Magnetic materials used for making permanent magnets \((P)\) and magnets in a transformer \((T)\) have different properties of the following, which property best matches for the type of magnet required \(?\)

In the reported figure, two bodies \(A\) and \(B\) of masses \(200\, {g}\) and \(800\, {g}\) are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(.....\,{rad} / {s}\) when \({k}=20 \,{N} / {m} .\)

A thermodynamic system is taken from an original state \(A\) to an intermediate state \(B\) by a linear process as shown in the figure. It's volume is then reduced to the original value from \(B\) to \(C\) by an isobaric process. The total work done by the gas from \(A\) to \(B\) and \(B\) to \(C\) would be :

An ideal fluid of density \(800 \; kgm ^{-3}\), flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from \(a\) to \(\frac{ a }{2}\). The pressure difference between the wide and narrow sections of pipe is \(4100 \; Pa\). At wider section, the velocity of fluid is \(\frac{\sqrt{x}}{6} \; ms ^{-1}\) for \(x = \dots\) \(\left(\right.\) Given \(g =10 \; m ^{-2}\) )

A capacitor of capacitance \(900\,\mu F\) is charged by a \(100\,V\) battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as \(x \times 10^{-2}\,J\). The value of \(x\) is \(..............\)

Match List\(-I\) with List\(-II.\)

List\(-I\)	List\(-II\)
\((a)\) Capacitance, \(C\)	\((i)\) \({M}^{1} {L}^{1} {T}^{-3} {A}^{-1}\)
\((b)\) Permittivity of free space, \(\varepsilon_{0}\)	\((ii)\) \({M}^{-1} {L}^{-3} {T}^{4} {A}^{2}\)
\((c)\) Permeability of free space, \(\mu_{0}\)	\((iii)\) \({M}^{-1} L^{-2} T^{4} A^{2}\)
\((d)\) Electric field, \(E\)	\((iv)\) \({M}^{1} {L}^{1} {T}^{-2} {A}^{-2}\)

Choose the correct answer from the options given below

\(100\) balls each of mass moving with speed \(v\) simultaneously strike a wall normally and reflected back with same speed, in time \(t s\). The total force exerted by the balls on the wall is

A particle is executing Simple Harmonic Motion \((SHM)\). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

A galvanometer having a coil resistance of \(100\ \Omega\). gives a full scale deflection, when a currect of \(I\ mA\) is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of \(10\ A\), is :......\(Ω\)

The mass density of a planet of radius \(R\) varies with the distance \(r\) from its centre as \(\rho( r )=\rho_{0}\left(1-\frac{ r ^{2}}{ R ^{2}}\right) .\) Then the gravitational field is maximum at