I do have some 10-12 independent variable, I want to know how these 10-12 variables are related to a single variable(X). so I can decide that some variables are positively correlated to X and some are negatively correlated. I thought of doing correlation between X and one of the independent variables individually and decide. is there is a way to calculate multiple correlation.
As @Analyst's answer implies, the level of measurement will matter, but if you have continuous data, you can calculate the multiple correlation ($R$) of a set of predictors with the dependent/outcome variable (your $X$) by performing multiple regression. The Wikipedia article @user603 linked specifies:
[$R$] is measured by the square root of the coefficient of determination, but under the particular assumptions that an intercept is included and that the best possible linear predictors are used, whereas the coefficient of determination is defined for more general cases, including those of nonlinear prediction and those in which the predicted values have not been derived from a model-fitting procedure.
There are many ways to accommodate categorical data in general linear models that may work for you as well, depending on the specific nature of your data.
You could try calculating partial correlation coefficients if you have at least interval scale measured variables.
Here is link for the implementation in R.
You can find it at the bottom of the page.