An infinitely long solenoid of radius a $=\frac{5}{\pi }\mathrm{cm}$ and $10 \mathrm{turns} {\mathrm{cm}}^{-1}$ is placed such that its axis of symmetry lies along the $X$-axis. A current $I$ is flowing through the solenoid ( $X$ means that $I$ is flowing into and $·$ means it is flowing out of the page). A straight infinite wire with current $25 I$ is placed parallel to the $X-$axis at a distance $\frac{a}{2}$ away from the center. Which of the following gives the direction of net magnetic field at the origin?

Choose the correct statement in the following:

(a) The magnetic field inside the solenoid is greater than that of outside
(b) The magnetic field inside an ideal solenoid is not at all uniform
(c) The magnetic field at the centre, inside an ideal solenoid is almost twice that at the ends
(d) The magnetic field at the centre, inside an ideal solenoid is almost half of that at the ends

A solenoid of $1000$ turns per metre has a core with relative permeability $500.$ Insulated windings of the solenoid carry an electric current of $5 \mathrm{A}.$ The magnetic flux density produced by the solenoid is:

(Permeability of free space$=4\pi \times {10}^{-7} \mathrm{H} {\mathrm{m}}^{-1}$)

Four identical long solenoids $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are connected to each other as shown in the figure. If the magnetic field at the center of $\mathrm{A}$ is $3 \mathrm{T}$ the field at the center of $\mathrm{C}$ would be : (Assume that the magnetic field is confined with in the volume of respective solenoid).