensions of electric and magnetic fields respectively, while $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $\left[L\right]\mathrm{a}\mathrm{n}\mathrm{d} \left[T\right]$ are dimensions of length and time respectively. All the quantities are given in $SI$ units

Question : The relation between $\left[{ϵ}_0\right] \mathrm{a}\mathrm{n}\mathrm{d} \left[{\mu }_0\right]$ is

Suppose a ${}_{88}{}^{226}Ra$ nucleus at rest and in ground state undergoes $\mathrm{\alpha }$ -decay to a ${}_{86}{}^{222}Rn$ nucleus in its excited state. The kinetic energy of the emitted $\mathrm{\alpha }$ particle is found to be $4.44\mathrm{ }\mathrm{M}\mathrm{e}\mathrm{V}.{}_{86}{}^{222}Rn$ nucleus then goes to its ground state by $\mathrm{\gamma }$ -decay. The energy of the emitted $\mathrm{\gamma }$ -photon is _______ $\mathrm{k}\mathrm{e}\mathrm{V},$
[Given: atomic mass of ${\mathrm{ }}_{88}^{226}\mathrm{R}\mathrm{a}=226.005\mathrm{u},$ atomic mass of ${\mathrm{ }}_{86}^{222}\mathrm{R}\mathrm{n}=222.000\mathrm{u},$ atomic mass of $\mathrm{\alpha }$ particle $=4.000\mathrm{u},1\mathrm{u}=931\mathrm{M}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2,\mathrm{c}$ is speed of the light]

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Consider the lines: \(L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}, L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3}\)Question:
The unit vector perpendicular to both \(L_1\) and \(L_2\) is