The data is a survey data from CXO's of Software product firms. If the dependent variable is measured in 7 point scale and Independent variable is in 5 point likert scale. which statistical test in Regression should be used
Short answer: if the Likert scale used to measure the IV and DV is appropriate to the distribution of the data in the population then it should not matter that one used a 7 point scale and the other a 5 point scale.
Longer answer: For each variable IV and DV, there is a distribution of values in the population from which the sample was taken. It is theoretically possible that this distribution is highly irregular. That is, 7% of people in the population would give a score of 1, 12% give a score of 2, 1% give a score of 3, 50% give a score of 5, 7% give a score of 6, 23% give a score of 7. While your survey results may look like this, the important question is whether the population behaves in this way.
If it does: then I am not sure the data can be analyzed. This is because the number of bins in your Likert scale will determine the perceived shape of the distribution.
If it does not: then the next assumption is that each scale correctly represents the distribution. So If the real peak of the distribution is at 25% for the 5 point scale, then the peak is entirely in a rating of 2, but if the peak is at 20% then half of it is at 1 and the other half at 2. The probability that this is an issue will decrease if you can assume that there is but one peak in the distribution.
To the extent that these issues do not exist, then I do not think that having two scales is relevant to the regression problem. Hence the short answer that I started with. However, if it is not good to assume that the Likert scale is appropriate to model the distribution of values in the population, then one might question if any other type of analysis would be valid.
I think if you provide the reader with the research question/hypothesis, then the appropriate statistical test will be figured out.
The level of measurement {based on Likert scale is continous, and this is important for the DV}, There are many assumptions for each test need to be considered to decide the test suitability.
Multinomial regression is for un-ordered categorical data. For categorical data that can be ordered, ordinal logistic regression (or even OLS regression, if some assumptions are met) is fine, as mentioned in the above answers.