Two bars of radius ' \(r\) ' and ' \(2 r\) ' are kept in contact as shown. An electric current \(I\) is passed through the bars. Which one of the following is correct?

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.

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Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS Maglev system.
There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If trains lower down then due to Lenz's law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force disc to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.
Disadvantage of Maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it leviated and as it moves forward according to Lenz law, there is an electromagnetic drag force.
Question:
Which force causes the train to elevate up?

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the \(4 \times 4\) matrix given in the ORS.

A wide slab consisting of two media of refractive indices $n_1$ and $n_2$ is placed in air as shown in the figure. A ray of light is incident from medium $n_1$ to $n_2$ at an angle $\theta$, where $\sin \theta$ is slightly larger than $\frac{1}{n_1}$. Take refractive index of air as $1$. Which of the following statement(s) is (are) correct?

Statement I The formula connecting \(u, v\) and \(f\) for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Statement II Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Two point charges \(-Q\) and \(+Q / \sqrt{3}\) are placed in the \(x y\)-plane at the origin \((0,0)\) and a point \((2,0)\), respectively, as shown in the figure. This results in an equipotential circle of radius \(R\) and potential \(V=0\) in the \(x y\)-plane with its center at \((b, 0)\). All lengths are measured in meters.

The value of $b$ is ________ meter.

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

An acidified solution of $0.05 \mathrm{M} {\mathrm{Zn}}^{2+}$ is saturated with $0.1 \mathrm{M} {\mathrm{H}}_2\mathrm{S}$. What is the minimum molar concentration $\left(\mathrm{M}\right)$ of ${\mathrm{H}}^{+}$ required to prevent the precipitation of $\mathrm{ZnS}$? Use ${\mathrm{K}}_{\mathrm{sp}}\left(\mathrm{ZnS}\right)=1.25\times {10}^{-22}$ and overall dissociation constant of ${\mathrm{H}}_2\mathrm{S}, {\mathrm{K}}_{\mathrm{NET}}={\mathrm{K}}_1{\mathrm{K}}_2=1\times {10}^{-21}$

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is

Let P be the point on the parabola $y^2=4x$ which is at the shortest distance from the center S of the circle $x^2+y^2-4x-16y+64=0.$ Let Q be the point on the circle dividing the line segment SP internally. Then -

The acidic hydrolysis of ether (X) shown below is fastest when

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The mass of a nucleus \({ }_{Z}^{A} X\) is less than the sum of the masses of \((A-Z)\) number of neutrons and \(Z\) number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass \(M\) can break into two light nuclei of masses \(m_{1}\) and \(m_{2}\) only if \(\left(m_{1}+m_{2}\right) \lt M\). Also two light nuclei of masses \(m_{3}\) and \(m_{4}\) can undergo complete fusion and form a heavy nucleus of mass \(M^{\prime}\) only if \(\left(m_{3}+m_{4}\right) \gt M^{\prime}\). The masses of some neutral atoms are given in the table below:


\(\left(1 u=932 M e V / c^{2}\right)\)

Question:

The correct statement is