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While molecular gas mass is usually derived from $^{12}$CO($J$=1-0) - themost fundamental line to explore molecular gas - it is often derived from$^{12}$CO($J$=2-1) assuming a constant $^{12}$CO($J$=2-1)/$^{12}$CO($J$=1-0)line ratio ($R_{2/1}$). We present variations of $R_{2/1}$ and effects of theassumption that $R_{2/1}$ is a constant in 24 nearby galaxies using $^{12}$COdata obtained with the Nobeyama 45-m radio telescope and IRAM 30-m telescope.The median of $R_{2/1}$ for all galaxies is 0.61, and the weighted mean of$R_{2/1}$ by $^{12}$CO($J$=1-0) integrated-intensity is 0.66 with a standarddeviation of 0.19. The radial variation of $R_{2/1}$ shows that it is high(~0.8) in the inner ~1 kpc while its median in disks is nearly constant at 0.60when all galaxies are compiled. In the case that the constant $R_{2/1}$ of 0.7is adopted, we found that the total molecular gas mass derived from$^{12}$CO($J$=2-1) is underestimated/overestimated by ~20%, and at most by 35%.The scatter of a molecular gas surface density within each galaxy becomeslarger by ~30%, and at most by 120%. Indices of the spatially resolvedKennicutt-Schmidt relation by $^{12}$CO($J$=2-1) are underestimated by 10-20%,at most 39% in 17 out of 24 galaxies. $R_{2/1}$ has good positive correlationswith star-formation rate and infrared color, and a negative correlation withmolecular gas depletion time. There is a clear tendency of increasing $R_{2/1}$with increasing kinetic temperature ($T_{\rm kin}$). Further, we found that notonly $T_{\rm kin}$ but also pressure of molecular gas is important tounderstand variations of $R_{2/1}$. Special considerations should be made whendiscussing molecular gas mass and molecular gas properties inferred from$^{12}$CO($J$=2-1) instead of $^{12}$CO($J$=1-0).

CO Multi-line Imaging of Nearby Galaxies (COMING). IX. $^{12}$CO($J$=2-1)/$^{12}$CO($J$=1-0) line ratio on kiloparsec scales