1. If a^{3}b = abc = 180 and a, b, c are positive integers, then the value of c is:

110

25

15

None of the above

2. (1 - 1/3)(1 - 1/4)(1 - 1/5)...(1 - 1/n) is equal to:

1/n

2/n

2/n(n+1)

2(n-1)/n

3. When simplified, the product (2 - 1/3)(2 - 3/5)(2 - 5/7)...(2 - 997/999) is equal to:

5/999

1001/999

1001/3

4. (256)^{.18} x (256)^{.07} is equal to:

4

6

8

64

5. Given that (1^{2} +2^{2} + 3^{2} + .... + 10^{2}) = 385, then the value of (2^{2} +4^{2} + 6^{2} + .... + 202) is equal to:

770

1540

1155

(385) x (385)

6. If (64)^{2} - (36)^{2} = 20z, the value of z is:

70

180

120

7. If x * y = (x +2)^{2} . (y-2), then the value of (7 * 5) is:

175

205

213

243

8. If 2^{x-1} + 2^{x+1} = 320, then the value of x is:

5

7

9. The sum of first 45 natural numbers is:

2070

1035

1280

2140

10. (51 + 52 + 53 +... + 100) is equal to:

2525

2975

3225

3775

11. The remainder obtained when 2^{11} is divided by 5 is:

2

3

1

12. What least value must be assigned to * so that 86325*6 is divisible by 11?

13. Which of the following numbers is exactly divisible by 99?

114345

135792

3572404

913464

14. If the number 42573* is completely divisible by 72, then which of the following numbers should replace * in the number?

15. 5*2 is a three digit number with * as a missing digit. If the number is divisible by 6, the missing digit is:

16. There is one number which is formed by writing one digit 6 times (e.g. 111111, 444444, etc.). Such number is always divisible by:

11

13

All of the above

17. Which of the following numbers should be added to 11158 to make it exactly divisible by 77?

9

18. The number nearest to 99547 which is exactly divisible by 687 is:

100166

98928

99479

99615

19. What least number must be subtracted from 13294 so that the remainder is exactly divisible by 97?

20. What largest number of five digits is divisible by 99?

99999

99981

99909

99990

21. What smallest number of six digits is divisible by 111?

111111

110011

100011

22. When a certain number is multiplied by 13, the product consists entirely of fives. The smallest such number is:

41625

42515

42735

42135

23. A four digit number divisible by 7 becomes divisible by 3, when 10 is added to it. The largest such number is:

9987

9989

9996

9947

24. Which of the following numbers is exactly divisible by all prime numbers between 1 and 17?

515513

440440

345345

510510

25. How many numbers between 200 and 600 are divisible by 4, 5 and 6?