  At scattered places in his first notebook, Ramanujan recorded the values for
107 class invariants or irreducible monic polynomials satisfied by them. On
pages 294-299 in his second notebook, he gave a table of values for 77 class
invariants $G_n$ and $g_n$ in his second notebook. Traditionally, $G_n$ is
determined for odd values of $n$ and $g_n$ for even values of $n$. On pages 338
and 339 in his first notebook, Ramanujan defined the remarkable product of
theta-functions $a_{m, n}$. Also, he recorded eighteen explicit values
depending on two parameters, namely, $m$, and $n$, where these are odd
integers. In this paper, we initiate to study explicit evaluations of $G_n$ for
even values of $n$. We establish a new general formula for the explicit
evaluations of $G_n$ involving class invariant $g_n$. For this purpose, we
derive a new P-Q modular equation of degree two. Further application of this
modular equation, we establish a new formula to explicit evaluation of $a_{m,
2}$. Also, we compute several explicit values of class invariant $g_{n}$ and
singular moduli $\alpha_n$.
