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We present here medium resolution (λ/Δλ\sim1200) H- and K-band spectra of M type dwarf stars covering the wavelength range 1.50 - 1.80 μm and 1.95 - 2.45 μm. The sample includes 53 dwarf stars (M0V-M7V) from new observations using the TIFR Near-Infrared Spectrometer and Imager (TIRSPEC) instrument on the 2-m Himalayan Chandra Telescope (HCT). Using interferometrically-measured effective temperature (T_{eff}), radius and luminosity of nearby bright calibrator stars, we have created new empirical relationships among those fundamental parameters and spectral indices. The equivalent widths of H-band spectral features like Mg (1.57 μm), Al (1.67 μm) and Mg (1.71 μm), and the H_{2}O-H index are found to be good indicators of T_{eff}, radius and luminosity and we establish the linear functions using these features relating to those stellar parameters. The root mean squared error (RMSE) of our best fits are 102K, 0.027R_{\sun} and 0.12dex respectively. Using spectral type standards along with known parallaxes, we calibrate both H and K-band H_{2}O indices as a tracer of spectral type and absolute K_{s} magnitude. Metallicities of M-dwarf samples are estimated using the K-band calibration relationships. The mass of M-dwarfs could be determined using the luminosity (L/L_{\sun}) and we establish a new empirical relation for this. We also compare and contrast our results with other similar work from the literature.