## QBM031

Q1. Let S_{n} = 1 + 1/2 + 1/3 + _ _ _+ 1/n (n = 1; 2; _ _ _). then S_{n} âˆ’ S_{m} is

(i)Always a prime number for m

(A)none

(B)1

(C)2

(D)3
Q10. 5^{6} - 1 is divisible by

(1)13

(2)31

(3)5

(4) None of these
Q11. Find the smallest whole numbers, M and N such that you can rearrange the digits of M to get N, and you can rearrange the digits of M3 to get N3.
Q12. Is there a set S of positive integers such that a number is in S if and only if it is a sum of two distinct members of S or a sum of two distinct positive integers not in S?
Q13. At a movie theater, the manager announces that a free ticket will be given to the first person in line whose birthday is the same as someone in line who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year, what position in line gives you the best chance of being the first duplicate birthday?
Q14. 1/m + 1/n = 1/94, where m and n are positive integers. Find m + n, given that m is half of n.

(1)49

(2)282

(3)423

(4)927
Q15. The units digit of 2006^{ 29} + 97^{2006} is:

a.2

b.4

c.6

d.8

e.0
END

## answer 2

**Q10. 5 ^{6} - 1 is divisible by**

**(1)13 (2)31 (3)5 (4) None of these **

**Answer: **

**5 ^{6} - 1 = (5^{2})^{3 }- 1 = [ (5^{2}) + 1 ] x [ ]**

**It is divisible by 26. .so must be by 13**