Test Index

CTET Paper II (Mathematics and Science) 23 Dec 2021 Solved Paper

Question : 33 of 150

Marks: +1, -0

Identify the statement which is NOT true.

Between any two rational numbers, there are infinitely many rational numbers.
Between a positive rational number and a negative rational number, there is always a whole number.
Every non-zero rational number has a multiplicative inverse.
There exist a pair of rational numbers such that there is only one rational number between them.

Solution:

Concept:

The density property of rational numbers states that between any two distinct rational numbers, there are infinitely many rational numbers. Also, every non-zero rational number has a multiplicative inverse (reciprocal).

Explanation:

Option A is true because rational numbers are dense – between any two, there are infinitely many others.

Option B is true because 0 (a whole number) always lies between a positive and a negative rational number.

Option C is true because for any non-zero rational

\frac{a}{b}

, its multiplicative inverse is

\frac{b}{a}

Option D is false: There cannot be a pair with only one rational between them because between any two rationals, infinitely many rationals exist.

Answer:

Go to Question:

Prev Question

Next Question