Consider the following list of reagents: Acidified ${\mathrm{K}}_2\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_7$ , alkaline $\mathrm{K}\mathrm{M}\mathrm{n}{\mathrm{O}}_4,\mathrm{C}\mathrm{u}\mathrm{S}{\mathrm{O}}_4,{\mathrm{H}}_2{\mathrm{O}}_2,\mathrm{C}{\mathrm{l}}_2,{\mathrm{O}}_3,\mathrm{F}\mathrm{e}\mathrm{C}{\mathrm{l}}_3,\mathrm{H}\mathrm{N}{\mathrm{O}}_3$ and $\mathrm{N}{\mathrm{a}}_2{\mathrm{S}}_2{\mathrm{O}}_3$ . The total number of reagents that can oxidise aqueous iodide to iodine is

A tin chloride $\mathrm{Q}$ undergoes the following reactions (not balanced)
$\mathrm{Q}+\mathrm{C}{\mathrm{l}}^{-}\to \mathrm{X}$
$\mathrm{Q}+\mathrm{M}{\mathrm{e}}_3\mathrm{N}\to \mathrm{Y}$
$\mathrm{Q}+\mathrm{C}\mathrm{u}\mathrm{C}{\mathrm{l}}_2\to \mathrm{Z}+\mathrm{C}\mathrm{u}\mathrm{C}\mathrm{l}$
$\mathrm{X}$ is a monoanion having pyramidal geometry. Both $\mathrm{Y}$ and $\mathrm{Z}$ are neutral compounds. Choose the correct option(s).

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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:
Ammonia is always added in this reaction. Which of the following must be incorrect?

Thermal decomposition of ${\mathrm{AgNO}}_3$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is _____ .

The given graph represent the variations of compressibility factor \((Z)=\frac{P V}{n R T}\) versus \(P\), for three real gases \(A, B\) and \(C\). Identify the only incorrect statement

Among the following, the state function(s) is (are)

The value of \(n\) in the molecular formula \(\mathrm{Be}_n \mathrm{Al}_2 \mathrm{Si}_6 \mathrm{O}_{18}\) is

The geometries of the ammonia complexes of $\mathrm{N}{\mathrm{i}}^{2+}\mathrm{ },\mathrm{ }\mathrm{P}{\mathrm{t}}^{2+}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }\mathrm{Z}{\mathrm{n}}^{2+}$ respectively, are :

For an ideal gas, consider only P-V work in going from an initial state \(\mathrm{X}\) to the final state \(\mathrm{Z}\). The final state \(\mathrm{Z}\) can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct?
[Take \(\Delta \mathrm{S}\) as change in entropy and w as work done].

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

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	\(\begin{array}{l}\text { (i) } \psi_{ n , 1, m_1} \\ \propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}\right)}\end{array}\)	(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	\(\begin{array}{l}\text { (iii) } \psi_{ n }, 1, m_{ l } \\ \propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}\right)} \cos \theta\end{array}\)	(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 the given orbital in column 1, the only correct combination for any hydrogen-like species is

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A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity \(\omega\) is an example of a non-inertial frame of reference.

The relationship between the force \(\vec{F}_{\text {rot }}\) experienced by a particle of mass \(m\) moving on the rotating disc and the force \(\vec{F}_{\text {in }}\) experienced by the particle in an inertial frame of reference is

\(\vec{F}_{\mathrm{rot}}=\vec{F}_{\mathrm{in}}+2 m\left(\vec{v}_{\mathrm{rot}} \times \vec{\omega}\right)+m(\vec{\omega} \times \vec{r}) \times \vec{\omega}\),

where \(\vec{v}_{\text {rot }}\) is the velocity of the particle in the rotating frame of reference and \(\vec{r}\) is the position vector of the particle with respect to the centre of the disc.

Now consider a smooth slot along a diameter of a disc of radius \(R\) rotating counter-clockwise with a constant angular speed \(\omega\) about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the \(x\)-axis along the slot, the \(y\)-axis perpendicular to the slot and the \(z\)-axis along the rotation axis \((\vec{\omega}=\omega \hat{k}) .\) A small block of mass \(m\) is gently placed in the slot at \(\vec{r}=(R / 2) \hat{i}\) at \(t=0\) and is constrained to move only along the slot.


Question:
The distance \(r\) of the block at time \(t\) is

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:
\(1 J=1 kg m ^2 s^{-2}, 1 Pa=1 kg m ^{-1} s^{-2} ;\) \(1 bar =10^5 Pa]\)