Recently the Cassini Ultraviolet Imaging Spectrograph has revealed the presence of N2 Vegard-Kaplan band emissions in Titan's dayglow limb observation. We present model calculations for the production of various N2 triplet states in the upper atmosphere of Titan. The Analytical Yield Spectra technique is used to calculate steady state photoelectron fluxes in Titan's atmosphere, which are in agreement with those observed by the Cassini's CAPS instrument. Considering direct electron impact excitation, inter-state cascading, and quenching effects, the population of different levels of N2 triplet states are calculated under statistical equilibrium. Densities of all vibrational levels of each triplet state and volume production rates for various triplet states are calculated in the model. Vertically integrated overhead intensities for the same date and lighting conditions as the reported by UVIS observations for N2 VK, 1P, 2P, Wu-Benesch, and Reverse First Positive bands of N2 are found to be 132, 114, 19, 22, and 22 R, respectively. Overhead intensities are calculated for each vibrational transition of all the triplet band emissions of N2, which span a wider spectrum of wavelengths from ultraviolet to infrared. The calculated limb intensities of total and prominent transitions of VK band are presented. The model limb intensity of VK emission within the 150-190 nm wavelength region is in good agreement with the Cassini UVIS observed limb profile. An assessment of the impact of solar EUV flux on the N2 triplet band emission intensity has been made by using three different solar flux models, viz., Solar EUV Experiment, SOLAR2000 model of Tobiska (2004), and HEUVAC model of Richards et al, (2006). The calculated N2 VK band intensity at the peak of limb intensity due to S2K and HEUVAC solar flux models is a factor of 1.2 and 0.9, respectively, of that obtained using SEE solar EUV flux. ; Comment: 25 pages, 11 figures; Icarus, 2012