# IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 647 - 651 of 968

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## Question 647

### Question

MCQ▾

Product of the fourth term and the fifth term of an arithmetic progression is 594. Division of the ninth term by the fourth term of the progression gives quotient as 2 and the remainder as 3. Find the first term of the progression

### Choices

Choice (4)Response

a.

6

b.

4

c.

9

d.

7

## Question 648

### Question

MCQ▾

The sum of all terms of the arithmetic progression having ten terms except for the first term, is 81, and except for the sixth term, 55. Find the third term of the progression if the sum of the first and the fifth term is equal to 12.

### Choices

Choice (4)Response

a.

5

b.

15

c.

8

d.

10

## Question 649

### Question

MCQ▾

If a, b, c are in A. P, then is equal to ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 650

### Question

MCQ▾

If in a certain language CHARCOAL is coded as 32143516 and MORALE is coded as 754168, then the REAL code is ________

### Choices

Choice (4)Response

a.

6216

b.

4862

c.

4816

d.

1648

## Question 651

### Question

MCQ▾

At a farm, there are ducks, Horses, buffalo and keepers to look after them. There are 134 heads less than legs. The number of horses is double than that of the buffalo but the number of horses and ducks is the same and there is one keeper per 30 birds and cattle. The total number of ducks plus horses and buffalo and their keepers does not exceed 80. How many houses are there?

### Choices

Choice (4)Response

a.

22

b.

23

c.

26

d.

24