Q6. 
Each of $X$ alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of $X$? 
A.  14 

B.  16 

C.  18 

D.  20 
Q7. 
A person uses the base x for his number system, where x ≤ 10. A student had to add twodigit numbers. None of the digits was 0. By oversight, he reversed the digits of both the numbers and added them. He later found that the difference between his answer and the correct answer was $(84)_10. If this value is the maximum possible for x, then what is the value of x. 
A.  6 

B.  7 

C.  8 

D.  9 
Q8. 
$N$ is the smallest number that has 5 factors. How many factors does $(N  1)$ have? 
A.  2 

B.  3 

C.  4 

D.  5 
Q9. 
Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation? 
A.  36 days 

B.  14 days 

C.  29 days 

D.  Cannot be determined 
Q10. 
A set of S consists of, i). All odd numbers from 1 to 55. What is the index of the highest power of 3 in the product of all the elements of the set $S$? 
A.  35 

B.  48 

C.  6 

D.  36 