For the cell $\mathrm{Zn} \left(\mathrm{s}\right)\left|{\mathrm{ZnSO}}_4 \left(\mathrm{aq}\right)\right|\left|{\mathrm{CuSO}}_4 \left(\mathrm{aq}\right)\right|\mathrm{Cu} \left(\mathrm{s}\right)$, when the concentration of ${\mathrm{Zn}}^{2+}$ is $10$ times the concentration of ${\mathrm{Cu}}^{2+}$, the expression for $\mathrm{\Delta G} \left(\mathrm{in}\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\right)$ is
$[\mathrm{F}=$Faraday's constant, $\mathrm{R}=$universal gas constant, $\mathrm{T}=$temperature, ${\mathrm{E}}^{\mathrm{o}}\mathrm{cell}=1.1\mathrm{V}]$

The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compounds, is

Atom $\mathrm{X}$ occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in $\%$) of the resultant solid is closest to

For the following compounds the correct statement(s) with respect to nucleophilic substitution reactions is(are)

The total number(s) of stable conformers with non-zero dipole moment for the following compound is(are)

Among \(H_2, H e_2^{+}, L i_2, B e_2, B_2, C_2, N_2, O_2^{-}\), and \(F_2\), the number of diamagnetic species is -
(Atomic number : \(H=1, H e=2, L i=3, B e=4, B=5,\) \(C=6, N =7, O=8, F=9\) )

Consider the following statements related to colloids.
(I) Lyophobic colloids are not formed by simple mixing of dispersed phase and dispersion medium.
(II) For emulsions, both the dispersed phase and the dispersion medium are liquid.
(III) Micelles are produced by dissolving a surfactant in any solvent at any temperature.
(IV) Tyndall effect can be observed from a colloidal solution with dispersed phase having the same refractive index as that of the dispersion medium.
The option with the correct set of statements is

In a galvanic cell, the salt bridge

Let \(A B C\) and \(A B C^{\prime}\) be two non-congruent triangles with sides \(A B=4\), \(A C=A C^{\prime}=2 \sqrt{2}\) and angle \(B=30^{\circ}\). The absolute value of the difference between the areas of these triangles is

Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively, as shown in the figure. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2 and 3 are ${\mathrm{E}}_1,\mathrm{}\mathrm{}{\mathrm{E}}_2$ and ${\mathrm{E}}_3$ respectively, then

Two rectangular blocks, having identical dimensions, can be arranged either in configuration$\text{I}$ or in configuration $\text{I}\text{I}$ as shown in the figure. One of the blocks has thermal conductivity $\text{K}$ and the other $\text{2 K}$. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes $\text{9 s}$ to transport a certain amount of heat from the hot end to cold end in the configuration $\text{I}$. The time to transport the same amount of heat in the configuration $\text{II}$ is

Three concentric metallic spherical shells of radii \(R, 2 R, 3 R\) are given charges \(Q_1, Q_2, Q_3\), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, \(Q_1: Q_2: Q_3\), is

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A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are \(20 \mathrm{~mm}\) and \(1 \mathrm{~mm}\), respectively. The upper end of the container is open to the atmosphere.

Question :
If the density of air is \(\rho_{a}\) and that of the liquid \(\rho_{\ell}\), then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to