Match the conversions in Column I with the type(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

An organic compound $\left({\mathrm{C}}_8{\mathrm{H}}_{10}{\mathrm{O}}_2\right)$ rotates plane-polarized light. It produces pink color with neutral ${\mathrm{FeCl}}_3$ solution. What is the total number of all the possible isomers for this compound?

For the following reaction, the equilibrium constant ${\mathrm{K}}_{\mathrm{e}}$ at $298\mathrm{ }\mathrm{K}$ is $1.6\times {10}^{17}.$
$\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{S}}^{2-}\left(\mathrm{a}\mathrm{q}\right)\mathrm{ }\rightleftharpoons \mathrm{F}\mathrm{e}\mathrm{S}\left(\mathrm{s}\right)$
When equal volumes of $0.06\mathrm{ }\mathrm{M}\mathrm{ }\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)$ and $0.2\mathrm{ }\mathrm{M}{\mathrm{ }\mathrm{S}}^{2-}\left(\mathrm{a}\mathrm{q}\right)$ solutions are mixed, the equilibrium concentration of $\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)$ is found to be $\mathrm{Y}\times {10}^{-17}\mathrm{M}.$ The value of $\mathrm{Y}$ is __________

The boiling point of water in a \(0.1\) molal silver nitrate solution (solution \(\mathbf{A}\) ) is \(\mathbf{x}^{\circ} \mathrm{C}\). To this solution \(\mathbf{A}\), an equal volume of \(0.1\) molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions \(\mathbf{A}\) and \(\mathbf{B}\) is \(\mathbf{y} \times 10^{-2}{ }^{\circ} \mathrm{C}\).
(Assume: Densities of the solutions \(\mathbf{A}\) and \(\mathbf{B}\) are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), \(K_{b}=0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\); Boiling point of pure water as \(100^{\circ} \mathrm{C}\).)
The value of $\left|\mathrm{y}\right|$ is ___.

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An aqueous solution of a mixture of two inorganic salts, when treated with dilute \(H C\) ?, gave a precipitate \((\boldsymbol{P})\) and a filtrate \((\boldsymbol{Q})\). The precipitate \(\boldsymbol{P}\) was found to dissolve in hot water. The filtrate \((\boldsymbol{Q})\) remained unchanged, when treated with \(\mathrm{H}_{2} \mathrm{~S}\) in a dilute mineral acid medium. However, it gave a precipitate \((\boldsymbol{R})\) with \(H_{2} S\) in an ammoniacal medium. The precipitate \(\boldsymbol{R}\) gave a coloured solution \((\boldsymbol{S})\), when treated with \(\mathrm{H}_{2} \mathrm{O}_{2}\) in an aqueous \(\mathrm{NaOH}\) medium.

Question:
The precipitate \(\boldsymbol{P}\) contains

The correct statement(s) for orthoboric acid is/are

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\(RCONH _2\) is converted into \(RNH _2\) by means of Hofmann bromamide degradation.

In this reaction, \(R \mathrm{CONHBr}\) is formed from which this reaction has derived its name. Electron donating group at phenyl activates the reaction. Hofmann degradation reaction is an intramolecular reaction.
Question:
Which is the rate determining step in Hofmann bromamide degradation?

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A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, \(C_{V}=2 R\). Here, \(R\) is the gas constant. Initially, each side has a volume \(V_{0}\) and temperature \(T_{0}\). The left side has an electric heater, which is turned on at very low power to transfer heat \(Q\) to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to \(V_{0} / 2\). Consequently, the gas temperatures on the left and the right sides become \(T_{L}\) and \(T_{R}\), respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.

Question :
The value of $\frac{Q}{R{T}_0}$ is:

A tangent \(P T\) is drawn to the circle \(x^{2}+y^{2}=4\) at the point \(P(\sqrt{3}, 1)\). A straight line \(L\), perpendicular to \(P T\) is a tangent to the circle \((x-3)^{2}+y^{2}-1\).

Question: A common tangent of the two circles is

Let \(f(x)=\frac{x^2-6 x+5}{x^2-5 x+6}\).

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)

A circular wire loop of radius \(R\) is placed in the \(x-y\) plane centered at the origin \(O\). A square loop of side \(a(a< < R)\) having two turns is placed with its centre at \(z=\sqrt{3} R\) along the axis of the circular wire loop, as shown in figure.

The plane of the square loop makes an angle of \(45^{\circ}\) with respect to the \(z\)-axis. If the mutual inductance between the loops is given by \(\frac{\mu_{0} a^{2}}{2^{p / 2} R}\), then the value of \(p\) is

Let $\omega$ be a complex cube root of unity with $\omega \ne 1$ and $\text{P}=\left[{\text{p}}_{\text{ij}}\right]$ be a n x n matrix with ${\text{p}}_{\text{ij}}={\omega }^{\text{i}+\text{j}}$. Then ${\text{P}}^2\ne 0$, when n =