132 = 11 * 3 * 4Clearly, 968 is not divisible by 3None of 462 and 2178 is divisible by 4And, 5284 is not divisible by 11Each one of the remaining four numbers is divisible by each one of 4, 3 and 11.So, there are 4 such numbers.
A total of (7 + 3) persons = 10 personal can sit in 10! ways.If we consider three girls as one unit, total persons = 7 + = 8 (here all three girls sit together).No. of ways = 81 and the three girls can be arranged in 31 ways among themselves.So, the total number of ways when three girls sit together = 81 x 31When the girls don't sit together, number of ways = 101 - (81 x 31) = 81 (10 x 9 - 6) = 81 x 84 = 3386880
Let the number be 10x + y.Therefore, x + y = 9 ..................(i)10x + y - (10y + x) = 4510x + y - 10y - x = 45Therefore, x - y = 5 ..................(ii)From (i) and (ii), x = 7, y = 2Number = 72Therefore, = x x y = 7 x 2 = 14
EXAMIANS