A physical quantity $$\overrightarrow S $$ is defined as $$\overrightarrow S = (\overrightarrow E \times \overrightarrow B )/{\mu _0}$$, where $$\overrightarrow E $$ is electric field, $$\overrightarrow B $$ is magnetic field and $$\mu$$₀ is the permeability of free space. The dimensions of $$\overrightarrow S $$ are the same as the dimensions of which of the following quantity(ies)?

A heavy nucleus N, at rest, undergoes fission N $$\to$$ P + Q, where P and Q are two lighter nuclei. Let $$\delta$$ = M_N $$-$$ M_P $$-$$ M_Q, where M_P, M_Q and M_N are the masses of P, Q and N, respectively. E_P and E_Q are the kinetic energies of P and Q, respectively. The speeds of P and Q are v_P and v_Q, respectively. If c is the speed of light, which of the following statement(s) is(are) correct?

Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I₁ in the anti-clockwise direction and the larger loop carries current I₂ in the clockwise direction, with I₂ > 2I₁. $$\overrightarrow B $$(x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmosphere pressure p₀ = 10⁵ Pa so that the volume of the trapped air is v₀ = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p₀ + $$\Delta$$p without changing its orientation. At this pressure, the volume of the trapped air is v₀ $$-$$ $$\Delta$$v. Let $$\Delta$$v = X cc and $$\Delta$$p = Y $$\times$$ 10³ Pa.



The value of X is _______________.