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Here is a sample Google Apps Script code that creates a new Google Sheets file with a particular range and sheets from an existing sheet when activated:

function createNewSheet() {
  // Get the source spreadsheet and the specific sheet
  var sourceSpreadsheet = SpreadsheetApp.getActive();

  // Define the source sheet and the range to copy
  var sourceSheet = sourceSpreadsheet.getSheetByName('Sheet1');
  var sourceRange = sourceSheet.getRange('A1:D10');

  // Create a new spreadsheet
  var newSpreadsheet = SpreadsheetApp.create("New Spreadsheet");

  // Copy the range to the new spreadsheet
  var destinationSheet = newSpreadsheet.getActiveSheet();
  sourceRange.copyTo(destinationSheet.getRange('A1'), {contentsOnly:true});

  // Add additional sheets to the new spreadsheet
  newSpreadsheet.insertSheet('Sheet2');
  newSpreadsheet.insertSheet('Sheet3');
}

To activate this script, simply run the createNewSheet function from the script editor or assign it to a button or trigger.