Statement-1 (A): 13 20 14 20 and 15 20 are three rational numbers… - Vidyadip

MCQ

Statement-1 (A): $\frac{13}{20}$ $\frac{14}{20}$ and $\frac{15}{20}$ are three rational numbers between $\frac{1}{2}$ and $\frac{4}{5}$
Statement-2 (R): A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(p+q)$.

✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
C
Statement-1 is True, Statement-2 is False.
D
Statement-1 is False, Statement-2 is True.

✓

Answer

Correct option: A.

Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3

(a)
Statement-2 is true. Using statement-2, a rational number between $\frac{1}{2}$and $\frac{4}{5}$ is $\frac{1}{2}\left(\frac{1}{2}+\frac{4}{5}\right)=\frac{13}{20}$. But, $\frac{4}{5}=\frac{16}{20}$, So, rational numbers between $\frac{13}{20}$ and $\frac{16}{20}$ are $\frac{14}{20}$ and $\frac{15}{20}$
Hence, $\frac{13}{20}$, $\frac{14}{20}$ and $\frac{15}{20}$ are rational numbers between $\frac{1}{2}$ and $\frac{4}{5}$.Hence, statement-1 is true and statement-2 is correct explanation for statement-1. So, option (a) is correct.

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