To measure the quantity of ${\mathrm{MnCl}}_2$ dissolved in an aqueous solution, it was completely converted to ${\mathrm{KMnO}}_4$ using the reaction,
\(\text{MnCl} _2+\text K _2\text S_2\text O _8+\text H _2\text O \rightarrow \text{KMnO} _4~+\) \(\text H _2 \text{SO} _4+ \text{HCl}\) (equation not balanced). Few drops of concentrated $\mathrm{HCl}$ were added to this solution and gently warmed. Further, oxalic acid $\left(225 \mathrm{mg}\right)$) was added in portions till the colour of the permanganate ion disappeared. What is the quantity of ${\mathrm{MnCl}}_2$ (in mg) present in the initial solution? (Atomic weights in $\mathrm{g}\mathrm{ }{\mathrm{mol}}^{-1}:\mathrm{ }\mathrm{Mn}=55, \mathrm{Cl}=35.5$)

List-I contains various reaction sequences and List-II contains different phenolic compounds.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

In the decay sequence:
${}_{92}{}^{238}\mathrm{U}\stackrel{-{\mathrm{x}}_1}{\to }{}_{90}{}^{234}\mathrm{T}\mathrm{h}\stackrel{-{\mathrm{x}}_2}{\to }{}_{91}{}^{234}\mathrm{P}\mathrm{a}\stackrel{-{\mathrm{x}}_3}{\to }{}_{\mathrm{ }}{}^{234}\mathrm{Z}\stackrel{-{\mathrm{x}}_4}{\to }{}_{90}{}^{234}\mathrm{T}\mathrm{h}$
${\mathrm{x}}_1,\mathrm{ }{\mathrm{x}}_2,\mathrm{ }{\mathrm{x}}_3$ and ${\mathrm{x}}_4$ are the particles/ radiation emitted by the respective isotopes. The correct option(s) is/are:

Match the reactions (in the given stoichiometry of the reactants) in List-I with one of their products given in List-II and choose the correct option.

List - I	List - II
(P) \(P _2 O _3\) \(+~3 H _2 O \rightarrow\)	(1) \(P ( O )\left( OCH _3\right)\) \(Cl _2\)
(Q) \(P _4+3 NaOH\) \(+~3 H _2 O \rightarrow\)	(2) \(H _3 PO _3\)
(R) \(PCl _5+ CH _3\) \(COOH \rightarrow\)	(3) \(PH _3\)
(S) \(H _3 PO _2\) \(+~2 H _2 O ~+\) \(4 AgNO _3 \rightarrow\)	(4) \(POCL _3\)
	(5) \(H _3 PO _4\)

In the following monobromination reaction, the number of possible chiral products is

The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

The correct order of acidity for the following compounds is :

A hydrogen atom, initially at rest in its ground state, absorbs a photon of frequency \(v_1\) and ejects the electron with a kinetic energy of 10 eV . The electron then combines with a positron at rest to form a positronium atom in its ground state and simultaneously emits a photon of frequency \(v_2\). The center of mass of the resulting positronium atom moves with a kinetic energy of 5 eV . It is given that positron has the same mass as that of electron and the positronium atom can be considered as a Bohr atom, in which the electron and the positron orbit around their center of mass. Considering no other energy loss during the whole process, the difference between the two photon energies (in eV ) is \(\qquad\)

The correct statement(s) regarding the binary transition metal carbonyl compounds is (are) (Atomic numbers: $Fe = 26, Ni = 28$ )

At \(400 \mathrm{~K}\), the root mean square (rms) speed of a gas \(X\) (molecular weight \(=40\) ) is equal to the most probable speed of gas \(Y\) at \(60 \mathrm{~K}\). The molecular weight of the gas \(Y\) is

The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, $\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}\mathrm{}$ and $\mathrm{C}{\mathrm{H}}_3{\left(\mathrm{C}{\mathrm{H}}_2\right)}_{11}\mathrm{O}\mathrm{S}{\mathrm{O}}_3^{-}\mathrm{}\mathrm{N}{\mathrm{a}}^{+}$ at room temperature. The correct assignment of the sketches is -

Statement 1 For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and Statement 2 The electrical potential of a sphere of radius \(R\) with charge \(Q\) uniformly distributed on the surface is given by \(\frac{Q}{4 \pi \varepsilon_0 R}\).

Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer using the code given below the lists.

	List – I		List – II
A.		P.
B.		Q.
C.		R.
D.		S.