Q.Intensity of magnetic field of the earth at the point inside a hollow iron box is (A) less than that outside (B) more than that outside (C) same as that outside (D) zero

[!TLDR] A closed soft-ferromagnetic shell (magnetic shielding) crowds field lines into its own material, so the field inside the enclosed space is much less than the field outside. [!ANSWER] (A) less than that outside

A hollow iron box is, physically, a closed shell of soft ferromagnetic material -- exactly the setup described as magnetic shielding in section 11.8. Because soft iron offers magnetic field lines a much easier (high-permeability) path than air, the vast majority of the field lines that would otherwise pass through the enclosed space instead crowd into the walls of the box itself, leaving only a small fraction to cross the hollow interior. The intensity of the field found inside the box is therefore LESS than the field just outside it -- not exactly zero (that would require an idealised, infinitely permeable or superconducting shell), but genuinely and substantially reduced. [!ANSWER] (A) less than that outside

Recognise a hollow iron box as a closed soft-ferromagnetic shell and apply the magnetic shielding concept of section 11.8: field lines crowd into the shell's material, sharply reducing the field in the enclosed cavity.

Assuming a magnetic shield reduces the field inside to exactly zero -- a real soft-iron shell only strongly reduces the field, it does not perfectly eliminate it (perfect exclusion, i.e. zero, only happens for an idealised superconducting shell with $\chi=-1$).