A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

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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:
What is the disadvantage of this system?

A circular wire loop of radius \(R\) is placed in the \(x-y\) plane centered at the origin \(O\). A square loop of side \(a(a< < R)\) having two turns is placed with its centre at \(z=\sqrt{3} R\) along the axis of the circular wire loop, as shown in figure.

The plane of the square loop makes an angle of \(45^{\circ}\) with respect to the \(z\)-axis. If the mutual inductance between the loops is given by \(\frac{\mu_{0} a^{2}}{2^{p / 2} R}\), then the value of \(p\) is

A fission reaction is given by ${}_{92}{}^{236}U\to {}_{54}{}^{140}Xe+{}_{38}{}^{94}Sr+x+y$ , where $x$ and $y$ are two particles. Considering ${}_{92}{}^{236}U$ to be at rest, the kinetic energies of the products are denoted by $K_{Xe},\mathrm{ }{K}_{Sr},\mathrm{ }{K}_x\left(2\mathrm{ }MeV\right)$ and $K_y\left(2\mathrm{ }MeV\right)$ , respectively. Let the binding energies per nucleon of ${}_{92}{}^{236}U,\mathrm{ }{}_{54}{}^{140}Xe\mathrm{ }$ and ${}_{38}{}^{94}Sr$ be 7.5 MeV, 8.5 MeV, and 8.5 MeV respectively. Considering different conservation laws, the correct option(s) is (are)

A thin and uniform rod of mass $\mathrm{M}$ and length $\mathrm{L}$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle ${60}^{\mathrm{o}}$ with vertical?
[ $\mathrm{g}$ is the acceleration due to gravity]

A mixture of ideal gas containing $5$ moles of monatomic gas and $1$ mole of rigid diatomic gas is initially at pressure ${\mathrm{P}}_0,$ volume ${\mathrm{V}}_0$ and temperature ${\mathrm{T}}_0.$ If the gas mixture is adiabatically compressed to a volume $\frac{{\mathrm{V}}_0}{4}$, then the correct statement(s) is/are,
(Given $2^{1.2}=\mathrm{ }2.3\text{;} 2^{3.2}=9.2\text{;}\mathrm{ }\mathrm{R}$ is gas constant)

Two large vertical and parallel metal plates having a separation of \(1 \mathrm{~cm}\) are connected to a DC voltage source of potential difference \(X\). A proton is released at rest midway between the two plates. It is found to move at \(45^{\circ}\) to the vertical JUST after release. Then \(X\) is nearly

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Let \(O\) be the origin, and \(\overrightarrow{O X}, \overrightarrow{O Y}, \overrightarrow{O Z}\) be three unit vectors in the directions of the sides \(\overrightarrow{Q R}, \overrightarrow{R P}\), \(\overrightarrow{P Q}\), respectively, of a triangle \(P Q R\).


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If the triangle \(P Q R\) varies, then the minimum value of

\(\cos (P+Q)+\cos (Q+R)+\cos (R+P)\) is

Three students \(S_1, S_2\) and \(S_1\) are given a problem to solve. Consider the following events :
\(U:\) At least one of \(S_1, S_2\) and \(S_3\) can solve the problem,
\(V: S_1\) can solve the problem, given that neither \(\mathrm{S}_2\) nor \(\mathrm{S}_3\) can solve the problem,
\(W: S_2\) can solve the problem and \(S_3\) cannot solve the problem,
\(T: S_3\) can solve the problem.
For any event \(E\), let \(P(E)\) denote the probability of \(E\).
If \(P(U)=\frac{1}{2}, P(V)=\frac{1}{10}\) and \(P(W)=\frac{1}{12}\), then \(P(T)\) is equal to

If \(a, b\) and \(c\) are the sides of a \(\triangle A B C\) such that \(x^2-2(a+b+c) x+3 \lambda(a b+b c+c a)=0\) has real roots, then

Let $f :\left(-\frac{\pi }{2},\frac{\pi }{2}\right)\to R$ be given by $f\left(x\right)={\left(\log \left(\sec x+\tan x\right)\right)}^3.$ Then

The electrochemical extraction of aluminium from bauxite ore involves

The calculated spin only magnetic moments of ${\left[\mathrm{Cr}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$ and ${\left[{\mathrm{CuF}}_6\right]}^{3-}$ in $\mathrm{BM},$ respectively, are (Atomic numbers of $\mathrm{Cr}$ and $\mathrm{Cu}$ are $24$ and $29,$ respectively)