Considering the following reaction sequence,

the correct option(s) is(are)

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?

Paragraph:
Tollen's reagent is used for the detection of aldehyde when a solution of \(\mathrm{AgNO}_3\) is added to glucose with \(\mathrm{NH}_4 \mathrm{OH}\) then gluconic acid is formed
\(\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \)
\( \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)\) \(+~2 \mathrm{H}^{+}+2 e^{-} ; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \)
\( \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; E_{\mathrm{red}}^{\circ}\) \(=0.337 \mathrm{~V}\)
[Use \(2.303 \times \frac{R T}{F}=0.0592\) and \(\frac{F}{R T}=38.92\) at \(298 \mathrm{~K}\)]
Question:
\(2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Ag}(\mathrm{s})\) \(+~\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_4+2 \mathrm{H}^{+}\). Find \(\ln \mathrm{K}\) of this reaction.

A student performs a titration with different burettes and finds titre values of \(25.2 \mathrm{~mL}, 25.25 \mathrm{~mL}\), and \(25.0 \mathrm{~mL}\).
The number of significant figures in the average titre value is

The maximum number of electrons that can have principal quantum number, \(n=3\) and spin quantum number, \(m_s=-\frac{1}{2}\), is

Match the reactions (in the given stoichiometry of the reactants) in List-I with one of their products given in List-II and choose the correct option.

List - I	List - II
(P) \(P _2 O _3\) \(+~3 H _2 O \rightarrow\)	(1) \(P ( O )\left( OCH _3\right)\) \(Cl _2\)
(Q) \(P _4+3 NaOH\) \(+~3 H _2 O \rightarrow\)	(2) \(H _3 PO _3\)
(R) \(PCl _5+ CH _3\) \(COOH \rightarrow\)	(3) \(PH _3\)
(S) \(H _3 PO _2\) \(+~2 H _2 O ~+\) \(4 AgNO _3 \rightarrow\)	(4) \(POCL _3\)
	(5) \(H _3 PO _4\)

The cubic unit cell structure of a compound containing cation $\mathrm{M}$ and anion $\mathrm{X}$ is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

The correct statement(s) regarding defects in solids is (are)

Two adjacent sides of a parallelogram \(A B C D\) are given by \(\overrightarrow{\mathbf{A B}}=2 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{A D}}=-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\). The side \(A D\) is rotated by an acute angle \(\alpha\) in the plane of the parallelogram so that \(A D\) becomes \(A D^{\prime}\). If \(A D^{\prime}\) makes a right angle with the side \(A B\), then the cosine of the angle \(\alpha\) is given by

Among \(\left[ I _3\right]^{+},\left[ SiO _4\right]^{4-}, SO _2 Cl _2, XeF _2, SF _4, ClF _3,\) \(Ni ( CO )_4, XeO _2 F_2,\left[ PtCl _4\right]^{2-}, XeF _4\), and \(SOCl _2\), the total number of species having \(sp ^3\) hybridised central atom is

Let \(A B C D\) be a quadrilateral with area 18 , with side \(A B\) parallel to the side \(C D\) and \(A B=2 C D\). Let \(A D\) be perpendicular to \(A B\) and \(C D\). If a circle is drawn inside the quadrilateral \(A B C D\) touching all the sides, then its radius is

The centres of two circles \(C_1\) and \(C_2\) each of unit radius are at a distance of 6 units from each other. Let \(P\) be the mid-point of the line segment joining the centres of \(C_1\) and \(C_2\) and \(C\) be a circle touching circles \(C_1\) and \(C_2\) externally. If a common tangents to \(C_1\) and \(C\) passing through \(P\) is also a common tangent to \(C_2\) and \(C\), then the radius of the circle \(C\) is

A large glass slab \(\left(\mu=\frac{5}{3}\right)\) of thickness 8 \(\mathrm{cm}\) is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius \(R \mathrm{~cm}\). What is the value of \(R\) ?