Do insulators allow electric field?

Two long concentric hollow metallic cylinders of radii$a$and$b$, respectively carry equal and opposite charges $-\sigma$ and $+\sigma$ per unit length, as shown. The space between the cylinders is filled with air. The distance measured from the central axis is denoted by $r.$

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Which of the following statements is NOT CORRECT?

A hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in figure. Let $V_A, V_B, V_C$ be the potentials at points $A, B$ and $C$, respectively. Then

An uncharged conducting large plate is placed as shown. Now an electric field $E$ towards the right is applied. Find the induced charge density on the right surface of the plate.

A spherical conductor of radius $12 \mathrm{cm}$ has a charge of $1.6\times {10}^{-7} \mathrm{C}$ distributed uniformly on its surface. What is the electric field at a point $18 \mathrm{cm}$ from the center of the sphere? Take, $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$

The figure shows a charge $q$ placed inside a cavity in an uncharged conductor. Now, if an external electric field is switched on