Answer: B 99! = 99*98*97*96.....*1 To find the highest power of 9 that divides the above product, it is required to find the sum of powers of all 3's in the expansion Sum of powers of 3's = 99/3 + 99/9 + 99/27 + 99/81 = 48(Ignoring the fractional part) The highest power of 9 = 48/2 = 24.
Q. No. 2:
How many five digit multiples of 11 are there, if the five digits are 3,4,5,6 and 7 in the same order?
Answer: A A number is divisible by 11, if the difference between the sum of digits at even places and odd places is either 0 or divisible by 11. Numbers 5 3 6 4 7 is a multiple of 11. The number at odd places 5,6,7 can be arranged in 3! ways and 3,4 can be arranged in 2! ways.. Therefore, total number of ways of such numbers = 3!*2! = 12.