IMO Mathematics Olympiad (SOF) Class 10: Questions 68  75 of 958
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Question number: 68
Question
According to the fundamental theorem of arithmetic, if p (a prime number) divides , and b is positive, then ________
Choices
Choice (4)  Response  

a.  P divides b 

b.  divides p 

c.  b divided p 

d.  divides 

Question number: 69
Question
is ________
Choices
Choice (4)  Response  

a.  An irrational number 

b.  An imaginary number 

c.  An rational number 

d.  None of the above 

Question number: 70
Question
is ________
Choices
Choice (4)  Response  

a.  Real number 

b.  A rational number 

c.  An irrational number 

d.  All of the above 

Question number: 71
Question
Sum of squares of the two consecutive natural numbers is 113. The two consecutive numbers respectively________
Choices
Choice (4)  Response  

a.  1 and 2 

b.  3 and 4 

c.  7 and 8 

d.  4 and 5 

Question number: 72
Question
The product of two consecutive natural numbers is always ________
Choices
Choice (4)  Response  

a.  A prime number 

b.  An odd number 

c.  Divisible by 3 

d.  An even number 

Question number: 73
Question
If , then b equals________
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 74
Question
Rationalizing factor of is ________
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 75
Question
A circular field has a circumference of 600 km. Two cyclists Sumeet and Samrat start together and can cycle at speeds of 15 km/hr and 20 km/hr respectively round the circular field. After how many hours will they meet again at the starting point?
Choices
Choice (4)  Response  

a.  160 hrs 

b.  90 hrs 

c.  100 hrs 

d.  120 hrs 
