Column II shows five systems in which two objects are labelled as \(X\) and \(Y\). Also in each case a point \(P\) is shown. Column-I gives some statements about \(X\) and/or \(Y\). Match these statements to the appropriate system(s) from Column-II.

A point object is placed at distance of \(20 \mathrm{~cm}\) from a thin planoconvex lens of focal length \(15 \mathrm{~cm}\). The plane surface of the lens is now silvered. The image created by the system is at

A stationary source is emitting sound at a fixed frequency \(f_0\), which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is \(1.2 \%\) of \(f_0\). What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is \(330 \mathrm{~ms}^{-1}\).

A uniform circular disc of mass $\text{50 kg}$ and radius $\text{0.4 m}$ is rotating with an angular velocity of ${\text{10 rad s}}^{-1}$ about its own axis, which is vertical. Two uniform circular rings, each of mass $\text{6.25 kg}$ and radius $\text{0.2 m}$, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity $\left({in\; rad\; s}^{-1}\right)$ of the system is

A charged particle is introduced at the origin $x=0, y=0, z=0$ with a given initial velocity $\overrightarrow{v}$ . A uniform electric field $\overrightarrow{E}$ and a uniform magnetic field $\overrightarrow{B}$ exist everywhere. The velocity $\overrightarrow{v}$ , electric field $\overrightarrow{E}$ and a uniform magnetic field $\overrightarrow{B}$ are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\overrightarrow{v}=2\frac{E_0}{B_0}\widehat{x}$	(i) $\overrightarrow{E}=E_0\widehat{z}$	(P) $\overrightarrow{B}=-B_0\widehat{x}$
2. Electron with $\overrightarrow{v}=\mathrm{}\frac{E_0}{B_0}\widehat{y}$	(ii) $\overrightarrow{E}=-E_0\widehat{y}$	(Q) $\overrightarrow{B}=B_0\widehat{x}$
3.Proton with $\overrightarrow{v}$ =0	(iii) $\overrightarrow{E}={-E}_0\widehat{x}$	(R) $\overrightarrow{B}=-B_0\widehat{y}$
4. Proton with $\overrightarrow{v}=2\frac{E_0}{B_0}\widehat{x}$	(iv) $\overrightarrow{E}=E_0\widehat{x}$	(S) $\overrightarrow{B}=-B_0\widehat{z}$

In which case will the particle move in a straight line with a constant velocity?

The dimensions of a cone are measured using a scale with a least count of \(2 \mathrm{~mm}\). The diameter of the base and the height are both measured to be \(20.0 \mathrm{~cm}\). The maximum percentage error in the determination of the volume is _______ .

An infinitely long solid cylinder of radius \(R\) has a uniform volume charge density \(\rho\). It has a spherical cavity of radius \(R / 2\) with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point \(P\), which is at a distance \(2 R\) from the axis of the cylinder, is given by the expression \(\frac{23 \rho R}{16 K \varepsilon_{0}}\). The value of \(k\) is

One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is

Paragraph:

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index \(n_{1}\) surrounded by a medium of lower refractive index \(n_{2}\). The light guidance in the structure takes place due to successive total internal reflections at the interface of the media \(n_{1}\) and \(n_{2}\) as shown in the figure. All rays with the angle of incidence \(i\) less than a particular value \(i_{m}\) are confined in the medium of refractive index \(n_{1}\). The numerical aperture (NA) of the structure is defined as \(\sin i_{m}\).



Question:

For two structures namely \(S_{1}\) with \(n_{1}=\sqrt{45} / 4\) and \(n_{2}=3 / 2\), and \(S_{2}\) with \(n_{1}=8 / 5\) and \(n_{2}=7 / 5\) and taking the refractive index of water to be \(4 / 3\) and that of air to be \(1\) , the correct option(s) is(are)

The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.
(given, order of migratory aptitude: aryl > alkyl hydrogen)

	LIST-I		LIST -II
A)		P)	${\mathrm{I}}_2,\mathrm{NaOH}$
B)		Q)	$\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\mathrm{OH}\right]$
C)		R)	Fehling solution
D)		S)	$\mathrm{H}\mathrm{C}\mathrm{H}\mathrm{O},\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}$
		T)	$\mathrm{NaOBr}$

A list of species having the formula XZ4 is given below.
\(\text{XeF} _4, \text{SF} _4, \text{SiF} _4, \text{BF} _4^{-}, \text{BrF} _4^{-},\left[\text{Cu} \left(\text{NH} _3\right)_4\right]^{2+},\) \(\left[\text{FeCl} _4\right]^{2-},\left[\text{CoCl} _4\right]^{2-}\) and \(\left[\text{PtCl} _4\right]^{2-}\)
Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is

Which one of the following statement is WRONG in the context of X-rays generated from X-ray tube?

Statement 1 For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and Statement 2 The electrical potential of a sphere of radius \(R\) with charge \(Q\) uniformly distributed on the surface is given by \(\frac{Q}{4 \pi \varepsilon_0 R}\).