The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is \(\left[a_{0}\right.\) is Bohr radius \(]\) :

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.

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition.
The limiting ionic conductivity \(\left(\Lambda_0\right)\) values (in \(\mathrm{mS} \mathrm{m}^2 \mathrm{~mol}^{-1}\)) for different ions in aqueous solutions are given below:

For different combinations of titrates and titrants given in List-I, the graphs of 'conductance' versus 'volume of titrant' are given in List-II.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

The correct statement(s) regarding,
(i) $\mathrm{H}\mathrm{C}\mathrm{l}\mathrm{O}$
(ii) $\mathrm{H}\mathrm{C}\mathrm{l}{\mathrm{O}}_2$
(iii) $\mathrm{H}\mathrm{C}\mathrm{l}{\mathrm{O}}_3$ and
(iv) $\mathrm{H}\mathrm{C}\mathrm{l}{\mathrm{O}}_4$ is /are

Liquids $\mathrm{A}$ and $\mathrm{B}$ form ideal solution for all compositions of $\mathrm{A}$ and $\mathrm{B}$ at ${25}^{\circ }C$. Two such solutions with $0.25$ and $0.50$ mole fractions of $\mathrm{A}$ have the total vapor pressures of $0.3$ and $0.4$ bar, respectively. What is the vapor pressure of pure liquid $\mathrm{B}$ in bar?

Aqueous solution of \(\text{Na} _2\text S_2\text O _3\) on reaction with \(\text{Cl} _2\) gives

\(75.2 \mathrm{~g}\) of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}\) (phenol) is dissolved in a solvent of \(K_f=14\). If the depression in freezing point is \(7 \mathrm{~K}\), then find the \(\%\) of phenol that dimerises.

The colour of the $X_2$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -

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 _____.

A monochromatic light is travelling in a medium of refractive index $n=1.6$ . It enters a stack of glass layers from the bottom side at an angle $\theta =30°.$ The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_m=n–m\mathrm{\Delta }n$ where $n_m$ is the refractive index of the $m^{th}$ slab and $\mathrm{\Delta }n=0.1$ (see the figure). The ray is refracted out parallel to the interface between the ${\left(m–1\right)}^{th}$ and $m^{th}$ slabs from the right side of the stack. What is the value of m?

An infinitely long thin non-conducting wire is parallel to the z - axis and carries a uniform line charge density $\lambda$ . It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle ${120}^o$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is ${ϵ}_0$ . Which of the following statements is (are) true?

If \(f^{\prime \prime}(x)=-f(x)\), where \(f(x)\) is a continuous double differentiable function and \(g(x)=f^{\prime}(x)\). If \(F(x)=\left(f\left(\frac{x}{2}\right)\right)^2+\left(g\left(\frac{x}{2}\right)\right)^2\) and \(F(5)=5\), then \(F(10)\) is

The dilution processes of different aqueous solutions with water are given in LIST-I. The effects of dilution of the solutions on $\left[{\mathrm{H}}^{+}\right]$ are given in LIST-II.
(Note: The degree of dissociation $\left(\mathrm{\alpha }\right)$ of a weak acid and a weak base is $<< 1;$ the degree of hydrolysis of salt is $<<1;\mathrm{ }\left[{\mathrm{H}}^{+}\right]$ represents the concentration of ${\mathrm{H}}^{+}$ ions)

List - I	List - II
A) 10 mL of \(0.1\text{ M NaOH} +20\text{ mL}\) of 0.1 M acetic acid diluted to 60 mL .	P) The value of \(\left[\text H ^{+}\right]\)does not change on dilution.
B) 20 mL of \(0.1\text{ M NaOH} +20\text{ mL}\) of 0.1 M acetic acid diluted to 80 mL .	Q) The value of \(\left[\text H ^{+}\right]\)changes to half of its initial value on dilution.
C) 20 mL of \(0.1\text{ M HCl} +20\text{ mL}\) of 0.1 M ammonia solution diluted to 80 mL .	R) The value of \(\left[\text H ^{+}\right]\)changes to two times its initial value on dilution.
D) 10 mL saturated solution of \(\text{Ni} (\text{OH})_2\) in equilibrium with excess of solid \(\text{Ni} (\text{OH})_2\) is diluted to 20 mL (solid \(\text{Ni} (\text{OH})_2\) is still present after dilution).	S) The value of \(\left[\text H ^{+}\right]\)changes to \(\sqrt{ }\) times its initial value on dilution.
	T) The value of \(\left[\text H ^{+}\right]\)changes to \(\sqrt{2}\) times its initial value on dilution.

Match each process given in LIST-I with one or more effect(s) in LIST-II. The correct option is