Olympiad/HOTS corner

Study the statement carefully

(i) Every integer is a rational number and every fraction is a rational number

(ii) A rational number $\frac{p}{q}$ is positive, if $p$and $q$ are either both positive or both negative.

(iii) A rational number $\frac{p}{q}$ is negative, if one of $p$ and $q$ is positive and other is negative.

(iv) If there are two rational numbers with common denominator, then one with the larger numerator is larger than the other.

Which of the following options hold?

Which of the following statements is incorrect?

Which of the following options is correct?

Read the statements carefully and select the correct option

Statement I: The product of an integer and a rational number can never be a natural number

Statemetn-II The quotient of division of an integer by a rational number can never be an integer.

Which of the following rational numbers satisfies the given property?

$a+\left(b+c\right)=\left(a+b\right)+c$

Which of the following options shows the numbers arranged in ascending order?

Which of the following options represents the value of $P$ shown on the number line?

State 'T' for true and 'F' for false ans select the correct option

(i) Every natural number is a rational number

(ii) Every rational number is a fraction

(iii) Zero is not  a rational number

(iv) The reciprocal of $0$ is $\frac{1}{0}$