In this paper, we obtain some new modular equations of degree 2 for the ratios of Ramanujan's theta-function f and also establish the general formulas for their explicit evaluations. As an application, we establish some new modular relations for Ramanujan-Göllnitz-Gordon continued fraction H(q) with H(qn/2), Ramanujan-Selberg continued fraction V(q) with V(qn/2) and Eisenstein continued fraction E(q) with E(qn/2) for n=3, 5 and 7