Consists of two statements, namely, Assertion (A) and Reason (R).… - Vidyadip

MCQ

Consists of two statements, namely, Assertion $(A)$ and Reason $(R).$ For selecting the correct answer, use the following code:

Assertion (A)	Reason (R)
Three rational numbers between $\frac{2}{3}$ and $\frac{3}{5}$ are $\frac{9}{20},\frac{10}{20}$ and $\frac{11}{20}.$	A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(\text{p}+\text{q}).$

The correct answer is: $(a), (b), (c), (d).$

✓
Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
B
Both Assertion $(A)$ and Reason $(R)$ are true but Reason is not a correct explanation of Assertion $(A).$
C
Assertion $(A)$ is true and Reason $(R)$ is false.
D
Assertion $(A)$ is false and Reason $(R)$ is true.

✓

Answer

Correct option: A.

Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$

We know that $\frac{1}{2}(\text{p}+\text{q})$ is a rational number between two given rational numbers $p$ and $q.$ Thus, Reason $(R)$ is true.
A rational number between $\frac{2}{5}$ and $\frac{3}{5}$ is $\frac{1}{2}\Big(\frac{2}{5}+\frac{3}{5}\Big)=\frac{5}{10}$
A rational number between $\frac{2}{5}$ and $\frac{5}{10}$ is $\frac{1}{2}\Big(\frac{2}{5}+\frac{5}{10}\Big)=\frac{9}{20}$
A rational number between $\frac{5}{10}$ and $\frac{3}{5}$ is $\frac{1}{2}\Big(\frac{5}{10}+\frac{3}{5}\Big)=\frac{11}{20}$
$\therefore$ Three rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$ are $\frac{9}{20},\frac{10}{20}$ and $\frac{11}{20}$
Thus, Assertion $(A)$ is true
Since Reason $(R)$ gives Assertion $(A),$ so $(a)$ holds.

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