Arithmetic Progressions (IMO Mathematics Olympiad (SOF) Class 10): Questions 50  55 of 84
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Question number: 50
» Arithmetic Progressions
Question
A circle with area is contained in the interior of a larger circle with area. If the radius of the larger circle is 3 units and are in A. P. , then the radius of the smaller circle is ________
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 51
» Arithmetic Progressions
Question
A number 100 is divided into four parts that are in A. P. such that the product of the first and fourth is to the product of the second and third is . Find the largest part.
Choices
Choice (4)  Response  

a.  30 

b.  60 

c.  10 

d.  40 

Question number: 52
» Arithmetic Progressions
Question
If six numbers are in A. P. such that their sum is 30 and the greatest number is 6 times the least, then the numbers are ________
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 53
» Arithmetic Progressions
Question
A number 196 is divided into four parts that are in A. P. such that the product of the first and fourth is to the product of the second and third is . Find the largest part.
Choices
Choice (4)  Response  

a.  70 

b.  28 

c.  42 

d.  56 

Question number: 54
» Arithmetic Progressions
Question
If , then is equal to ________
Choices
Choice (4)  Response  

a.  1228 

b.  1428 

c.  1328 

d.  1128 

Question number: 55
» Arithmetic Progressions
Question
Find the sum of all threedigit natural numbers, which on being divided by 4, leave remainder equal to 2.
Choices
Choice (4)  Response  

a.  1,99,270 

b.  4,41,680 

c.  1,94,780 

d.  1,23,525 
