The region between two concentric spheres of radii '\(a\)' and '\(b\)' , respectively (see figure), has volume charge density \(\rho=\frac{A}{r}\), where \(A\) is a constant and \(r\) is the distance from the centre. At the centre of the spheres is a point charge \(Q\). The value of \(A\) such that the electric field in the region between the spheres will be constant, is:
             
1. \( \frac{Q}{2 \pi a^2} \)
2. \(\frac{Q}{2 \pi\left(b^2-a^2\right)} \)
3. \(\frac{2 Q}{\pi\left(a^2-b^2\right)} \)
4. \(\frac{2 Q}{\pi a^2}\)

A point charge of \(+12~\mathrm{\mu C}\) is at a distance \(6\) cm vertically above the centre of a square of side \(12\) cm as shown in figure. The magnitude of the electric flux through the square will be:

1. \( 226 \times 10^2 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)
2. \( 226 \times 10^3 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)
3. \(326 \times 10^3 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)
4. \( 326 \times 10^2 ~\frac{\mathrm{Nm}^2}{\mathrm{C}}\)

A charge '\(q\)' is placed at one corner of a cube as shown in figure. The flux of electrostatic field \(\vec{E}\) through the shaded area is:

 
1. \(\frac{q}{4\varepsilon_0}\)
2. \(\frac{q}{24\varepsilon_0}\)
3. \(\frac{q}{48\varepsilon_0}\)
4. \(\frac{q}{8\varepsilon_0}\)

Given below are two statements :