Lines of force for an electric field varying in magnitude but having a constant direction How will the electric lines of force look for an electric field varying in magnitude but having a constant direction, say along +ve z axis ? 
According to me, since the electric field is varying in magnitude, the density of the field lines in space should also vary accordingly. But since the direction is constant, the tangents to every point on the lines of force should point in the same direction. But these two statements seem to contradict each other !
 A: You are right! The trick to remember here is that vector fields permeate all of space (literally all of it) and field lines are only a convenient representation of this. 
When a new field line is added due to the increased magnitude of the field at that point in space, the field vector 'arrow' that is introduced always existed there but was just small enough in magnitude for us to ignore it when using the field line representation. For this reason, the direction of the vector at that point is unchanged.
Parallel plate capacitor example
Let's consider the most simple case: the parrallel plate capacitor.

We know that the electric field strength $E$ across the plates is given by 
$$E = \frac{V}{d},$$
where $d$ is the separation of the plates; or in vector form
$$\mathbf{E} = \frac{V}{d}\,\mathbf{\hat{I}},$$
where $\hat{\mathbf{I}}$ is the direction of the current. Now, let's increase the voltage across the plates to $V_2 = 2 V_1$ and see what happens to the field.

As we can see, the magnitude of the electric field has changed to $E_2 > E_1$ due to the increased density of field lines but the direction is still the same since the arrangement of charges is the same -- there's just more of them now!
Does this mean new vectors have been created? No, we're now simply introducing more vector lines to represent the field.
It's for this reason I much prefer the use of individual vector arrows spaced evenly with different magnitudes. This helps to clarify exactly what the vector field is and what it's doing. 
I find it easiest to think of the spacing of field lines as the flux of the field through a particular surface in space (shown below as a circular contour in 2D,) since the lines per unit area represent the magnitude; vector arrows represent the vector field itself at arbitrarily defined points in space. I know this is unconventional but it might be helpful. So, the following two representations are in many ways equivalent:
 
Gauss' Law
It is also worth noting that an electric field's magnitude cannot change under a fixed charge separation without a change in charge itself (recall $V = Q/C$ for the capacitor scenario.) Thus, since the enclosed charge $Q_\text{enc}$ is changed, Gauss' law allows a resulting change in the field flux through a surface $S_{\Gamma}$ by
$$\iint_{S_\Gamma}\mathbf{E}\cdot\mathrm{d}\mathbf{S} = \frac{Q_\text{enc}}{\epsilon_0}.$$
However, this is only applicable with a change in either $Q_\text{enc}$ or $S$.
A: By Gauss's law, the scenario you describe can only happen when there are electric charges within this volume. If they are positive charges, you need to draw field lines coming out of them. If they are negative charges, you need to draw field lines ending at them.
A: I don't think this situation is possible.Consider finite field lines passing through a given area vector in vaccum.Now If you enclose the given field lines and charge by Gaussian surface where one of the plane is parallel to x-y plane.By Gauss's law the net electric flux is constant.
While changing the magnitude of electric field with same enclosure i.e surface through which it get passed, which is the electric flux,you are violating Gauss's law or violating the 1/$r^2$ relationship. 
