International Maths Olympiad Forum By SOF Olympiad Trainer - Page 82

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Subject :IMO    Class : Class 10

Given below are the steps of construction of a pair of tangents to a circle of radius 6 cm from a point on the concentric circle of radius 8 cm. Find which of the following steps is INCORRECT?
Steps of Construction
Step I : Take a point O on the plane paper and draw a circle of radius OA = 6 cm. Also, draw a concentric circle of radius OB = 8 cm.
Step II : Find the mid-point A of OB and draw a circle of radius BA = AO. Suppose this circle intersects the circle of radius 6 cm at P and Q.
Step III : Join BP and BQ to get the desired tangents.

A Step I
B Step II
C Step I and Step II
D Step II and Step III


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Subject :IMO    Class : Class 3

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Subject :IMO    Class : Class 8

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Subject :IMO    Class : Class 6

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Subject :IMO    Class : Class 7

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Subject :IMO    Class : Class 8

Ans 1:

Class : Class 9
Its 301875

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Subject :IMO    Class : Class 9

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Subject :IMO    Class : Class 4

Ans 1:

Class : Class 5
see as we know 7th muliple is 301 so in option a 4 is an even number so it would be incorrect in option b the last digit is not 5 or 0 so option b will be incorrect in option c 6 is an even number so it would be incorrectin option d 301 ÷ 7 has the remainder 0 so answer is D option

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Subject :IMO    Class : Class 7

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Subject :IMO    Class : Class 8

Given question is followed by information given in three statements (I, II and III). You have to study the question along with statements and decide the information given in which of the statement(s) is necessary to answer the question.
What will be the compound interest earned on an amount of ₹ 6000 in 2 years?
I. The simple interest on the same amount at the same rate of interest in 4 years is ₹ 3600.
II. The compound interest and simple interest for one year is same.
III. The amount becomes more than double on compound interest in 10 years.

AI only
BI and II only
CII and III only
DI and III only


Isn't Statement two necessary to know that the interest is compounded annually, and not half-yearly or monthly? In my opinion, option (B) should be the correct answer, not option (A).

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