I am looking out for some kind of short code where i should not be repeating the column names in database and it should directly be inserted with respective column name index to array value . Below i have uploaded the image for understanding.

Use mysql_fetch_assoc() rather than mysql_fetch_row() and the array will be associative (using the column names as the key) rather than numeric.
$query = mysql_query("SELECT * FROM users_table WHERE User_ID = 1");
while ($r1 = mysql_fetch_assoc($query))
{
echo $r1['User_ID'] . ': ' . $r1['First_Name'] . ' ' . $r1['Last_Name'] . '<br />';
}
Check this:
$query = mysql_query( "SELECT * FROM users_table WHERE user_id=1;" );
$row = mysql_fetch_array( $query );
print_r( $row );
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