Statement I A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
Statement II For every action there is an equal and opposite reaction.

A perfectly reflecting mirror of mass $\mathrm{M}$ mounted on a spring constitutes a spring-mass system of angular frequency $\mathrm{\Omega }$ such that $\frac{4\mathrm{\pi }\mathrm{M}\mathrm{\Omega }}{\mathrm{h}}={10}^{24}{\mathrm{m}}^{-2}$ with $\mathrm{h}$ as Planck's constant. $\mathrm{N}$ photons of wavelength $\mathrm{\lambda }=8\mathrm{\pi }\times {10}^{-6}\mathrm{m}$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1\mathrm{\mu }\mathrm{m}.$ If the value of $\mathrm{N}$ is $\mathrm{x}\times {10}^{12},$ then the value of $\mathrm{x}$ is________.
[Consider the spring as massless]

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is 

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $\mathrm{\theta }$ with the horizontal floor. The coefficient of friction between the wall and the ladder is ${\mathrm{\mu }}_1$ and that between the floor and the ladder is ${\mathrm{\mu }}_2$ . The normal reaction of the wall on the ladder is ${\mathrm{N}}_1$ and that of the floor is ${\mathrm{N}}_2$ If the ladder is about to slip, then

A disk of radius \(\frac{a}{4}\) having a uniformly distributed charge \(6 \mathrm{C}\) is placed in the \(x-y\) plane with its centre at \(\left(\frac{-a}{2}, 0,0\right)\). A rod of length a carrying a uniformly distributed charge \(8 \mathrm{C}\) is placed on the \(x\)-axis from \(x=\frac{a}{4}\) to \(x=\frac{5 a}{4}\). Two point charges \(-7 \mathrm{C}\) and \(3 \mathrm{C}\) are placed at \(\left(\frac{a}{4}, \frac{-a}{4}, 0\right)\) and \(\left(\frac{-3 a}{4}, \frac{3 a}{4}, 0\right)\), respectively. Consider a cubical surface formed by six surfaces \(x=\pm \frac{a}{2}, y=\pm \frac{a}{2}, z=\pm \frac{a}{2}\).
The electric flux through this cubical surface is

Two soap bubbles \(A\) and \(B\) are kept in a closed chamber where the air is maintained at pressure \(8 \mathrm{Nm}^{-2}\). The radii of bubbles \(A\) and \(B\) are \(2 \mathrm{~cm}\), respectively. Surface tension of the soap-water used to make bubbles is \(0.04\) \(\mathrm{Nm}^{-1}\). Find the ratio \(\frac{n_B}{n_A}\), where \(n_A\) and \(n_B\) are the number of moles of air in bubbles \(A\) and \(B\), respectively. [Neglect the effect of gravity]

A parallel plate capacitor of capacitance $\mathrm{C}$ has spacing d between two plates having area $\mathrm{A}.$ The region between the plates is filled with $\mathrm{N}$ dielectric layers, parallel to its plates, each with thickness $\mathrm{\delta }=\frac{\mathrm{d}}{\mathrm{N}}.$ The dielectric constant of the ${\mathrm{m}}^{\mathrm{t}\mathrm{h}}$ layer is ${\mathrm{K}}_{\mathrm{m}}=\mathrm{K}\left(1+\frac{\mathrm{m}}{\mathrm{N}}\right).$ For a very large $\mathrm{N}\left(>{10}^3\right),$ the capacitance $\mathrm{C}$ is $\mathrm{\alpha }\left(\frac{\mathrm{K}{\in }_0\mathrm{A}}{\mathrm{d}\mathrm{l}\mathrm{n}2}\right).$ The value of $\mathrm{\alpha }$ will be____
$[{\in }_0$ is the permittivity of free space]

Paragraph :
A wooden cylinder of diameter \(4 r\), height \(H\) and density \(\rho / 3\) is kept on a hole of diameter \(2 r\) of a tank, filled with liquid of density \(\rho\) as shown in the figure.

Question :
If height \(h_2\) of water level is further decreased, then

\(\mathrm{Ag}^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+} ; k_1=3.5 \times 10^{-3}\) \(\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+} ; k_2\) \(=1.7 \times 10^{-3}\) then the formation constant of \(\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}\)is

The correct statement(s) regarding the binary transition metal carbonyl compounds is (are) (Atomic numbers: $Fe = 26, Ni = 28$ )

According to kinetic theory of gases

Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction as shown in the given scheme.

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.