Match the physical quantities given in List - I with dimensions in List - II.

List - I			List - II
A	Gravitational potential	I	${\mathrm{M}}^0 {\mathrm{L}}^2 {\mathrm{T}}^{-2} {\mathrm{K}}^{-1}$
B	Stefan's constant	II	${\mathrm{M}}^0 {\mathrm{L}}^2 {\mathrm{T}}^{-2}$
C	Permittivity	III	${\mathrm{ML}}^0 {\mathrm{T}}^{-3} {\mathrm{K}}^{-4}$
D	Specific heat capacity	IV	${\mathrm{M}}^{-1} {\mathrm{L}}^{-3} {\mathrm{T}}^4{\mathrm{I}}^2$

  (The dimensions of mass, length, time, temperature and current are $\mathrm{M},\mathrm{L},\mathrm{T},\mathrm{K}$ and $\mathrm{I}$ respectively)

An ideal gas at pressure \(\mathrm{P}\) is enclosed in a container that is placed in a reservoir at temperature \(T\). If the volume of the gas is increased to two times its original value, then the new pressure \(\mathrm{P}^{\prime}=\) \(\mathrm{P}\)

An air bubble rises from the bottom of a water tank of height $5 \mathrm{m}$. If the initial volume of the bubble is $3 {\mathrm{mm}}^3$. What will be its volume as it reaches the surface. Assume that its temperature does not change. [$g=9.8 \mathrm{m} {\mathrm{s}}^{-2},1 \mathrm{atm}={10}^5 \mathrm{Pa}$, density of water $=1 \mathrm{gm} {\mathrm{cc}}^{-1}$]

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

Assertion: The zero velocity of a particle at any instant always implies zero acceleration at that instant Reason: A body is momentarily at rest when reverses its direction of motion. The correct option among the following is

A particle moves in \(X Y\)-plane with \(x\) and \(y\) varying with time \(t\) as \(x(t)=5 t, y(t)=5 t\left(27-t^2\right)\). At what time in seconds, the direction of velocity and acceleration will be perpendicular to each other?

A body is falling freely from the top of a tower of height 125 m . The distance covered by the body during the last second of its motion is \(x \%\) of the height of the tower. Then \(x\) is (Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

The height of water level is a tank of uniform crosssection is 5 m . The volume of the water leaked in 5 s through a hole of area \(2.4 \mathrm{~mm}^2\) made at the bottom of the tank is (Assume the level of the water in the tank remains constant and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

A circular hole of radius \(3 \mathrm{~cm}\) is cut out from a uniform circular disc of radius \(6 \mathrm{~cm}\). The centre of the hole is at \(3 \mathrm{~cm}\), from the centre of the original disc. The distance of centre of gravity of the resulting flat body from the centre of the original disc is

On a particular day, the sun delivers an average power of \(\left(\frac{6}{\pi} \times 10^3\right) \frac{\mathrm{W}}{\mathrm{m}^2}\) to the top of Earth's atmosphere. Find the amplitude of magnetic field for the electromagnetic waves above atmosphere. (Take \(\mu_0=4 \pi \times 10^{-7}\) SI unit)

If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are \(a, b\) and \(c\) respectively, the ratio between the increase in lengths of brass and steel wires would be

An alternating emf given by the equation \(\mathrm{E}=200 \sin\) \((50 \pi \mathrm{t})\) (Where \(\mathrm{E}\) is in volts and \(\mathrm{t}\) is in seconds) is applied across a series combination of an inductor and a resistor having inductive reactance \(40 \Omega\) and resistance \(30 \Omega\) respectively. At time \(t=1 \mathrm{~s}\), the power dissipated by the resistor is close to \[ \left(\cos 53^{\circ}=0.6\right) \]

An aircraft is flying at a height of ' \(H\) ' above the ground and at a speed of ' \(V\) '. The maximum angle subtended at a ground observation point by the aircraft after time \(T\) is