Charges $$Q,$$ $$2Q$$ and $$4Q$$ are uniformly distributed in three dielectric solid spheres $$1,2$$ and $$3$$ of radii $$R/2,R$$ and $$2R$$ respectively, as shown in figure. If magnitude of the electric fields at point $$P$$ at a distance $$R$$ from the center of sphere $$1,2$$ and $$3$$ are $${E_1}$$, $${E_2}$$ and $${E_3}$$ respectively, then

Parallel rays of light of intensity $$I$$ = 912 Wm^–2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant $$\sigma $$ = 5.7 $$ \times $$ 10^–8 Wm^–2K^–4 and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lift’s motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the options given below the lists.

List - I	List - II
P. Lift is accelerating vertically up.	1. d=1.2 m
Q. Lift is accelerating vertically down with an acceleration less than the gravitational acceleration.	2. d > 1.02 m
R. Lift is moving vertically up with constant speed.	3. d < 1.2 m
S. Lift is falling freely.	4. No water leaks out of the jar

A planet of radius R = $${1 \over {10}} \times $$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $${R \over 5}$$ on it and lower a wire of the same length and of linear mass density 10^-3 kg m^-1 into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 $$ \times $$ 10⁶ m and the acceleration due to gravity of Earth is 10 ms ^-2)