Amongst the following, the total number of compounds soluble in aqueous \(\mathrm{NaOH}\) is

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Redox reaction play a pivotal role in chemistry and biology. The values of standard redox potential \(\left(E^{\circ}\right)\) of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their \(E^{\circ}(V\) with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 14-19.
\(\mathrm{I}_2+2 e^{-} \longrightarrow 2 \mathrm{I}^{-} E^{\circ}=0.54 \)
\( \mathrm{Cl}_2+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-} E^{\circ}=1.36 \)
\( \mathrm{Mn}^{3+}+e^{-} \longrightarrow \mathrm{Mn}^{2+} E^{\circ}=1.50 \)
\( \mathrm{Fe}^{3+}+e^{-} \longrightarrow \mathrm{Fe}^{2+} E^{\circ}=0.77 \)
\( \mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \longrightarrow 2 \mathrm{H}_2 \mathrm{O} E^{\circ}=1.23\)
Question:
While \(\mathrm{Fe}^{3+}\) is stable, \(\mathrm{Mn}^{3+}\) is not stable in acid solution because

The edge length of unit cell of a metal having molecular weight \(75 \mathrm{~g} / \mathrm{mol}\) is 5 Å which crystallizes in cubic lattice. If the density is \(2 \mathrm{~g} / \mathrm{cc}\) then find the radius of metal atom, \(\left(N_A=6 \times 10^{23}\right)\). Give the answer in pm.

A compound ${\mathrm{H}}_2\mathrm{X}$ with molar weight of 80g is dissolved in a solvent having density of $0.4\mathrm{ }\mathrm{g}\mathrm{m}{\mathrm{l}}^{–1}$ . Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is

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)

Fusion of $\mathrm{M}\mathrm{n}{\mathrm{O}}_2$ with $\mathrm{K}\mathrm{O}\mathrm{H}$ in presence of ${\mathrm{O}}_2$ produces a salt $\mathrm{W}.$ Alkaline solution of $\mathrm{W}$ upon electrolytic oxidation yields another salt $\mathrm{X}.$ The manganese containing ions present in $\mathrm{W}$ and $\mathrm{X},$ respectively, are $\mathrm{Y}$ and $\mathrm{Z}.$ Correct statement(s) is (are)

The total number of stereoisomers that can exist for M is

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A point charge \(Q\) is moving in a circular orbit of radius \(R\) in the \(x-y\) plane with an angular velocity \(\omega .\) This can be considered as equivalent to a loop carrying a steady current \(\frac{Q \omega}{2 \pi}\). A uniform magnetic field along the positive \(z\)-axis is now switched on, which increases at a constant rate from 0 to \(B\) in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant \(\gamma\).

Question:

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

The slope of the tangent to the curve ${\left(y-x^5\right)}^2=\text{x}{\left(1+{\text{x}}^2\right)}^2$ at the point (1, 3) is ________.

The value of $\underset{-\frac{\pi }{2}}{\overset{\frac{\pi }{2}}{\int }}\frac{x^2\cos x}{1+e^x} dx$ is equal to

Consider the following frequency distribution :

Value	4	5	8	9	6	12	11
Frequency	5	\(f_1\)	\(f_2\)	2	1	1	3

Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6. For the given frequency distribution, let \(\alpha\) denote the mean deviation about the mean, \(\beta\) denote the mean deviation about the median, and \(\sigma^2\) denote the variance.
Match each entry in List-I to the correct entry in List-II and choose the correct option.
\(\begin{array}{|l|l|l|l|} \hline & \text{LIST - I} & & \text{LIST - II} \\ \hline (P) & 7 f_1+9 f_2 \text{ is equal to} & (1) & 146 \\ \hline (Q) & 19 \alpha \text{ is equal to} & (2) & 47 \\ \hline (R) & 19 \beta \text{ is equal to} & (3) & 48 \\ \hline (S) & 19 \sigma^2 \text{ is equal to} & (4) & 145 \\ \hline & & (5) & 55 \\ \hline \end{array}\)

Two satellites $P$ and $Q$ are moving in different circular orbits around the Earth(radius $R$). The heights of $P$ and $Q$ from the Earth surface are $h_P$ and $h_Q$, respectively, where $h_P=\frac{R}{3}$. The accelerations of $P$ and $Q$ due to Earth’s gravity are $g_P$ and $g_Q$, respectively. If $\frac{g_P}{g_Q}=\frac{36}{25}$, what is the value of $h_Q$?

Extraction of metal from the ore cassiterite involves