Which of the given statement(s) about \(\mathbf{N}, \mathbf{O}, \mathbf{P}\) and \(\mathbf{Q}\) with respect to \(\mathbf{M}\) is (are) correct?

Considering the following reaction sequence,

the correct option(s) is(are)

Oxidation states of the metal in the minerals haematite and magnetite, respectively, are

Aqueous solution of \(\text{Na} _2\text S_2\text O _3\) on reaction with \(\text{Cl} _2\) gives

The reagent(s) for the following conversion,

is/are

In the chemical reaction between stoichiometric quantities of ${\mathrm{KMnO}}_4$ $\mathrm{KI}$ in weakly basic solution, what is the number of moles of ${\mathrm{I}}_2$ released for $4$ ${\mathrm{KMnO}}_4$ consumed?

Match the following

Column I	Column II
(A) \(CH _3- CHBr - CD _3\) on treatment with alc. KOH gives \(CH _2= CH - CD _3\) as a major product.	(P) E1 reaction
(B) \(Ph - CHBr - CH _3\) reacts faster than \(Ph - CHBr - CD _3\)	(Q) E2 reaction
(C) \(Ph - CH _2- CH _2 Br\) on treatment with \(C _2 H _5 OD / C _2 H _5 O ^{-}\)gives \(Ph - CD = CH _2\) as the major product	(R) El cb reaction
(D) \(PhCH _2 CH _2 Br\) and \(PhCH _2 CH _2 Br\) react with same rate	(S) First order reaction

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The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.
Question:
It is found that the excitation frequency from ground to the first excited state of rotation for the \(\mathrm{CO}\) molecule is close to \(\frac{4}{\pi} \times 10^{11} \mathrm{~Hz}\). Then the moment of inertia of CO molecule about its centre of mass is close to (Take \(h=2 \pi \times 10^{-34} J-s\) )

The following carbohydrate is

Let \(f_{1}:(0, \infty) \rightarrow \mathbb{R}\) and \(f_{2}:(0, \infty) \rightarrow \mathbb{R}\) be defined by

\[

f_{1}(x)=\int_{0}^{x} \prod_{j=1}^{21}(t-j)^{j} d t, \quad x > 0

\(

and

\]

f_{2}(x)=98(x-1)^{50}-600(x-1)^{49}+2450, \quad x > 0

\)

where, for any positive integer \(n\) and real numbers \(a_{1}, a_{2}, \ldots, a_{n}, \prod_{i=1}^{n} a_{i}\) denotes the product of \(a_{1}, a_{2}, \ldots, a_{n} .\) Let \(m_{i}\) and \(n_{i}\), respectively, denote the number of points of local minima and the number of points of local maxima of function \(f_{i}, i=1,2\), in the interval \((0, \infty)\).

The value of $6m_2+4n_2+8m_2{n}_2$ is ____.

In a one-litre flask, $6$ moles of $\mathrm{A}$ undergoes the reaction $\mathrm{A}( \mathrm{g})\rightleftharpoons \mathrm{P}( \mathrm{g})$. The progress of product formation at two temperatures (in Kelvin), ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, is shown in the figure: If ${\mathrm{T}}_1=2{\mathrm{T}}_2$ and$\left({\mathrm{\Delta G}}_2^{\mathrm{o}}-{\mathrm{\Delta G}}_1^{\mathrm{o}}\right)={\mathrm{RT}}_2\mathrm{lnx}$ , then the value of $\mathrm{x}$ is
[ ${\mathrm{\Delta G}}_1^{\mathrm{o}}$ and ${\mathrm{\Delta G}}_2^{\mathrm{o}}$ are standard Gibb's free energy change for the reaction at temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, respectively.]

A colorless aqueous solution contains nitrates of two metals, $\mathrm{X}$ and $\mathrm{Y}$. When it was added to an aqueous solution of $\mathrm{NaCl}$, a white precipitate was formed. This precipitate was found to be partly soluble in hot water to give a residue $\mathrm{P}$ and a solution $\mathrm{Q}$. The residue $\mathrm{P}$ was soluble in aq. ${\mathrm{NH}}_3$ and also in excess sodium thiosulfate. The hot solution $\mathrm{Q}$ gave a yellow precipitate with $\mathrm{KI}$. The metals $\mathrm{X}$ and $\mathrm{Y}$, respectively, are

In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of $1 \mathrm{A}$ flows through the $1 \Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?
[Given : $e^{–1}=0.36$]