The correct option(s) related to the extraction of iron from its ore in the blast furnace operating in the temperature range $900-1500 \mathrm{K}$ is(are)

Extraction of metal from the ore cassiterite involves

In a metal deficient oxide sample, \(\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4\) ( \(\mathbf{M}\) and \(\mathbf{Y}\) are metals), \(\mathbf{M}\) is present in both +2 and +3 oxidation states and \(\mathbf{Y}\) is in +3 oxidation state. If the fraction of \(\mathbf{M}^{2+}\) ions present in \(\mathbf{M}\) is \(\frac{1}{3}\), the value of \(\mathbf{X}\) is ________.

Dissolving $1.24 \mathrm{g}$ of white phosphorous in boiling $\mathrm{NaOH}$ solution in an inert atmosphere gives a gas $\mathrm{Q}$. The amount of ${\mathrm{CuSO}}_4$ (in $\mathrm{g}$) required to completely consume the gas $\mathrm{Q}$ is____
[Given: Atomic mass of
\(\text H =1,\text O =16, \text{Na} =23,\text P =31,\text S=32,\) \(\text{Cu} =63]\)

Hydrogen bonding plays a central role in the following phenomena:

Not considering the electronic spin, the degeneracy of the second excited state (n = $3$) of H atom is $9$, while the degeneracy of the second excited state of ${\mathrm{H}}^{-}$ is :

Consider the strong electrolytes ${\mathrm{Z}}_{\mathrm{m}}{\mathrm{X}}_{\mathrm{n}}, {\mathrm{U}}_{\mathrm{m}}{\mathrm{Y}}_{\mathrm{p}}$ and ${\mathrm{V}}_{\mathrm{m}}{\mathrm{X}}_{\mathrm{n}}$. Limiting molar conductivity of ${\mathrm{U}}_{\mathrm{m}}{\mathrm{Y}}_{\mathrm{p}}$ and ${\mathrm{V}}_{\mathrm{m}}{\mathrm{X}}_{\mathrm{n}}$ are $250$ and $440 \mathrm{S} {\mathrm{cm}}^2 {\mathrm{mol}}^{-1}$, respectively. The value of $\left(\mathrm{m}+\mathrm{n}+\mathrm{p}\right)$ is Given:

Ion	\(Z ^{ n +}\)	\(U ^{ p +}\)	\(V ^{ n +}\)	\(X ^{ m }\)	\(Y ^{ m -}\)
\(\lambda^0(\text{S cm} ^2\) \(\text{mol}^{-1})\)	50.0	25.0	100.0	80.0	100.0

${\lambda }^0$ is the limiting molar conductivity of ions The plot of molar conductivity $\left(\Lambda \right)$ of ${\mathrm{Z}}_{\mathrm{m}}{\mathrm{X}}_{\mathrm{n}}$ vs ${\mathrm{c}}^{\frac{1}{2}}$ is given below. If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places.

The pair(s) of reagents that yield paramagnetic species is/are

Let $F:R\to R$ be a function. We say that $f$ has:
 PROPERTY $1$  if $\underset{h\to 0}{\lim }\frac{f\left(h\right)-f\left(0\right)}{\sqrt{\left|h\right|}}$ exists and is finite, and 
PROPERTY $2$  if $\underset{h\to 0}{\lim }\frac{f\left(h\right)-f\left(0\right)}{h^2}$ exists and is finite.
Then which of the following options is/are correct?

Statement I Glucose gives a reddish-brown precipitate with Fehling's solution.
Statement II Reaction of glucose with Fehling's solution gives \(\mathrm{CuO}\) and gluconic acid.

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 ____.

The correct statement(s) regarding defects in solids is (are)

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\mathrm{t}\mathrm{h}}$ orbit of the atom and List-II contains options showing how they depend on $n$ .
 

List - I	List - II
(I) Radius of the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{P}\right)$ $\propto n^{-2}$
(II) Angular momentum of the electron in the $n^{th}$ orbit	$\left(\mathrm{Q}\right)$ $\propto n^{-1}$
(III) Kinetic energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{R}\right)$ $\propto n^0$
(IV) Potential energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{S}\right)$ $\propto n^1$
	$\left(\mathrm{T}\right)$ $\propto n^2$
	$\left(\mathrm{U}\right)$ $\propto n^{1/2}$

Which of the following options has the correct combination considering List-I and List-II?