The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus.
Which of the following statement(s) is(are) correct?

Two identical concave mirrors each of focal length \(f\) are facing each other as shown in the schematic diagram. The focal length \(f\) is much larger than the size of the mirrors. A glass slab of thickness \(t\) and refractive index \(n_0\) is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source \(S\) is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on \(S\) itself, which of the following distances between the two mirrors is/are correct:

A thin ring of mass \(2 \mathrm{~kg}\) and radius \(0.5 \mathrm{~m}\) is rolling without slipping on a horizontal plane with velocity 1 \(\mathrm{m} / \mathrm{s}\). A small ball of mass \(0.1 \mathrm{~kg}\), moving with velocity \(20 \mathrm{~m} / \mathrm{s}\) in the opposite directions, hits the ring at a height of \(0.75 \mathrm{~m}\) and goes vertically up with velocity 10 \(\mathrm{m} / \mathrm{s}\). Immediately after the collision

A planar structure of length $\mathrm{L}$ and width $\mathrm{W}$ is made of two different optical media of refractive indices ${\mathrm{n}}_1=1.5$ and ${\mathrm{n}}_2=1.44$ as shown in figure. If $\mathrm{L}>>\mathrm{W},$ a ray entering from end $\mathrm{A}\mathrm{B}$ will emerge from end $\mathrm{C}\mathrm{D}$ only if the total internal reflection condition is met inside the structure. For $\mathrm{L}=9.6\mathrm{}\mathrm{m},$ if the incident angle $\mathrm{\theta }$ is varied, the maximum time taken by a ray to exit the plane $\mathrm{C}\mathrm{D}$ is $\mathrm{t}\times {10}^{-9}\mathrm{s},$ where $\mathrm{t}$ is ____.
[Speed of light $\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}]$

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

A small object of uniform density rolls up a curved surface with an initial velocity \(v\). It reaches up to a maximum height of \(\frac{3 v^2}{4 g}\) with respect to the initial\(
\text { position. The object is }
\)

Paragraph:
The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.
The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2,+4\) and \(+6 . \mathrm{XeF}_4\) reacts violently with water to give \(\mathrm{XeO}_3\). The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.
Question:
Argon is used in are welding because of its

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of \(50 \mathrm{~Hz}\) frequency (the next three circuits) in different ways as shown in Column II. When a current \(I\) (steady state for DC or rms for \(A C\) ) flows through the circuit, the corresponding voltage \(V_1\) and \(V_2\) (indicated in circuits) are related as shown in Column I. Match the two

Let the curve C be the mirror image of the parabola ${\mathrm{y}}^{\mathrm{2 }}$$=4\mathrm{x}$ with respect to the line $\mathrm{x}+\mathrm{y}+4=0.$ If A and B are the points of intersection of C with the line $\mathrm{y}=\mathrm{ }-5,$ then the distance between A and B is

Passing \(\mathrm{H}_2 \mathrm{~S}\) gas into a mixture of \(\mathrm{Mn}^{2+}, \mathrm{Ni}^{2+}, \mathrm{Cu}^{2+}\) and \(\mathrm{Hg}^{2+}\) ions in an acidified aqueous solution precipitates

Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, \(\mathrm{Na}, \mathrm{Ti}\)

Paragraph: Let $S$ be the circle in the $xy$ – plane defined by the equation $x^2 + y^2 = 4.$

Question : Let $P$ be a point on the circle $S$ with both coordinates being positive. Let the tangent to $S$ at $P$ intersect the coordinate axes at the points $M$ and $MN$ Then, the mid-point of the line segment must lie on the curve