The complete hydrolysis of \(\mathrm{ICl}_2 \mathrm{ClF}_3\) and \(\mathrm{BrF}_5\), respectively, gives

Hydrogen peroxide in its reaction with KIO₄ and NH₂OH respectively, is acting as a

Consider the following volume-temperature \((\mathrm{V}-\mathrm{T})\) diagram for the expansion of 5 moles of an ideal monoatomic gas.

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence \(\mathbf{X} \rightarrow \mathbf{Y} \rightarrow \mathbf{Z}\) is ________.
[Use the given data: Molar heat capacity of the gas for the given temperature range, \(\mathrm{C}_{\mathrm{V}, \mathrm{m}}=12 \mathrm{~J} \mathrm{~K}^{-1}\) \(\mathrm{mol}^{-1}\) and gas constant, \(\left.\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]\)

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The reaction of \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with freshly prepared \(\mathrm{FeSO}_{4}\) solution produces a dark blue precipitate called Turnbull's blue. Reaction of \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) with the \(\mathrm{FeSO}_{4}\) solution in complete absence of air produces a white precipitate \(\mathbf{X}\), which turns blue in air. Mixing the \(\mathrm{FeSO}_{4}\) solution with \(\mathrm{NaNO}_{3}\), followed by a slow addition of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) through the side of the test tube produces a brown ring.
Question:
Among the following, the brown ring is due to the formation of

Statement I Molecules that are not superimposable on their mirror images are chiral.
Statement II All chiral molecules have chiral centres.

An ideal gas is expanded from $({\mathrm{p}}_1\mathrm{ },\mathrm{ }{\mathrm{V}}_1\mathrm{ },\mathrm{ }{\mathrm{T}}_1)\mathrm{ }\mathrm{to}\mathrm{ }({\mathrm{p}}_2\mathrm{ },\mathrm{ }{\mathrm{V}}_2\mathrm{ },\mathrm{ }{\mathrm{T}}_2)$ under different conditions. The correct statement(s) among the following is(are)

The wave function, ${\mathrm{\psi }}_{\mathrm{n},\mathrm{}\mathrm{l},\mathrm{}{\mathrm{m}}_{\mathrm{l}}}$ is a mathematical function whose value depends upon spherical polar coordinates $\left(\mathrm{r},\mathrm{}\mathrm{\theta },\mathrm{}\mathrm{\varphi }\right)$ of the electron and characterized by the quantum numbers $\mathrm{n},\mathrm{}\mathrm{l}$ and ${\mathrm{m}}_{\mathrm{l}}$ . Here $\mathrm{r}$ is the distance from the nucleus, $\mathrm{\theta }$ is colatitude and $\mathrm{\varphi }$ is azimuth. In the mathematical functions given in the Table, $\mathrm{Z}$is the atomic number and ${\mathrm{a}}_{\mathrm{o}}$ is Bohr radius

Column 1	Column 2	Column 3
(I) 1s orbital	\(\text {(i) } \psi_{ n , 1, m_1}\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}\right)}\)	(P)
(II) 2s orbital	(ii) One radial node	(Q) Probability density at the nucleus \(\propto \frac{1}{ a _{ o }^3}\).
(III) \(2 p _{ z }\) orbital	\(\text {(iii) } \psi_{ n }, 1, m_{ l }\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}\right)} \cos \theta\)	(R) Probability density is maximum at the nucleus.
(IV) \(3 d_{ z }^2\) orbital	(iv) \(x y\)-plane is a nodal plane	(S) Energy needed to excite an electron from \(n =2\) state to \(n =4\) state is \(\frac{27}{32}\) times the energy needed to excite are electron from \(n =2\) state to \(n =6\) state.

For hydrogen atom, what is the only CORRECT combination?

Tangents drawn from the point \(P(1,8)\) to the circle \(x^2+y^2-6 x-4 y-11=0\) touch the circle at the points \(A\) and \(B\). The equation of the circumcircle of \(\triangle P A B\) is

The total number of possible isomers for $\left[\mathrm{Pt}{\left({\mathrm{NH}}_3\right)}_4{\mathrm{Cl}}_2\right]{\mathrm{Br}}_2$ is___.

Let \(f:[-1,2] \rightarrow[0, \infty)\) be a continuous function such that \(f(x)=f(1-x)\) for all \(x \in[-1,2]\). Let \(R_1=\int_{-1}^2 x f(x) d x\) and \(R_2\) be the area of the region bounded by \(y=f(x), x=-1, x=2\) and the \(X\)-axis. Then,

For a dilute solution containing \(2.5 \mathrm{~g}\) of a non-volatile non-electrolyte solute in \(100 \mathrm{~g}\) of water, the elevation in boiling point at 1 atm pressure is \(2^{\circ} \mathrm{C}\). Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure ( \(\mathrm{mm}\) of \(\mathrm{Hg}\) ) of the solution is (take \(K_{b}=0.76 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) )

A series \(R\) - \(C\) circuit is connected to \(A C\) voltage source. Consider two cases; \((A)\) when \(C\) is without a dielectric medium and \((B)\) when \(C\) is filled with dielectric of constant 4. The current \(I_R\) through the resistor and voltage \(V_C\) across the capacitor are compared in the two cases. Which of the following is/are true?

In the following reaction, compound $\mathrm{Q}$ is obtained from compound $\mathrm{P}$ via an ionic intermediate.

What is the degree of unsaturation of $\mathrm{Q}$?