1). If (32) ^ (x-2) = 64 / (8^x).
Find the value of x.
Options: (a) - 2 (b) 3 (c) 2 (d) - 3

2). The largest number that always divides the product of 3 consecutive multiples of 2 is
Options: (a) 8 (b) 16 (c) 24 (d) 48

3). By what smallest number, 21600 must be divided or multiplies in order to make it a perfect square
Options: (a) 6 (b) 5 (c) 8 (d) 10

4). How many numbers are there between 500 & 600 in which 9 occurs only once ?
Options: (a) 19 (b) 20 (c) 21 (d) 18

5). How many even integers n, where 100<=n<=200 are divisible neither by 7 nor by 9.
Options: (a) 40 (b) 37 (c) 39 (d) 38

6). Which is the greatest 4 digit number which when divided by 5 leaves the remainder 4 ?
Options: (a) 9990  (b) 9999  (c) 9998  (d) 9995
7). What is the total number of positive integer solutions that satisfy the equation
4x + 3y = 120 ?
Options: (a) 9 (b) 10 (c) 8 (d) None of these

8). How many 2 digit natural numbers are there so that ten’s digit is never less than the unit’s digit ?
Options: (a) 44 (b) 55 (c) 54 (d) None of these

9). If P is a prime number, then the LCM of P & (P+1) is
Options: (a) P(P+1) (b) (P+2)P (c) (P+1)(P-1) (d) None of these

10). What is the remainder when 17^23 is divided by 16 ?
Options: (a) 0 (b) 1 (c) 2 (d) 3

11). The product of two numbers is 16200. If their LCM is 216, find their HCF.
Options: (a) 75 (b) 70 (c) 80 (d) Data Inconsistent

12). The LCM of two numbers is 72 & their HCF is 12. If one of the numbers is 24, what is the other number?
Options: (a) 38 (b) 26 (c) 36 (d) 42

13). Dividing by 3/8 and then multiplying by 5/6 is equivalent to dividing by what number?
Options: (a) 5/16 (b) 16/40 (c) 9/20 (d) 40/18

14). How many zeros are there at the end of the product 33 x 175 x 180 x 12 x 44 x 80 x 66 ?
Options: (a) 2 (b) 4 (c) 5 (d) 6

15). Convert 1153 from base 10 to base 15.
Options: (a) 51D (b) 51E (c) 51C (d) None of these

16). What is the highest power of 31 in 1000!
Options: (a) 31 (b) 32 (c) 33 (d) None of these

17). Convert 413 from base 7 to base 8
Options: (a) 613 (b) 361 (c) 316 (d) None of these

18). (9^6) + 1 when divided by 8, would have a remainder
Options: (a) 0 (b) 1 (c) 2 (d) 3

19). What is the highest power of 54 that divides 31 ! completely
Options: (a) 0 (b) 1 (c) 4 (d) None of these

20). The positive integer nearest to 1000 & divisible by 2, 3, 4, 5 & 6 is
Options: (a) 1020 (b) 1040 (c) 960 (d) 1030