The electric potential \(V\) at any point \((x,y,z)\), all in meters in space is given by \(V= 4x^2~\text{volt}\). The electric field at the point \((1,0,2)\) in volt/meter, is:

1.	\(8\) along the negative \(X\text-\)axis
2.	\(8\) along the positive \(X\text-\)axis
3.	\(16\) along the negative \(X\text-\)axis
4.	\(16\) along the positive \(X\text-\)axis

Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is:

The effective capacity of the network between terminals \(\mathrm{A}\) and \(\mathrm{B}\) is:

A bullet of mass \(2\) g is having a charge of \(2\) µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of \(10\) m/s?
1. \(50\) kV
2. \(5\) V
3. \(50\) V
4. \(5\) kV

A capacitor of capacity \(C_1\) is charged up to \(V\) volt and then connected to an uncharged capacitor \(C_2\). Then final P.D. across each will be:
1. \(\frac{C_{2} V}{C_{1} + C_{2}}\)
2. \(\frac{C_{1} V}{C_{1} + C_{2}}\)
3. \(\left(1 + \frac{C_{2}}{C_{1}}\right)\)
4. \(\left(1 - \frac{C_{2}}{C_{1}} \right) V\)

The variation of electrostatic potential with radial distance \(r\) from the centre of a positively charged metallic thin shell of radius \(R\) is given by the graph:

1.		2.
3.		4.

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness \(d_1\) and dielectric constant \(K_1\) and the other has thickness \(d_2\) and dielectric constant \(K_2\), as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness \(d= d_1+d_2\) and effective dielectric constant \(K\). The \(K\) is:  

Choose the correct statement(s): 
1. (b) and (c)
2. (a) and (c)
3. (b) and (d)
4. (c) and (d)