# IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 184 - 190 of 968

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## Question number: 184

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MCQ▾

### Question

For how many values of k does the following system of equations have at least one solution?

### Choices

Choice (4)Response

a.

2

b.

Infinitely many

c.

1

d.

0

## Question number: 185

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MCQ▾

### Question

Places and are 400 km apart from each other on a national highway. A car starts from and another from at the same time. If they go in the same direction then they meet in 10 hours and if they go in opposite directions they meet in hours. The speeds of the cars are ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 186

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MCQ▾

### Question

The number of values of k for which the system of equations has atleast one solution is ________

### Choices

Choice (4)Response

a.

1

b.

0

c.

3

d.

2

## Question number: 187

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MCQ▾

### Question

If are the roots of the equation , then the equation whose roots are and is ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 188

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MCQ▾

### Question

For to be a factor of , the value of p and q should respectively be ________

### Choices

Choice (4)Response

a.

5,25

b.

5,2

c.

6,25

d.

2,5

## Question number: 189

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MCQ▾

### Question

When is divided by , the quotient and remainder is ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 190

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MCQ▾

### Question

A boat goes 40 km upstream and 55 km downstream in 20 hours. In 23 hours, it can go 50 km upstream and 66 km downstream. If x represents the speed of the boat in still water in km/hr and y represent the speed of the stream in km/hr, then ________

### Choices

Choice (4)Response

a.

b.

c.

d.

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