The standard state Gibb's free energies of formation of  $\mathrm{C}$ (graphite) and $\mathrm{C}$ (diamond) at $\mathrm{T}=298\mathrm{ }\mathrm{K}$ are
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\mathrm{o}}\left[\mathrm{C} (\mathrm{graphite}\right]=0\mathrm{ }\mathrm{kJ}\mathrm{ }{\mathrm{mol}}^{-1}$
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\mathrm{o}}\left[\mathrm{C} \left(\mathrm{diamond}\right)\right]=2.9\mathrm{ }\mathrm{kJ}\mathrm{ }{\mathrm{mol}}^{-1}$
The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [$\mathrm{C}$ (graphite)] to diamond [$\mathrm{C}$ (diamond)] reduces its volume by $2\times {10}^{-6}\mathrm{ }{\mathrm{m}}^3 {\mathrm{mol}}^{-1}$ . If $\mathrm{C}$ (graphite) is converted to $\mathrm{C}$ (diamond) isothermally at $\mathrm{T}=298 \mathrm{K}$, the pressure at which $\mathrm{C}$ (graphite) is in equilibrium with $\mathrm{C}$ (diamond), is
[Useful information:
\(1 J=1 kg m ^2 s^{-2}, 1 Pa=1 kg m ^{-1} s^{-2} ;\) \(1 bar =10^5 Pa]\)

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The coordination number of \(\mathrm{Ni}^{2+}\) is 4 .
\(\mathrm{NiCl}_2+\mathrm{KCN}\) (excess) \(\rightarrow A\) (cyano complex)
\(\mathrm{NiCl}_2+\) conc. \(\mathrm{HCl}\) (excess) \(\rightarrow B\) (chloro complex)
Question:
Predict the magnetic nature of \(A\) and \(B\) are

To measure the quantity of ${\mathrm{MnCl}}_2$ dissolved in an aqueous solution, it was completely converted to ${\mathrm{KMnO}}_4$ using the reaction,
\(\text{MnCl} _2+\text K _2\text S_2\text O _8+\text H _2\text O \rightarrow \text{KMnO} _4~+\) \(\text H _2 \text{SO} _4+ \text{HCl}\) (equation not balanced). Few drops of concentrated $\mathrm{HCl}$ were added to this solution and gently warmed. Further, oxalic acid $\left(225 \mathrm{mg}\right)$) was added in portions till the colour of the permanganate ion disappeared. What is the quantity of ${\mathrm{MnCl}}_2$ (in mg) present in the initial solution? (Atomic weights in $\mathrm{g}\mathrm{ }{\mathrm{mol}}^{-1}:\mathrm{ }\mathrm{Mn}=55, \mathrm{Cl}=35.5$)

The correct statement(s) concerning the structures E, F and G is are

For one mole of a van der Waal's gas when \(b=0\) and \(\mathrm{T}=300 \mathrm{~K}\), the PV vs, \(1 / \mathrm{V}\) plot is shown below. The value of the van der Waal's constant \(a\) (atm. liter \({ }^{2} \mathrm{~mol}^{-2}\) ) is :

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An aqueous solution of a mixture of two inorganic salts, when treated with dilute \(H C\) ?, gave a precipitate \((\boldsymbol{P})\) and a filtrate \((\boldsymbol{Q})\). The precipitate \(\boldsymbol{P}\) was found to dissolve in hot water. The filtrate \((\boldsymbol{Q})\) remained unchanged, when treated with \(\mathrm{H}_{2} \mathrm{~S}\) in a dilute mineral acid medium. However, it gave a precipitate \((\boldsymbol{R})\) with \(H_{2} S\) in an ammoniacal medium. The precipitate \(\boldsymbol{R}\) gave a coloured solution \((\boldsymbol{S})\), when treated with \(\mathrm{H}_{2} \mathrm{O}_{2}\) in an aqueous \(\mathrm{NaOH}\) medium.
Question:
The coloured solution \(\boldsymbol{S}\) contains

The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.
(given, order of migratory aptitude: aryl > alkyl hydrogen)

	LIST-I		LIST -II
A)		P)	${\mathrm{I}}_2,\mathrm{NaOH}$
B)		Q)	$\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\mathrm{OH}\right]$
C)		R)	Fehling solution
D)		S)	$\mathrm{H}\mathrm{C}\mathrm{H}\mathrm{O},\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}$
		T)	$\mathrm{NaOBr}$

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Consider the lines: \(L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}, L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3}\)Question:
The shortest distance between \(L_1\) and \(L_2\) is

A spherical bubble inside water has radius $R$. Take the pressure inside the bubble and the water pressure to be $p_0.$ The bubble now gets compressed radially in an adiabatic manner so that its radius becomes $(R-a)$. For $a\ll R$ the magnitude of the work done in the process is given by $\left(4\pi P_{0}R{a}^2\right)X,$ where $X$ is a constant and $\gamma =C_p/C_V=41/30$. The value of $X$ is______

Consider a triangle $\mathrm{\Delta }$ whose two sides lie on the $x$-axis and the line $x+y+1=0$. If the orthocenter of $\mathrm{\Delta }$ is $(1,1)$, then the equation of the circle passing through the vertices of the triangle $\mathrm{\Delta }$ is

\[
\text { Let } M \text { be a } 3 \times 3 \text { matrix satisfying }
\]

\[
M\left[\begin{array}{l}
0 \\
1 \\
0
\end{array}\right]=\left[\begin{array}{c}
-1 \\
2 \\
3
\end{array}\right], M\left[\begin{array}{c}
1 \\
-1 \\
0
\end{array}\right]=\left[\begin{array}{c}
1 \\
1 \\
-1
\end{array}\right] \text { and } M\left[\begin{array}{l}
1 \\
1 \\
1
\end{array}\right]=\left[\begin{array}{c}
0 \\
0 \\
12
\end{array}\right]
\]
Then, the sum of the diagonal entries of \(M\) is

For the following electrochemical cell at $\text{289 K,}$
\(\operatorname{Pt}( s ) \mid H _2(g, 1\) bar \() \mid H ^{+}( aq , 1 M ) \| M ^{4+}(\) aq. \(), M ^{2+}(\) aq. \() \mid \operatorname{Pt}( s )\)
${\mathrm{E}}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}=0.092\mathrm{ }\mathrm{V}$ when $\frac{\left[{\mathrm{M}}^{2+}\left(\mathrm{a}\mathrm{q}.\right)\right]}{\left[{\mathrm{M}}^{4+}\left(\mathrm{a}\mathrm{q}.\right)\right]}={10}^{\mathrm{x}}$
Given: ${\mathrm{E}}_{{\mathrm{M}}^{4+}/{\mathrm{M}}^{2+}}^0=0.151\mathrm{ }\mathrm{V}\mathrm{ };2.303\frac{\mathrm{R}\mathrm{T}}{\mathrm{F}}=0.059$
The value of $\text{x}$ is -

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is