Arithmetic Progressions (IMO- Mathematics Olympiad Class 10): Questions 45 - 50 of 84

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Question number: 45

» Arithmetic Progressions

MCQ▾

Question

If in an A. P. , Sn=n2pandSm=m2p , where Sr denotes the sum of r terms of the A. P, then sp is equal to ________

Choices

Choice (4) Response

a.

p3

b.

mnp

c.

12p3

d.

(m+n)p2

Question number: 46

» Arithmetic Progressions

MCQ▾

Question

Three numbers are inserted between the 2 numbers and 30 such that an A. P. results. Find the fourth numbers.

Choices

Choice (4) Response

a.

42

b.

24

c.

23

d.

32

Question number: 47

» Arithmetic Progressions

MCQ▾

Question

If the sum of p terms of an A. P. is q and the sum of q terms is p , then the sum of p+q terms is ________

Choices

Choice (4) Response

a.

p+1

b.

0

c.

pq

d.

(p+q)

Question number: 48

» Arithmetic Progressions

MCQ▾

Question

If the sum of first n even natural numbers is equal to K times the sum of first n odd natural numbers, and then K is equal to ________

Choices

Choice (4) Response

a.

1n

b.

n+12n

c.

n+1n

d.

n1n

Question number: 49

» Arithmetic Progressions

MCQ▾

Question

If b1,b2,b3,. Belongs to A. P. such that b1+b6++b30=330 , then the value of b1+b2+b3++b30 equals ________

Choices

Choice (4) Response

a.

1584

b.

1654

c.

1650

d.

1325

Question number: 50

» Arithmetic Progressions

MCQ▾

Question

A circle with area A1 is contained in the interior of a larger circle with area A1+A2 . If the radius of the larger circle is 3 units and A1,A2,A1+A2 are in A. P. , then the radius of the smaller circle is ________

Choices

Choice (4) Response

a.

2units

b.

5units

c.

4.5units

d.

32units

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