Try to solve these questions on number system (PART 2) ???

post your answers........

16. find the lowest of three nos. as described: if the cube of the first no exceeds the product by 2, the cube of 2nd no. is smaller than therir product by 3, and the cube of the third no. exceeds their product by 3.
A) 3^1/3 b)9^1/3 c)2 d)any of these


17. find the Gcd of (2^100 -1, 2^120 -1)

a) 2^20 -1 b)2^40 – 1 C)2^60 -1 d)2^10 -1

18. find the gcd of (111111....1111 hundred ones ; 1111....111 sixty ones)

A) 1111....forty ones b)11111.....twenty five ones
C) 11111.... twenty ones d) none of these

19. find the number of numbers between 200 and 300, both included, which are not divisible by 2, 3, 4 and 5.
(a) 27 (b) 26 (c) 25 (d) none of these

20. 12^55/3^11 + 8^48/16^18 will give the digit at unit's place as
(a) 4 (b) 6 (c) 8 (d) 0

21. Let N be the product of five different odd prime numbers. If N is the five-digit number abcab, 4 < a < 8, how many values of N are possible?
a. 1 b. 2 c. 3 d. 4 e. more than 4

22. Which of the following numbers can be written as the sum of the squares of three odd numbers?

a. 4445 b. 1233 c. 3339 d. 5021

23. The product P of three positive integers is 9 times their sum, and one of the integers is the sum of the other two. The sum of all possible values of P is
a 702 b. 540 c. 336 d. 1404

24. What is the remainder when (81)^21 + (27)^21 + (9)^21 + (3)^21 + 1 is divided by (3)^20 + 1
a. 0 b. 61 c. 1 d. 121

25. A three-digit number in base 10 is written in base 9 and base 11 to give two numbers N1 and N2,respectively. What is the probability that N1and N2 are also three-digit numbers?
a. 0.42 b. 0.67 c. 0.55 d. 0.88 e. 0.33

26. What is the sum of the sum of the sum of the digits of 55!?
a. 27 b. 36 c. 5 d. 9

27 .If , then the value of S is
a. 588 b. 373 c. 256 d. 504

28. Let N = 2^15 × 3^12. How many factors of N^2 are less than N but do not divide N completely?

29. How many two-digit positive integers are there which are one and a half times larger than the product of their digits?
a. 0 b. 1 c. 2 d. 3

30. N is a number such that 200 < N < 300 and it has exactly 6 positive divisors. How many different values of N are possible?
a. 12 b. 13 c. 14 d. 15