Printing chessboard with *(asterisk) and .(dot)
Your current code limits the number of rows/columns to a single integer. Is this desired behavior?

For clarity sake, I would probably generate the even/odd rows and then print each until you have printed enough rows

Function to specify the input

def get_int_digits(l):
    try:
        inp = input()
    except SyntaxError:
        print "You did not enter anything"
        return 0
    if type(inp) != int:
        print "You did not enter an integer."
        return 0
    if l is not None and len(str(inp)) != l:
        print "You did not enter the correct number of digits."
        print "{} digits expected.".format(l)
        return 0
    return inp


Function to output the "board"

def print_board(row, column):
    even_string = ("*." * (column // 2 + 1)) [0:column]
    odd_string = (".*" * (column // 2 + 1)) [0:column]

    for i in xrange(row):
        print odd_string if i % 2 else even_string 


Driver

if __name__ == __main__:
    cases = get_int_digits(None)
    for i in xrange(cases):
        row_col = get_int_digits(2)
        print_board(row_col // 10, row_col % 10)