For a solution formed by mixing liquids $\text{L}$ and $\text{M}$, the vapour pressure of $\text{L}$ plotted against the mole fraction of $\text{M}$ in solution is shown in the following figure, Here, ${\mathrm{X}}_{\mathrm{L}}$ and ${\mathrm{X}}_{\mathrm{M}}$ represent mole fractions of $\text{L}$ and $\text{M}$, respectively, in the solution. The correct statement(s) applicable to this system is(are) -

Consider the following complex ions, P, Qand R.

The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is

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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

Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.
Question:
\(25 \mathrm{~mL}\) of household solution was mixed with \(30 \mathrm{~mL}\) of \(0.50\) M KI and \(10 \mathrm{~mL}\) of \(4 \mathrm{~N}\) acetic acid. In the titration of the liberated iodine, \(48 \mathrm{~mL}\) of \(0.25 \mathrm{~N~} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) was used to reach the end point. The molarity of the household bleach solution is

The electrochemical cell shown below is a concentration cell. \(\mathrm{M} \mid \mathrm{M}^{2+}\) (saturated solution of a sparingly soluble salt, \(\left.\mathrm{MX}_{2}\right) \| \mathrm{M}^{2 \perp}\left(0.001 \mathrm{~mol} \mathrm{dm}^{-3}\right) \mid \mathrm{M}\).
The emf of the cell depends on the difference in concentrations of \(\mathrm{M}^{2+}\) ions at the two electrodes. The emf of the cell at \(298 \mathrm{~K}\) is \(0.059 \mathrm{~V}\).
Question:
The value of \(\Delta \mathrm{G}\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\) for the given cell is (take 1 \(\mathrm{F}=96500 \mathrm{Cmol}^{-1}\) )

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The coordination number of \(\mathrm{Ni}^{2+}\) is 4 .
\(\mathrm{NiCl}_2+\mathrm{KCN}\) (excess) \(\rightarrow A\) (cyano complex)
\(\mathrm{NiCl}_2+\) conc. \(\mathrm{HCl}\) (excess) \(\rightarrow B\) (chloro complex)
Question:
The IUPAC name of \(A\) and \(B\) are

\(75.2 \mathrm{~g}\) of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}\) (phenol) is dissolved in a solvent of \(K_f=14\). If the depression in freezing point is \(7 \mathrm{~K}\), then find the \(\%\) of phenol that dimerises.

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Tangents are drawn from the point \(P(3,4)\) to the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) touching the ellipse at points \(A\) and \(B\).Question:
The equation of the locus of the point whose distance from the point \(P\) and the line \(A B\) are equal, is

A charged particle is introduced at the origin $x=0, y=0, z=0$ with a given initial velocity $\overrightarrow{v}$ . A uniform electric field $\overrightarrow{E}$ and a uniform magnetic field $\overrightarrow{B}$ exist everywhere. The velocity $\overrightarrow{v}$ , electric field $\overrightarrow{E}$ and a uniform magnetic field $\overrightarrow{B}$ are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\overrightarrow{v}=2\frac{E_0}{B_0}\widehat{x}$	(i) $\overrightarrow{E}=E_0\widehat{z}$	(P) $\overrightarrow{B}=-B_0\widehat{x}$
2. Electron with $\overrightarrow{v}=2\frac{E_0}{B_0}\widehat{y}$	(ii) $\overrightarrow{E}=-E_0\widehat{y}$	(Q) $\overrightarrow{B}=B_0\widehat{x}$
3.Proton with $\overrightarrow{v}$ =0	(iii) $\overrightarrow{E}={-E}_0\widehat{x}$	(R) $\overrightarrow{B}=-B_0\widehat{y}$
4. Proton with $\overrightarrow{v}=2\frac{E_0}{B_0}\widehat{x}$	(iv) $\overrightarrow{E}=E_0\widehat{x}$	(S) $\overrightarrow{B}=-B_0\widehat{z}$

In which case would the particle move in a straight line along the negative direction of y axis

The center of a disk of radius \(r\) and mass \(m\) is attached to a spring of spring constant \(k\), inside a ring of radius \(R>r\) as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following the Hooke's law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as \(T=\frac{2 \pi}{\omega}\). The correct expression for \(\omega\) is ( \(g\) is the acceleration due to gravity):

A cubical region of side \(a\) has its centre at the origin. It encloses three fixed point charges, \(-q\) at \((0,-a / 4,0),+3 q\) at \((0,0,0)\) and \(-q\) at \((0,+a / 4,0)\). Choose the correct options(s)

Consider an electric field \(\mathbf{E}=E_0 \hat{\mathbf{x}}\) where \(\bar{E}_0\) is a constant. The flux through the shaded area ( as shown in the figure) due to this field is

Match the statements/expressions given in Column I with the values given in Column II.