Is there any relation between dielectric constant of material and its resistance /resistivity? For conductors dielectric constant is infinite as electric field cant exist inside it .And conductors have very low resistance too .So is there any relation btw dielectric constant and resistance of material .
 A: Dielectrics are characterized by being polarizable, i.e. the ability to experience internal charge displacement as a response to an external electric field.
A conductor, on the other hand, is characterized by the fact that there is no static electric field in them when an external electric field is applied ("Faraday cage"). This is because the free charges in the conductor get displaced by the external field as long as there is a remaining electric field inside the conductor or a tangential field component on its surface. This process ends when there are just enough (suitably distributed) charges on the surface of the conductor (and only there!) to neutralize the field in the interior.
In this sense (displacement of charges upon external influence) a conductor could be considered an "ideal dielectric". The usual dielectrics neutralize the external field only partially, while the conductor neutralizes it perfectly.
Be careful, however, not to overstretch this analogy. Specifically the mechanisms are pretty different. While the polarizable electrons in dielectrics are bound to the atom bodies, the conducting electrons in a conductor are (quasi) free. Also, with respect to your question, the value of its resistance is in no way related to the "ideal polarizability" of a conductor. No matter if it is a good or a bad conductor, the static end result (no static electric field inside) is always the same, while the amount of polarization of the dielectric depends on whether it is a good or a bad dielectric (high or low permittivity). So it is definitely illegal to consider resistance as a kind of static polarizability of the conductor!
On the other hand, when transitioning from electrostatics to electrodynamics, the picture gets a little more blurry. The reason is that you can formulate electrodynamics in matter so that conductivity introcuces an imaginary component of the complex dielectric permittivity. This takes into account the "lossy" properties of resistance, pretty similarly like for a damped mechanical harmonic oscillator the damping constant introduces an imaginary component of complex frequency (which causes the attenuation of its exponentially decaying vibrations).
So in electrodynamics, resistance is indeed related to dielectric permittivity, but only in a generalized sense (i.e. making the normally real quantity complex, in order to describe damped waves/attenuation of the electromagnetic field). This treatment leads for example to the understanding of the well-known skin-effect: alternating currents (not charges as for the Farraday cage!) tend to move to the surface of the conductor, the more, the higher the frequency.
A: Dielectrics are insulators, which means the have effectively infinite resistance within the range of voltage for which their dielectric properties are present.  Resistance is a property of conductors.  So basically you have one or the other.
