We present the results of N2H+(1-0) observations of 35 dense molecular cloud cores from the northern and southern hemispheres where massive stars and star clusters are formed. Line emission has been detected in 33 sources, for 28 sources detailed maps have been obtained. The optical depth of (23-12) component toward peak intensity positions of 10 sources is ~ 0.2-1. In total, 47 clumps have been revealed in 26 sources. Integrated intensity maps with aspect ratios < 2 have been fitted with a power-law radial distribution $r^{-p}$ convolved with the telescope beam. Mean power-law index is close to unity corresponding to the $sim r^{-2}$ density profile provided N2H+ excitation conditions do not vary inside these regions. Line widths of the cores either decrease or stay constant with distance from the center. The ratio of rotational to gravitational energy is too low for rotation to play a significant role in the dynamics of the cores. A correlation between mean line widths and sizes of clumps has been found.
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