When it is mentioned in the question that the spring is massless and inextensible does it mean that we don't have to account for the value of spring constant k..??!

The spring is massless and inextensible just means that we do not have to consider the mass of spring per unit length while dealing with the questions basically in some questions when the spring has mass that we cannot neglect then we answer those questions by considering mass per unit length and dealing with the situations that are mentioned in the questions but for basic questions it is given that spring is mass less while the inextensible means that the spring will recoil after you have extended it or you can say basically it has enough Young's modulus that it will not reach its fracture point Or elastic limit while extending it it is again used in basic questions where we deal simple steps of kinetics and mechanics it does not means that you have to neglect the value of k or do not have to consider the value of spring constant k .that's all Hope it helps..