21). Find the greatest 4 digit number which when divided by 15, 18, 21 and 27 leaves in each case a remainder 7.
A). 9457 
B). 9547 
C). 9947 
D). 9967 

22). Which of the following fraction is the greatest? \( \Large \frac{7}{8} \), \( \Large \frac{6}{7} \), \( \Large \frac{4}{5} \), \( \Large \frac{5}{6} \)
A). \( \Large \frac{6}{7} \) 
B). \( \Large \frac{5}{6} \) 
C). \( \Large \frac{4}{5} \) 
D). \( \Large \frac{7}{8} \) 

23). A number when divided by 32 leaves the remainder 29. This number when divided by 8 will leave the remainder

24). A number lying between 1000 and 2000 is such that on division by 2, 3, 4, 5, 6, 7 and 8 leaves remainder respectively 1, 2, 3, 4, 5, 6 and 7. The number is
A). 1876 
B). 1679 
C). 1778 
D). 1654 

25). Three persons begin to walk around a circular track. They complete their revolutions in \( \Large 15\frac{1}{6}\ secs., 16\frac{1}{4}] secs.\ and\ 18\frac{2}{3}\ secs. \) rerspectively. After what time will they be together at the starting point again?
A). \( \Large 303\frac{1}{3} \) secs. 
B). 364 secs. 
C). 3604 secs, 
D). 3640 secs. 

26). The greatest number, which divides 171, and 251 leaving remainders 3 and 6 respectively is

27). The HCF of two positive integers is 5 and their LCM is 105. The numbers are
A). 5, 105 
B). 15, 35 
C). 5, 105 or 15, 35 
D). None of these 

28). The LCM of \( \Large x^{3}1 \), \( \Large x^{2}1 \) and \( \Large \left(x1\right)^{2} \) is
A). \( \Large \left(x+1\right) \left(x1\right) \left(x^{2}+x+1\right) \) 
B). \( \Large \left(x+1\right)^{2} \left(x1\right) \left(x^{2}x+1\right) \) 
C). \( \Large \left(x1\right)^{2} \left(x1\right) \left(x^{2}+x+1\right) \) 
D). \( \Large \left(x1\right)^{2} \left(x+1\right) \left(x^{2}x+1\right) \) 
