# Pair of Linear Equations in Two Variables (IMO- Mathematics Olympiad Class 10): Questions 10 - 14 of 82

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## Question number: 10

» Pair of Linear Equations in Two Variables

MCQ▾

### Question

A pair of linear equations in two variables x and y is and, such that , then it has ________.

### Choices

Choice (4) Response

a.

Unique solution

b.

Can’t say

c.

No solution

d.

Infinitely many solutions

## Question number: 11

» Pair of Linear Equations in Two Variables

MCQ▾

### Question

The digit at the ten’s place of a two digit number is twice the digit at the unit’s place. If the sum of this number and the number formed by reversing the digits is 165, find the number.

### Choices

Choice (4) Response

a.

63

b.

24

c.

105

d.

52

## Question number: 12

» Pair of Linear Equations in Two Variables

MCQ▾

### Question

The value of k for which the system of equations has a non-zero solution, is ________

### Choices

Choice (4) Response

a.

2

b.

0

c.

6

d.

8

## Question number: 13

» Pair of Linear Equations in Two Variables

MCQ▾

### Question

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

### Choices

Choice (4) Response

a.

1

b.

0

c.

3

d.

6

## Question number: 14

» Pair of Linear Equations in Two Variables

MCQ▾

### Question

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 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.

f Page