# IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 205 - 212 of 968

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## Question 205

### Question

MCQ▾

If are two numbers such that . Then are the roots of the quadratic equation ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 206

### Question

MCQ▾

If are the zeroes of the quadratic polynomial such that , then the value of k is ________

### Choices

Choice (4)Response

a.

25

b.

-24

c.

24

d.

-25

## Question 207

### Question

MCQ▾

The solution of the system of equations and , is ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 208

### Question

MCQ▾

The sum of two numbers is 18 and the sum of their squares is 38. The numbers are ________

### Choices

Choice (4)Response

a.

13 and 18

b.

16 and 20

c.

21 and 25

d.

11 and 13

## Question 209

### Question

MCQ▾

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

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 210

### Question

MCQ▾

The value of k for which the system of equations , has infinite number of solutions, is ________

### Choices

Choice (4)Response

a.

10

b.

3

c.

9

d.

4

## Question 211

### Question

MCQ▾

If are the roots of the cubic , the value of is ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 212

### Question

MCQ▾

The value of k, for which the system of equations represent parallel lines is ________

### Choices

Choice (4)Response

a.

25

b.

45

c.

15

d.

35