Paragraph:
A fixed mass $\text{'}\mathrm{m}\text{'}$ of a gas is subjected to transformation of states from $\mathrm{K}$ to $\mathrm{L}$ to $\mathrm{M}$ to $\mathrm{N}$ and back to $\mathrm{K}$ as shown in the figure

Question :
The pair of isochoric processes among the transformation of states is

Calamine, malachite, magnetite and cryolite, respectively are:

The number of resonance structures for N is

The reaction of $4$-methyloct-$1$-ene $(\mathrm{P},2.52 \mathrm{g})$ with $\mathrm{HBr}$ in the presence of ${\left({\mathrm{C}}_6{\mathrm{H}}_5\mathrm{CO}\right)}_2{\mathrm{O}}_2$ gives two isomeric bromides in a $9: 1$ ratio, with a combined yield of $50\%$. Of these, the entire amount of the primary alkyl bromide was reacted with an appropriate amount of diethylamine followed by treatment with aq. ${\mathrm{K}}_2{\mathrm{CO}}_3$ to give a non-ionic product $\mathrm{S}$ in $100\%$ Yield. The mass (in $\mathrm{mg}$ ) of $\mathrm{S}$ obtained is
[Use molar mass (in ${\mathrm{gmol}}^{-1}$ ): $\mathrm{H}=1,\mathrm{C}=12, \mathrm{N}=14,\mathrm{Br}=80$ ]

The wave function, ${\mathrm{\psi }}_{\mathrm{n},\mathrm{}\mathrm{l},\mathrm{}{\mathrm{m}}_{\mathrm{l}}}$ is a mathematical function whose value depends upon spherical polar coordinates $\left(\mathrm{r},\mathrm{}\mathrm{\theta },\mathrm{}\mathrm{\varphi }\right)$ of the electron and characterized by the quantum numbers $\mathrm{n},\mathrm{}\mathrm{l}$ and ${\mathrm{m}}_{\mathrm{l}}$ . Here $\mathrm{r}$ is the distance from the nucleus, $\mathrm{\theta }$ is colatitude and $\mathrm{\varphi }$ is azimuth. In the mathematical functions given in the Table, $\mathrm{Z}$is the atomic number and ${\mathrm{a}}_{\mathrm{o}}$ 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 hydrogen atom, what is the only CORRECT combination?

Regarding the molecular orbital (MO) energy levels for homonuclear diatomic molecules, the INCORRECT statement(s) is(are)

The compound(s) with \(\mathrm{P}-\mathrm{H}\) bond(s) is(are)

A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

Consider the lines $L_1\text{:}\frac{x-1}{2}=\frac{y}{-1}=\frac{z+3}{1}\text{,}{L}_2\text{:}\frac{x-4}{1}=\frac{y+3}{1}=\frac{z+3}{2}$ and the planes $P_1\text{:}7x+y+2z=3\text{,}{P}_2\text{:}3x+5y-6z=4\text{.}$ Let $ax+by+cz=d$ be the equation of the plane passing through the point of intersection of L₁ and L₂, and perpendicular to planes P₁ and P₂.
Match List- I with List - II and select the correct answer using the code given below the lists :
 

	List I		List II
A.	a =	P.	13
B.	b =	Q.	-3
C.	c =	R.	1
D.	d =	S.	-2

A solid sphere of radius \(R\) has a charge \(Q\) distributed in its volume with a charge density \(\rho=k r^a\), where \(k\) and \(a\) are constants and \(r\) is the distance from its centre. If the electric field at \(r=\frac{R}{2}\) is \(\frac{1}{8}\) times that at \(r=R\), find the value of \(a\).

To form a complete monolayer of acetic acid on \(1 \mathrm{~g}\) of charcoal, \(100 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 \(\mathrm{mL}\) of \(1 \mathrm{M} \mathrm{NaOH}\) solution was required. If each molecule of acetic acid occupies \(\mathbf{P} \times 10^{-23} \mathrm{~m}^2\) surface area on charcoal, the value of \(\mathbf{P}\) is _______ [Use given data: Surface area of charcoal \(=1.5 \times 10^2 \mathrm{~m}^2 \mathrm{~g}^{-1} ;\) Avogadro's number \(\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}\) \(\left.\mathrm{mol}^{-1}\right]\)

If the normal of the parabola ${\mathrm{y}}^2=4\mathrm{x}$ drawn at the end points of its latus rectum are tangents to the circle ${\left(\mathrm{x}-3\right)}^2+{\left(\mathrm{y}+2\right)}^2={\mathrm{r}}^2,$ then the value of ${\mathrm{r}}^2$ is

For a solution formed by mixing liquids $\text{L}$ and $\text{M}$, the vapour pressure of $\text{L}$ plotted against the mole fraction of $\text{M}$ in solution is shown in the following figure, Here, ${\mathrm{X}}_{\mathrm{L}}$ and ${\mathrm{X}}_{\mathrm{M}}$ represent mole fractions of $\text{L}$ and $\text{M}$, respectively, in the solution. The correct statement(s) applicable to this system is(are) -