When \(10^{19}\) electrons are removed from a neutral metal plate, the electric charge on it is? 
1. \(-1.6~\text{C}\)
2. \(+1.6~\text{C}\)
3. \(10^{19}~\text{C}\)
4. \(10^{-19}~\text{C}\)

Five balls numbered \(1\) to \(5\) are suspended using separate threads. Pairs \((1, 2), (2, 4),\) and \((4, 1)\) show electrostatic attraction, while pairs \((2, 3)\) and \((4, 5)\) show repulsion. Therefore ball \((1)\) must be:

1. positively charged
2. negatively charged
3. neutral
4. made of metal

Two spherical conductors \(B\) and \(C\) having equal radii and carrying equal charges in them repel each other with a force \(F\) when kept apart at some distance. A third spherical conductor having same radius as that of \(B\) but uncharged is brought in contact with \(B\), then brought in contact with \(C\) and finally removed away from both. The new force of repulsion between \(B\) and \(C\) is:
1. \(\frac{F}{4}\)
2. \(3\frac{F}{4}\)
3. \(\frac{F}{8}\)
4. \(3\frac{F}{8}\)

Three identical positive point charges, as shown are placed at the vertices of an isosceles right-angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point \(M\) of the hypotenuse?
                 
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

An electron enters an electric field with its velocity in the direction of the electric lines of force. Then: 

A charged ball \(B\) hangs from a silk thread \(S,\) which makes an angle \(\theta\) with a large charged conducting sheet \(P,\) as shown in the figure. The surface charge density \(\sigma\) of the sheet is proportional to: 

1. \(\sin\theta\)
 2. \(\tan\theta\)
 3. \(\cos\theta\)
 4. \(\cot\theta\)

A point charge \(q\) is placed at a distance \(\dfrac{a}{2}\) directly above the centre of a square of side \(a.\) The electric flux through the square (i.e., one face) is:
1. \(\dfrac{q}{\varepsilon_0}\)
2. \(\dfrac{q}{\pi\varepsilon_0}\)
3. \(\dfrac{q}{4\varepsilon_0}\)
4. \(\dfrac{q}{6\varepsilon_0}\)

An infinite number of electric charges each equal to \(5\) nC (magnitude) are placed along the \(x\text-\)axis at \(x=1\) cm, \(x=2\) cm, \(x=4\) cm, \(x=8\) cm ………. and so on. In the setup if the consecutive charges have opposite sign, then the electric field in Newton/Coulomb at \(x=0\) is: \(\left(\frac{1}{4 \pi \varepsilon_{0}} = 9 \times10^{9} ~\text{N-m}^{2}/\text{C}^{2}\right)\)
1. \(12\times 10^{4}\)
2. \(24\times 10^{4}\)
3. \(36\times 10^{4}\)
4. \(48\times 10^{4}\)