# Arithmetic Progressions (IMO- Mathematics Olympiad Class 10): Questions 53 - 59 of 84

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## Question number: 53

» Arithmetic Progressions

MCQ▾

### 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

MCQ▾

### Question

If , then is equal to ________

### Choices

Choice (4) Response

a.

1228

b.

1428

c.

1328

d.

1128

## Question number: 55

» Arithmetic Progressions

MCQ▾

### Question

Find the sum of all three-digit 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

## Question number: 56

» Arithmetic Progressions

MCQ▾

### Question

If the sum of terms of an A. P. are respectively, then is ________

### Choices

Choice (4) Response

a.

1

b.

2

c.

0

d.

3

## Question number: 57

» Arithmetic Progressions

MCQ▾

### Question

Find the sum of all four-digit natural numbers, which on being divided by 20, leave remainder equal to 5.

### Choices

Choice (4) Response

a.

69, 65, 000

b.

24, 70, 500

c.

60, 27, 000

d.

32, 23, 001

## Question number: 58

» Arithmetic Progressions

MCQ▾

### Question

The value of is ________

### Choices

Choice (4) Response

a.

97

b.

99

c.

96

d.

92

## Question number: 59

» Arithmetic Progressions

MCQ▾

### Question

The sum of all terms of the arithmetic progression having ten terms except for the first term, is 126, and except for the sixth term, 62. Find the third term of the progression if the sum of the first and the fifth term is equal to 16.

### Choices

Choice (4) Response

a.

7

b.

3

c.

9

d.

8

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