A solution of a metal ion when treated with \(\mathrm{KI}\) gives a red precipitate which dissolved in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt (II) thiocyanate gives rise to a deep blue crystalline precipitqte. The metal ion is

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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:
When ammonia is added to the solution, \(\mathrm{pH}\) is raised to 11 . Which half-cell reaction is affected by \(\mathrm{pH}\) and by how much?

Upon treatment with ammoniacal ${\text{H}}_2\text{S}$, the metal ion that precipitates as a sulphide is

According to the Arrhenius equation,

For the reaction, \(\mathbf{X}(s) \rightleftharpoons \mathbf{Y}(s)+\mathbf{Z}(g)\), the plot of \(\ln \frac{p_{\mathbf{Z}}}{p^{\theta}}\) versus \(\frac{10^{4}}{T}\) is given below (in solid line), where \(p_{\mathbf{Z}}\) is the pressure (in bar) of the gas \(\mathbf{Z}\) at temperature \(T\) and \(p^{\theta}=1\) bar.

(Given, \(\frac{\mathrm{d}(\ln K)}{\mathrm{d}\left(\frac{1}{T}\right)}=-\frac{\Delta H^{\theta}}{R}\), where the equilibrium constant, \(K=\frac{p_{z}}{p^{\theta}}\) and the gas constant, \(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) )
The value of standard enthalpy, $∆{\mathrm{H}}^{\mathrm{o}}$ (in $\mathrm{kJ} {\mathrm{mol}}^{-1}$) for the given reaction is ___.

Consider the kinetic data given in the following table for the reaction $\mathrm{A}+\mathrm{B}+\mathrm{C}\to$ Product.

Ex peri ment No.	\([\text A]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	\([\text B]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	\([\text C]\) \((\text{mol}\) \(\text{dm} ^{-3})\)	Rate of reaction \((\text{mol}\) \(\text{dm} ^{-3}\) \(\text s^{-1})\)
1	0.2	0.1	0.1	\(6.0 \times\) \(10^{-5}\)
2	0.2	0.2	0.1	\(6.0 \times \) \(10^{-5}\)
3	0.2	0.1	0.2	\(1.2 \times \) \(10^{-4}\)
4	0.3	0.1	0.1	\(9.0 \times \) \(10^{-5}\)

The rate of the reaction for $\left[\mathrm{A}\right]=0.15\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3},\mathrm{ }\left[\mathrm{B}\right]=0.25\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}$ and $\left[\mathrm{C}\right]=0.15\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}$ is found to be $\mathrm{Y}\times {10}^{-5}\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{d}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}.$ The value of $\mathrm{Y}$ is __________

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?

Let $T$ be the line passing through the points $P\left(-2,7\right)$ and $Q\left(2,-5\right)$. Let $F_1$ be the set of all pairs of circles $\left(S_1,S_2\right)$ such that $T$ is tangents to $S_1$ at $P$ and tangent to $S_2$ at $Q$, and also such that $S_1$ and $S_2$ touch each other at a point, say, $M$. Let $E_1$ be the set representing the locus of $M$ as the pair $\left(S_1, S_2\right)$ varies in $F_1$. Let the set of all straight line segments joining a pair of distinct points of $E_1$ and passing through the point $R\left(\mathrm{1,1}\right)$ be $F_2$ . Let $E_2$ be the set of the mid-points of the line segments in the set $F_2$ . Then, which of the following statement(s) is (are) TRUE?

A wooden block performs SHM on a frictionless surface with frequency \(v_0\). The block carries a charge \(+Q\) on its surface. If now a uniform electric field \(\mathbf{E}\) is switched on as shown, then the SHM of the block will be

A temperature difference can generate e.m.f. in some materials. Let \(S\) be the e.m.f. produced per unit temperature difference between the ends of a wire, \(\sigma\) the electrical conductivity and \(\kappa\) the thermal conductivity of the material of the wire. Taking \(M, L, T, I\) and \(K\) as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity \(Z=\frac{S^2 \sigma}{\kappa}\) is :-

A bob of mass \(M\) is suspended by a massless string of length \(L\). The horizontal velocity \(v\) at position \(A\) is just sufficient to make it reach the point \(B\). The angle \(\theta\) at which the speed of the bob is half of that at \(A\), satisfies

A cubical region of side \(a\) has its centre at the origin. It encloses three fixed point charges, \(-q\) at \((0,-a / 4,0),+3 q\) at \((0,0,0)\) and \(-q\) at \((0,+a / 4,0)\). Choose the correct options(s)

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $v_n$. At a fixed temperature and pressure, which of the following is the correct option?