The treatment of galena with ${\mathrm{HNO}}_3$ produces a gas that is

The number of aldol reaction(s) that occurs in the given transformation is :

Among the following, the correct statement(s) is(are)

Consider the following cell reaction,
\(2 \mathrm{Fe}(\mathrm{s})+\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q) \longrightarrow \)
\( 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{H}_2 \mathrm{O}(l), E^{\circ}=1.67 \mathrm{~V} \)
\( \text {At } {\left[\mathrm{Fe}^{2+}\right]=10^{-3} \mathrm{M}, \mathrm{P}\left(\mathrm{O}_2\right)=0.1 \mathrm{~atm}}\)
and \(\mathrm{pH}=3\), the cell potential at \(25^{\circ} \mathrm{C}\) is

In the following reaction, the product(s) formed is/are:

LIST-$\mathrm{I}$ contains metal species and LIST-$\mathrm{II}$ contains their properties.

List - I	List - II
(I) \(\left[ Cr ( CN )_6\right]^{4-}\)	(P) \(t _{2 g}\) orbitals contain 4 electrons
(II) \(\left[ RuCl _6\right]^{2-}\)	(Q) \(\mu\) spin - only \(=4.9\) BM
(III) \(\left[ Cr \left( H _2 O \right)_6\right]^{2+}\)	(R) low spin complex ion
(IV) \(\left[ Fe \left( H _2 O \right)_6\right]^{2+}\)	(S) metal ion in 4 + oxidation state
	(T) \(d ^4\) species

[Given: Atomic number of $\mathrm{Cr}=24,\mathrm{Ru}=44,\mathrm{Fe}=26$]
Match each metal species in LIST-$\mathrm{I}$ with their properties in LIST-$\mathrm{II}$, and choose the correct option

The structure of a peptide is given below.
If the absolute values of the net charge of the peptide at $\mathrm{pH}=2,\mathrm{pH}=6,$ and $\mathrm{pH}=11$ are $\left|{\mathrm{z}}_1\right|,\left|{\mathrm{z}}_2\right|,$ and $\left|{\mathrm{z}}_3\right|,$ respectively, then what is $\left|{\mathrm{z}}_1\right|+\left|{\mathrm{z}}_2\right|+\left|{\mathrm{z}}_3\right|$?

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 ____.

Consider the following reversible reaction:
$\mathrm{A} \left(\mathrm{g}\right)+\mathrm{B}\mathrm{ }\left(\mathrm{g}\right)\rightleftharpoons \mathrm{AB} \left(\mathrm{g}\right)$
The activation energy of the backward reaction exceeds that of the forward reaction by $2\mathrm{RT}$ (in $\mathrm{ }{\mathrm{mol}}^{-1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of $∆{\mathrm{G}}^{⊝} \left(\mathrm{in}\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\right)$ for the reaction at $300 \mathrm{K}$ is ____.
(Given; $\ln \left(2\right)=\mathrm{ }0.7, =\mathrm{ }2500\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\mathrm{ }\mathrm{at}\mathrm{ }300\mathrm{ }\mathrm{K}$ and $\mathrm{G}$ is the Gibbs energy)

A point charge $q$ of mass $m$ is suspended vertically by a string of length $l.$ A point dipole of dipole moment $\overrightarrow{p}$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N\times \left(mgh\right)$, where $g$ is the acceleration due to gravity, then the value of $N$ is ____________ (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{\mathrm{F}}{\sin \theta }$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)

The vector(s) which is/are coplanar with vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\), are perpendicular to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) is/are

Suppose a ${}_{88}{}^{226}Ra$ nucleus at rest and in ground state undergoes $\mathrm{\alpha }$ -decay to a ${}_{86}{}^{222}Rn$ nucleus in its excited state. The kinetic energy of the emitted $\mathrm{\alpha }$ particle is found to be $4.44\mathrm{ }\mathrm{M}\mathrm{e}\mathrm{V}.{}_{86}{}^{222}Rn$ nucleus then goes to its ground state by $\mathrm{\gamma }$ -decay. The energy of the emitted $\mathrm{\gamma }$ -photon is _______ $\mathrm{k}\mathrm{e}\mathrm{V},$
[Given: atomic mass of ${\mathrm{ }}_{88}^{226}\mathrm{R}\mathrm{a}=226.005\mathrm{u},$ atomic mass of ${\mathrm{ }}_{86}^{222}\mathrm{R}\mathrm{n}=222.000\mathrm{u},$ atomic mass of $\mathrm{\alpha }$ particle $=4.000\mathrm{u},1\mathrm{u}=931\mathrm{M}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2,\mathrm{c}$ is speed of the light]

A stationary source is emitting sound at a fixed frequency \(f_0\), which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is \(1.2 \%\) of \(f_0\). What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is \(330 \mathrm{~ms}^{-1}\).