Number System Test

Result

Number System Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is false?

A
The sum of two rational numbers is always a rational number.

B
The product of two irrational numbers is always an irrational number.

C
The division of an integer by an integer may not yield another integer.

D
The sum of a rational number and an irrational number is always an irrational number.

Solution

(i) Adding two rational numbers produces another rational number like (1/2) + (1/2) = 1, where 1/2 is a rational number and 1 is also a rational number.
(ii) The product of two irrational numbers like √2 × √2 is 2, which is a rational number. Thus, the statement given in this option is false.
(iii) The division of an integer by an integer may not yield another integer. This statement is true as 3 ÷ 2 = 1.5, which is not an integer.
(iv) The sum of a rational number and an irrational number is always an irrational number. For example, the sum of 1 and √2 is 2.41421..., which is an irrational number.
Question 2
1 / -0

Read the statements carefully and mark the correct option accordingly:

Statement 1: √2 cannot be represented on a number line.
Statement 2: 0.3 can be represented on a number line.

A
Both statements 1 and 2 are true.

B
Statement 1 is true and statement 2 is false.

C
Statement 1 is false and statement 2 is true.

D
Both statements 1 and 2 are false.

Solution

Since both √2 and 0.3 are real numbers, both can be represented on a number line.

Therefore, statement 1 is false and statement 2 is true.