As per IUPAC nomenclature, the name of the complex \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}_{3}\) is :

The wave function, \(\psi_{ n , 1, m_{ l }}\) is a mathematical function whose value depends upon spherical polar coordinates \(( r , \theta, \phi)\) of the electron and characterized by the quantum numbers \(n , 1\) and \(m _{ l }\). Here \(r\) is the distance from the nucleus, \(\theta\) is colatitude and \(\phi\) is azimuth. In the mathematical functions given in the Table, Z is the atomic number and \(a_0\) is Bohr radius

Column 1	Column 2	Column 3
(I) 1s orbital	\(\text {(i) } \psi_{ n , 1, m_1}\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}\right)}\)	(P)
(II) 2s orbital	(ii) One radial node	(Q) Probability density at the nucleus \(\propto \frac{1}{ a _{ o }^3}\).
(III) \(2 p _{ z }\) orbital	\(\text {(iii) } \psi_{ n }, 1, m_{ l }\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}\right)} \cos \theta\)	(R) Probability density is maximum at the nucleus.
(IV) \(3 d_{ z }^2\) orbital	(iv) \(x y\)-plane is a nodal plane	(S) Energy needed to excite an electron from \(n =2\) state to \(n =4\) state is \(\frac{27}{32}\) times the energy needed to excite are electron from \(n =2\) state to \(n =6\) state.

For \(\text{He} ^{+}\)ion, the only incorrect combination

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)

The Fischer projection of $\mathrm{D}$-erythrose is shown below.
$\mathrm{D}$-Erythrose and its isomers are listed as $\mathrm{P},\mathrm{Q},\mathrm{R},$ and $\mathrm{S}$ in Column I. Choose the correct relationship of $\mathrm{P},\mathrm{Q},\mathrm{R},$ and $\mathrm{S}$ with $\mathrm{D}$-erythrose from Column II.

	Column - I		Column -II
P.		1.	Diastereomer
Q.		2.	Identical
R.		3.	Enantiomer
S.

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K ) at which the reduction of cassiterite by coke would take place.

\(298 K: \Delta_{ f } H ^0\left( SnO _2(s)\right)=-581.0 kJ mol ^{-1}\), \(\Delta_{ f } H ^0\left( CO _2(g)\right)=-394.0 kJ mol ^{-1}\)

\(S ^0\left( SnO _2(s)\right)=56.0 JK ^{-1} mol^{-1}, S^0( Sn ( s ))\) \(=52.0 JK ^{-1} mol^{-1}\)

\(S ^0( C ( s ))=6.0 JK ^{-1} mol^{-1}, S^0\left( CO _2(g)\right)\) \(=210.0 JK ^{-1} mol^{-1}\)

Assume that the enthalpies and the entropies are temperature independent.

Match the conversions in Column I with the type(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

Paragraph:
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of \(\mathrm{NH}_3\) and \(\mathrm{PH}_3\). Phosphine is a flammable gas and is prepared from white phosphorus.
Question:
Among the following, the correct statement is

Consider a reaction \(a G+b H \rightarrow\) products. When concentration of both the reactants \(G\) and \(H\) is doubled, the rate increases by eight times. However, when concentration of \(G\) is doubled keeping the concentration of \(H\) fixed, the rate is doubled. The overall order of the reaction is

In the following carbocation, \(\mathrm{H} / \mathrm{CH}_3\) that is most likely to migrate to the positively charged carbon is

Consider the lines given by
\[
L_1: x+3 y-5=0, L_2: 3 x-k y-1=0, L_3: 5 x+2 y-12=0
\]
Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Paragraph:

Let \(S=S_{1} \cap S_{2} \cap S_{3}\), where

\(S_{1}=\{z \in \mathbb{C}:|z|<4\}, \quad S_{2}=\left\{z \in \mathbb{C}: \operatorname{Im}\left[\frac{z-1+\sqrt{3} i}{1-\sqrt{3} i}\right]>0\right\}\) and \(S_{3}=\{z \in \mathbb{C}: \operatorname{Re} z>0\}\).


Question:

Area of \(S=\)

A soft plastic bottle, filled with water of density \(1 \mathrm{gm} / \mathrm{cc}\), carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of \(5 \mathrm{gm}\), and it is made of a thick glass of density \(2.5 \mathrm{gm} / \mathrm{cc}\). Initially the bottle is sealed at atmospheric pressure \(p_{0}=10^{5} \mathrm{~Pa}\) so that the volume of the trapped air is \(v_{0}=3.3 \mathrm{cc}\). When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure \(p_{0}+\Delta p\) without changing its orientation. At this pressure, the volume of the trapped air is \(v_{0}-\Delta v\).
Let \(\Delta v=X\) cc and \(\Delta p=Y \times 10^{3} \mathrm{~Pa}\).

The value of $Y$ is _____.