Statement-1 (A): There are infinitely many rational numbers betwe… - Vidyadip

MCQ

Statement-1 (A): There are infinitely many rational numbers between any two integers.
Statement-2 (R):The square of an irrational number is always a rational number.

A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-5
B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
✓
Statement-1 is True, Statement-2 is False.
D
Statement-1 is False, Statement-2 is True.

✓

Answer

Correct option: C.

Statement-1 is True, Statement-2 is False.

(c)
Between any two integers a and b, there is a rational number $\frac{a+b}{2}$.Between a and $\frac{a+b}{2}$, there is a rational number $\frac{a+\frac{a+b}{2}}{2}$.Continuing in this manner, we can find infinitely many rational numbers between a and b. So, statement-1 is true.
Let $x=\sqrt{\sqrt{3}}$, be an irrational number, then $x^2=\sqrt{3}$ is an irrational number. So, square of an irrational number is not necessarily a. rational number. Thus, statement-2 is not true.
Hence, option (c) is correct.

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